As demonstrated in previous chapters, money must originate as a commodity. One cannot use praxeology to determine which commodity will do so. Still, praxeology tells us that the commodity must have a wide acceptance among people, and that they must see that it will be accepted as a means of exchange for other goods.
The recognition that a good is widely accepted and will serve as a medium of exchange need not occur slowly. It can happen quite quickly. Cigarettes in prison camps for example arose quite quickly as media of exchange without any formal decision.
Historically gold and silver have arisen as near universal money because of their qualities (divisibility, durability, wide acceptance).
If there are two monies, like gold and silver, how can both be used? The market solves this problem. Gold and silver will simply trade at a ratio to one another as other goods do with them. This ratio, like other ratios can not be expected to remain constant.
Furthermore, goods priced in silver will tend to be priced the same in gold as it relates to silver. Should a good cost more in gold than in silver, its price in gold will fall This will happen for one of two reasons, or a combination of both.
For one, suppliers of that particular good will bid for less and less gold until the amount of gold suppliers want for the good matches its ratio to silver. For another, holders of gold will want more of a good for the amount of gold they are offering until the amount reaches the same they could get if they had silver. At some point the amount of a good the demander could obtain with his gold will match what he could get with silver at the ratio gold and silver are trading.
Economic reformers posit that the fluctuation of the ratio between gold and silver is a problem. They contend the fluctuation can occur to quickly for some market participants to respond, and that it opportunity for arbitrage continually presents itself. To address these problems reformers advocate fixing the ratio between gold and silver to make it easier for market participants to calculate prices and eliminate the opportunity for arbitrage.
The reformers, however, are obligated to demonstrate why price fluctuation and arbitrage are ethically wrong. They cannot trot in a value judgment such as they have without making the case for why it must be recognized.
Specifically, why is it that the rate at which the ratio between gold and silver fluctuates be instantaneous? The reformer is right to say that a change takes time, but when he suggests it takes too much time he is making an ethical judgment that requires an argument to support.
The other assumption the reformer must explain is why arbitrage opportunities must be eliminated or reduced. He must explain why arbitrage is wrong.
These ethical cases may be valid, but one is not obligated to recognize them without an argument for their support.
Leaving aside the ethical questions, fixing the ratio introduces the problem of Gresham’s Law.
Say a gold mine is discovered which increases the supply of gold. The market ratio of silver to gold falls from 16 to 1 to 15 to 1. Meanwhile the ‘official’ ratio between them remains at 16 to 1. What will happen?
Holders of gold will happily trade their once of gold for 16 oz. of silver when the market values gold at only 15 oz. Those who hold silver, however, will be reluctant to trade silver at that price. Moreover, they will be unwilling to spend it into circulation to pay for other goods as these goods will be more expensive in terms of silver than gold.
As gold and silver are not only money, but also commodities, a fixed price between them will cause shortages and surpluses of them. As silver is undervalued by the fixed price it will not be offered for sale and experience a shortage. Gold, on the other hand, being overvalued by the fixed price will enjoy a surplus. In short, silver will be driven from the market in preference for gold. Gresham’s law states bad money will drive out good money. It is more accurate to say that overvalued money will drive out undervalued money.
As shown above, two commodities can coexist as money without issue on the market. Still, one commodity may eventually dominate, eventually causing the other to lose value until it is valued strictly for utility and not exchange. Though not a praxeological law, one can expect a single metal currency standard to arise on the free market and replace the tow metal currency standard. Between gold and silver the one to do so would probably be gold.
Showing posts with label Economic Reasoning. Show all posts
Showing posts with label Economic Reasoning. Show all posts
Sunday, May 10, 2009
Introduction to Economic Reasoning - Chapter 9: Money, Part 2
In the last chapter Dr. Gordon showed that actors converge on the use of a few goods to use as a medium exchange. He defines money as a good almost universally accepted in a market for purposes of exchange.
Various goods have served as money throughout history (sugar, sea shells, cattle), but certain commodities like gold and silver became almost universally acceptable. History shows goods with certain qualities tend to become money.
The most popular monies tend to be durable, divisible, and widely acceptable commodities. For these reasons people have tended to adopt gold and silver as money.
Gold, because it was widely accepted, not only expanded the space over which goods could be exchanged, but also the time. Because it is durable, gold can be stored for use later to purchase other goods. Money, then, also serves as a store of value.
Once a good, like gold, becomes the preferred medium of exchange, other goods that served as competing media of exchange will fall in value. They will retain their ‘use’ value, but their exchange value will fall to zero. The preferred media of exchange will be valued according to its general acceptability.
Where did money come from? The money regression theorem explains the origin of money. Government edicts or explicit agreements do not create money. Money arises spontaneously in the market place. Gold began as a good desired for its use in creating jewelry and other goods. It then gained in value because people realized it could be traded for other gods they wanted. Gold did not begin as a media of exchange, it developed into one. Carl Menger was the first economist to develop this account of the development of money. Before him, economists like John Locke theorized that money originated through an explicit agreement to accept a certain substance as money.
We learned earlier that the supply and demand for a good determine its value. Demand and supply, in turn, depend on the utility of the demanders and suppliers. A question then arises, what determines the utility of gold? People want gold because they can use it to buy other things. In explaining the value of gold in this way, however, we are using circular reasoning. We are explaining the utility of gold in terms of its value; that is that the utility of gold is determined by the value of gold in being able to purchase other goods. Its value is in turn determined by its utility.
Mises found a way out of this circular explanation for the value of gold using utility theory. He began by stating that people determined the value of gold today according to its value yesterday. (This is not the same thing as saying people valued it the same as they did the day before). The value of gold going back in time depended on its value the previous day. Going back far enough in time there will be a day in which gold was not valued as a media of exchange at all, but as a commodity used to directly satisfy a human need or want. Mises thus showed that utility theory did apply to money just as it did to other goods. The value of the good the day before it started being used as money was based on its direct utility. People thus had a basis upon which to value the good before it became a media of exchange. A good without such a value could not begin as money.
Note that Mises’ theory does not state that fiat money (paper money not redeemable for a commodity) is not possible. Mises’ theory does explain that fiat money could not have first come about unless it had been based on a commodity that had arisen as a media of exchange.
Various goods have served as money throughout history (sugar, sea shells, cattle), but certain commodities like gold and silver became almost universally acceptable. History shows goods with certain qualities tend to become money.
The most popular monies tend to be durable, divisible, and widely acceptable commodities. For these reasons people have tended to adopt gold and silver as money.
Gold, because it was widely accepted, not only expanded the space over which goods could be exchanged, but also the time. Because it is durable, gold can be stored for use later to purchase other goods. Money, then, also serves as a store of value.
Once a good, like gold, becomes the preferred medium of exchange, other goods that served as competing media of exchange will fall in value. They will retain their ‘use’ value, but their exchange value will fall to zero. The preferred media of exchange will be valued according to its general acceptability.
Where did money come from? The money regression theorem explains the origin of money. Government edicts or explicit agreements do not create money. Money arises spontaneously in the market place. Gold began as a good desired for its use in creating jewelry and other goods. It then gained in value because people realized it could be traded for other gods they wanted. Gold did not begin as a media of exchange, it developed into one. Carl Menger was the first economist to develop this account of the development of money. Before him, economists like John Locke theorized that money originated through an explicit agreement to accept a certain substance as money.
We learned earlier that the supply and demand for a good determine its value. Demand and supply, in turn, depend on the utility of the demanders and suppliers. A question then arises, what determines the utility of gold? People want gold because they can use it to buy other things. In explaining the value of gold in this way, however, we are using circular reasoning. We are explaining the utility of gold in terms of its value; that is that the utility of gold is determined by the value of gold in being able to purchase other goods. Its value is in turn determined by its utility.
Mises found a way out of this circular explanation for the value of gold using utility theory. He began by stating that people determined the value of gold today according to its value yesterday. (This is not the same thing as saying people valued it the same as they did the day before). The value of gold going back in time depended on its value the previous day. Going back far enough in time there will be a day in which gold was not valued as a media of exchange at all, but as a commodity used to directly satisfy a human need or want. Mises thus showed that utility theory did apply to money just as it did to other goods. The value of the good the day before it started being used as money was based on its direct utility. People thus had a basis upon which to value the good before it became a media of exchange. A good without such a value could not begin as money.
Note that Mises’ theory does not state that fiat money (paper money not redeemable for a commodity) is not possible. Mises’ theory does explain that fiat money could not have first come about unless it had been based on a commodity that had arisen as a media of exchange.
Introduction to Economic Reasoning - Chapter 8: Money: Part 1
The discussions about labor and price controls have depended upon the same basic principles of economics identified in earlier chapters.
One of these principles is that if two parties expect to benefit from a trade, they will trade. If one or both parties do not expect to benefit, there will be no trade. If and only if both parties expect to benefit will a trade take place. An actor chooses to trade because he believes doing so will maximize his utility compared to other alternatives. (Remember utility does not necessarily mean psychological satisfaction).
A trade will not take place if at least one of the actors does not want what the other has. If the other actor, however, finds something else his trading partner wants, a trade will take place. In other words, just because at least on actor does not want what the other has does not mean an exchange won’t take place. It will take place of this other actor finds what his trading partner wants.
The implication of the forgoing discussion is that one may value a good more than some other good not for the benefits the good itself provides, but for the other goods for which that good can be exchanged. When one trades for a good in order to trade that good for another good, he is engaging in indirect exchange.
An indirect exchange can become even more complicated if it takes two, three or more exchanges in order to obtain a good that one wants to consume.
Indirect exchanges are problematic. First, an actor must find other actors that want he has and have what his potential trading partners want. This is known as a ‘Double Coincidence of Wants.’ Second, an actor in a long series of indirect exchanges may find guess wrong and exchange for something that other actors do not want. Finally, even if an actor guesses correctly, the process of many indirect exchanges takes time and is inefficient. Thus, involved indirect exchanges involve transaction costs.
An actor might avoid transaction costs by engaging in direct exchanges only. In this case, though, the actor would have to produce something that everyone wants. If they produce something that few people want they will not be as successful.
If someone who produces goods that few people want is able to trade the goods they produce for goods many people want, they will then be better able to trade for other goods. They will reduce the occurrence of a double coincidence of wants, and thus reduce their transaction costs. They will, however have to pay a ‘premium’ to obtain goods in greater demand. The holder of goods in greater demand must be paid more in order to give up such goods as they are more valuable. Someone who produces something more in demand, however, would not have to pay as high a premium for the good in greater demand.
A good, such us an orange, will increase in value should it become regarded as a means of exchanging for other goods. Initially a good will begin by being valued for the benefits its consumption brings the actor. Should the actor then see that it is also demanded by other actors as a means of exchange for other goods, its value will increase. Should this value as means of exchange become even more widely dispersed, its value will still increase even more. Dr. Gordon stresses that all one need remember is that a good that people think will be accepted readily in exchange will gain in value.
When certain goods are perceived as more high valued than others in exchange, they will become even more highly demanded by other actors. Their value will exceed those of other goods that had also been used in exchange, which will now be valued less. This process is known as convergence.
Note that the process of convergence does follow from praxeology. Praxeology tells us that people choose their highest preference. If a good can better help them fulfill a preference, an actor will choose it over other goods.
One of these principles is that if two parties expect to benefit from a trade, they will trade. If one or both parties do not expect to benefit, there will be no trade. If and only if both parties expect to benefit will a trade take place. An actor chooses to trade because he believes doing so will maximize his utility compared to other alternatives. (Remember utility does not necessarily mean psychological satisfaction).
A trade will not take place if at least one of the actors does not want what the other has. If the other actor, however, finds something else his trading partner wants, a trade will take place. In other words, just because at least on actor does not want what the other has does not mean an exchange won’t take place. It will take place of this other actor finds what his trading partner wants.
The implication of the forgoing discussion is that one may value a good more than some other good not for the benefits the good itself provides, but for the other goods for which that good can be exchanged. When one trades for a good in order to trade that good for another good, he is engaging in indirect exchange.
An indirect exchange can become even more complicated if it takes two, three or more exchanges in order to obtain a good that one wants to consume.
Indirect exchanges are problematic. First, an actor must find other actors that want he has and have what his potential trading partners want. This is known as a ‘Double Coincidence of Wants.’ Second, an actor in a long series of indirect exchanges may find guess wrong and exchange for something that other actors do not want. Finally, even if an actor guesses correctly, the process of many indirect exchanges takes time and is inefficient. Thus, involved indirect exchanges involve transaction costs.
An actor might avoid transaction costs by engaging in direct exchanges only. In this case, though, the actor would have to produce something that everyone wants. If they produce something that few people want they will not be as successful.
If someone who produces goods that few people want is able to trade the goods they produce for goods many people want, they will then be better able to trade for other goods. They will reduce the occurrence of a double coincidence of wants, and thus reduce their transaction costs. They will, however have to pay a ‘premium’ to obtain goods in greater demand. The holder of goods in greater demand must be paid more in order to give up such goods as they are more valuable. Someone who produces something more in demand, however, would not have to pay as high a premium for the good in greater demand.
A good, such us an orange, will increase in value should it become regarded as a means of exchanging for other goods. Initially a good will begin by being valued for the benefits its consumption brings the actor. Should the actor then see that it is also demanded by other actors as a means of exchange for other goods, its value will increase. Should this value as means of exchange become even more widely dispersed, its value will still increase even more. Dr. Gordon stresses that all one need remember is that a good that people think will be accepted readily in exchange will gain in value.
When certain goods are perceived as more high valued than others in exchange, they will become even more highly demanded by other actors. Their value will exceed those of other goods that had also been used in exchange, which will now be valued less. This process is known as convergence.
Note that the process of convergence does follow from praxeology. Praxeology tells us that people choose their highest preference. If a good can better help them fulfill a preference, an actor will choose it over other goods.
Sunday, April 26, 2009
Introduction to Economic Reasoning - Chapter 7: Minimum Wages and Wage Controls
Minimum wages and wage control are no different from the discussion about price control. Still they are very important topics associated with the notion of equality.
Many people express concerns over the presence of income gaps. It is often taken for granted that the more equality there is in income, the better.
Advocates of equality often demonstrate its inherent goodness by asking whether it is fair that a millionaire should pass by a homeless person without sharing any of his income. Gordon, acknowledging the anecdote might say something about helping the destitute, disagrees that it makes a persuasive case for equality. Gordon doubts whether an equality advocate would say it is unfair that a billionaire pass by a millionaire without sharing his wealth as well. If not, then what does then what is the status of equality?
Wages, like prices, are set by demand and supply. A wage earner is free to accept or not accept a wage offered him. Demand and supply are brought into balance. Should the government impose higher wages, more people will want to work for that wage, but at the same time fewer suppliers of labor will be able or willing to supply it at that price. Demand and supply are thrown out of balance which creates unemployment.
Like price controls, wage controls may or may not affect unemployment. If the minimum wage is set below the market wage, or the market wage is expected to climb above the minimum wage, the wage control will have no effect on unemployment. Wage controls either cause unemployment or do not affect employment.
It does not follow that the minimum wage is bad because it causes unemployment. As with price controls, one may argue that there are other benefits the minimum wage provides that are more important than resulting unemployment. The problem, however, is that many who advocate the minimum wage do not acknowledge that it causes unemployment, and do not cite any benefits that outweigh this cost.
Some economists argue that there is a zone of indeterminancy around a given market wage. Wages are not exact, but can be set within a narrow zone without affecting unemployment. The problem with this theory is that there is no proof that a zone of inderterminancy actually exists. No argument is made that such a zone exists for the prices of material goods. Why should it exist only for labor and not other goods? Furthermore, even if the zone does exist, why assume most wages will end up at the bottom of the zone, and not the top? Also, if wages end up at the bottom of the zone, should one accept the government must intervene to correct this?
It is not just the minimum wage that causes problems. Income includes not just wages but benefits. The government mandates that employers offer certain benefits and pay certain taxes and fees to support social programs like social security. Like the minimum wage these also increase employment costs and cause unemployment.
Labor unions also cause unemployment by forcing employers to raise wages. In a free market unions cannot ask for more than the market price. With the protections given to unions by the federal government, however, they can coerce employees to raise their wages. This also contributes to unemployment.
Many people express concerns over the presence of income gaps. It is often taken for granted that the more equality there is in income, the better.
Advocates of equality often demonstrate its inherent goodness by asking whether it is fair that a millionaire should pass by a homeless person without sharing any of his income. Gordon, acknowledging the anecdote might say something about helping the destitute, disagrees that it makes a persuasive case for equality. Gordon doubts whether an equality advocate would say it is unfair that a billionaire pass by a millionaire without sharing his wealth as well. If not, then what does then what is the status of equality?
Wages, like prices, are set by demand and supply. A wage earner is free to accept or not accept a wage offered him. Demand and supply are brought into balance. Should the government impose higher wages, more people will want to work for that wage, but at the same time fewer suppliers of labor will be able or willing to supply it at that price. Demand and supply are thrown out of balance which creates unemployment.
Like price controls, wage controls may or may not affect unemployment. If the minimum wage is set below the market wage, or the market wage is expected to climb above the minimum wage, the wage control will have no effect on unemployment. Wage controls either cause unemployment or do not affect employment.
It does not follow that the minimum wage is bad because it causes unemployment. As with price controls, one may argue that there are other benefits the minimum wage provides that are more important than resulting unemployment. The problem, however, is that many who advocate the minimum wage do not acknowledge that it causes unemployment, and do not cite any benefits that outweigh this cost.
Some economists argue that there is a zone of indeterminancy around a given market wage. Wages are not exact, but can be set within a narrow zone without affecting unemployment. The problem with this theory is that there is no proof that a zone of inderterminancy actually exists. No argument is made that such a zone exists for the prices of material goods. Why should it exist only for labor and not other goods? Furthermore, even if the zone does exist, why assume most wages will end up at the bottom of the zone, and not the top? Also, if wages end up at the bottom of the zone, should one accept the government must intervene to correct this?
It is not just the minimum wage that causes problems. Income includes not just wages but benefits. The government mandates that employers offer certain benefits and pay certain taxes and fees to support social programs like social security. Like the minimum wage these also increase employment costs and cause unemployment.
Labor unions also cause unemployment by forcing employers to raise wages. In a free market unions cannot ask for more than the market price. With the protections given to unions by the federal government, however, they can coerce employees to raise their wages. This also contributes to unemployment.
Introduction to Economic Reasoning - Chapter 6: Price Controls
Dr. Gordon illustrates the effects of price controls by first showing that at the market price there is buyer for every seller and vice versa using reductio proof. In a reductio proof, the negative of the proposition to be proved is shown to be contradictory, thus proving the proposition itself is true.
Starting with an assumed price for a gallon of gasoline at $1, Dr. Gordon assumes there are more buyers than sellers. This, he explains, will lead to buyers bidding the price up to a price of, say, $1.30. Buyers unwilling to pay the $1.30 will leave the market until the number of buyers matches the number of sellers. This contradicts the proposition that supply and demand do not balance, proving the opposite.
One can show supply and demand balance without resorting to a reductio proof. Who bids prices up or down? Buyers who are willing to pay for a good than a marginal buyer cause prices to rise. For example, a marginal buyer will not pay more than a $1 for a gallon of gasoline, and are driven out of the market by buyers willing to pay $1.30. There are also marginal sellers who will not sell below a certain price, whereas other sellers will. Sellers willing to sell gas at $0.80 a gallon will drive out sellers who will not sell below $1.00. At a market price there are no sellers looking for buyers, nor buyers looking for sellers.
When governments intervene to keep prices low by establishing price controls, say by imposing a price of $1.00 when the market price is $1.30, shortages result. Demand for gas at $1.00 will exceed the supply available. Note that if the government imposed a price of a $1.60, though, no shortages would result in this case. Demand for gas at $1.30 would still match supply. On the other hand, should buyers expect the price of gas to exceed $1.60 in the future, the price control would have an affect. Still another case; if a price control of $1.00 is imposed when the market price is $1.30, but market participants expect the market price to fall to $0.95 the price control will have no effect. Price controls either cause shortages or have no effect.
Price controls can cause shortages. Does this mean they should not be instituted? Not necessarily; it does not follow that because price controls can cause shortages that they are bad. Many people acknowledge that price controls cause shortages but argue there are benefits that result from them that outweigh the costs. For example, because dentists cause pain, and pain is bad, would it follow that dentists should be outlawed?
Those who advocate price controls, however, while maintaining that they do not cause shortages are mistaken. It is this idea that is irrational.
Starting with an assumed price for a gallon of gasoline at $1, Dr. Gordon assumes there are more buyers than sellers. This, he explains, will lead to buyers bidding the price up to a price of, say, $1.30. Buyers unwilling to pay the $1.30 will leave the market until the number of buyers matches the number of sellers. This contradicts the proposition that supply and demand do not balance, proving the opposite.
One can show supply and demand balance without resorting to a reductio proof. Who bids prices up or down? Buyers who are willing to pay for a good than a marginal buyer cause prices to rise. For example, a marginal buyer will not pay more than a $1 for a gallon of gasoline, and are driven out of the market by buyers willing to pay $1.30. There are also marginal sellers who will not sell below a certain price, whereas other sellers will. Sellers willing to sell gas at $0.80 a gallon will drive out sellers who will not sell below $1.00. At a market price there are no sellers looking for buyers, nor buyers looking for sellers.
When governments intervene to keep prices low by establishing price controls, say by imposing a price of $1.00 when the market price is $1.30, shortages result. Demand for gas at $1.00 will exceed the supply available. Note that if the government imposed a price of a $1.60, though, no shortages would result in this case. Demand for gas at $1.30 would still match supply. On the other hand, should buyers expect the price of gas to exceed $1.60 in the future, the price control would have an affect. Still another case; if a price control of $1.00 is imposed when the market price is $1.30, but market participants expect the market price to fall to $0.95 the price control will have no effect. Price controls either cause shortages or have no effect.
Price controls can cause shortages. Does this mean they should not be instituted? Not necessarily; it does not follow that because price controls can cause shortages that they are bad. Many people acknowledge that price controls cause shortages but argue there are benefits that result from them that outweigh the costs. For example, because dentists cause pain, and pain is bad, would it follow that dentists should be outlawed?
Those who advocate price controls, however, while maintaining that they do not cause shortages are mistaken. It is this idea that is irrational.
Sunday, April 12, 2009
Introduction to Economic Reasoning - Chapter 5: The Labor Theory of Value
Dr. Gordon begins by clarifying an apparent contradiction from the last Chapter. In the beginning of that chapter Dr. Gordon noted that even though one can know that two actors will benefit from an exchange, one cannot determine at what ratio an exchange will take place until it actually does take place.
Later in the chapter, Dr Gordon showed that if one knows the preference scales of the actors involved in an exchange (also illustrated with Demand and Supply curves) one can determine the ratio at which an exchange will take place.
It appears these statements are contradictory. The first statement says one cannot know the ratio at which an exchange will take place. The second statement says one can.
Actually, the two statements are not contradictory. The first is categorical and says given only preferences one cannot determine an exchange ratio. The second is hypothetical. It says if one knows the preference scales of the actors, then one can determine the ratio of exchange prior to it taking place. The second statement is conditional based whether or not one has the information and therefore does not contradict the first statement.
If one need only know the supply and demand curves prior to a transaction in order to determine its exchange ratio, then why doesn’t one just use them? One could, if one had them, but preference scales need not exist prior to a transaction. One cannot derive from the logic of action (praxeology) that a preference scale must be known by the actor prior to a transaction. It might not be known to the actor until the transaction is under way. One cannot derive from the logic of action whether preference scales are known ahead of time or at the point of the transaction.
A further point is made about the seemingly contradictory statements made earlier. Regarding the first statement, though the ratio of exchange is indeterminate to an outside observer, it does not follow that it is in fact indeterminate. Some economists believe that all preference scales are fixed at the time a transaction takes place. In this view even the actor may not know his own preference scale prior to the transaction. Again, though, one cannot determine whether this is the case from the logic of action. The logic of action cannot tell us anything about how preference scales are formed or when they are actually know. All we can know is that an exchange took place at a given ratio when it does.
Dr. Gordon has argued the Austrian Economists case that value is subjective. This notion of value contradicts the theories of classical economists (Adam Smith, David Ricardo), who argued value was based on the cost of production. Karl Marx, who created ‘scientific socialism’, based his theories upon the classical economist’s notion of value. Dr. Gordon turns to the basis of Marx’s system and shows why it is wrong.
Marx described the idea that prices are determined by individual preferences as ‘vulgar economics.’ According to him, the point of science is to discover the underlying laws that govern behavior, and in this case the laws underlying the behavior of prices. Marx, however, did agree with a kernel of the theory he attacked. He acknowledged that to be valued goods must have some utility. Thus he agreed that mud pies, which are not useful, would not be valuable no matter how long one spent making them.
Marx believed that goods did not only possess value solely based on their utility. He believed this because he recognized that such a value, being subjective, could not be measured. If one could not measure value objectively then it could not serve as a basis for developing any sort of science.
To remedy the problem, Marx held that goods not only had use value, but also exchange value. Besides valuing a good for a ‘use’ one also values a good based on what one could gain by exchanging it. Furthermore, one can measure the exchange value of a good by simply noting what other goods could be obtained for it. Having established a property of a good’s value that one could measure Marx argued one could begin developing a science from it.
The first problem with Marx’s idea of exchange value is that the actors exchanging goods do not view their values as equal. Their values are unequal; the value of the good exchanged is valued less than the good for which the exchange is made. Marx responded to this criticism saying that this shows the utility values are not equal, but the exchange values are equal.
The idea that some sort of exchange value exists on its own apart from any use value the good has is problematical. It implies that there is an exchange value that exists completely separate from a ‘use’ value. In fact, a good is valued in exchange precisely because it is valued for its use somewhere else.
Marx might suggest Gordon is just attached to a subjective value theory. So be it; Marx must still show how exchange value exists separately from use value. Anticipating this Marx also responded that there must be an exchange value which can be measured otherwise there can be no scientific basis for why goods exchange the way they do. There must be some underlying feature of value that makes goods identical. According to Marx this feature was labor. Two goods exchange because the labor used to produce them is identical.
Eugen von Bohm-Bawerk criticized Marx’s labor theory in his works Capital and Interest and Karl Marx and the Close of His System. For the sake of argument, von Bohm-Bawerk acknowledged that there was such a thing as exchange value. Given that, why should labor aside from all other factors be the basis of this value? Furthermore, there are many goods in which labor is but a fraction of the total value of a good. The value of wine, for example, depends more upon its aging than the amount of grape picking.
Another problem with labor was its heterogeneity. Different people are more efficient at making certain goods than others. Should the products they make, though identical, be valued differently then?
Marx had a response to this last criticism. He said that the labor to make a product is based on the ‘socially necessary’ labor needed to produce it. Bohm Bawerk argued that to avoid an arbitrary definition of ‘socially necessary’ labor Marx must use market prices as the means for establishing what is ‘socially necessary’. Marx therefore reasoned in a circle; the market price of a good should be based on the value of labor used to make it, the amount of the labor used to produce a good is based on the socially necessary labor needed to produce it, and the socially necessary labor needed to produce the good is based on market prices. Marx was proving that market prices should be used to determine market prices.
Furthermore, how did Marx’s theory explain how different types of labor, i.e. brain surgery vs. house painting, could be compared? Marx again responded they could be compared using ‘socially necessary’ labor. Again, this demanded the use of market prices.
Marx faced another problem. As he himself admitted, his theory did not in fact explain prices as they existed on the market. That is, goods did not exchange at their labor prices on the market. Nevertheless, he insisted, his theory did explain how actual market prices come about and what “the ‘laws of motion’ of capitalism really are”. Bohm Bawerk, using arguments beyond the scope presented so far, again show Marx to be wrong. Even without referring to Bohm Bawerk’s argument however, all Marx’s theory showed was that two goods exchanged because their exchange values were equal. There is no underlying law of motion.
Later in the chapter, Dr Gordon showed that if one knows the preference scales of the actors involved in an exchange (also illustrated with Demand and Supply curves) one can determine the ratio at which an exchange will take place.
It appears these statements are contradictory. The first statement says one cannot know the ratio at which an exchange will take place. The second statement says one can.
Actually, the two statements are not contradictory. The first is categorical and says given only preferences one cannot determine an exchange ratio. The second is hypothetical. It says if one knows the preference scales of the actors, then one can determine the ratio of exchange prior to it taking place. The second statement is conditional based whether or not one has the information and therefore does not contradict the first statement.
If one need only know the supply and demand curves prior to a transaction in order to determine its exchange ratio, then why doesn’t one just use them? One could, if one had them, but preference scales need not exist prior to a transaction. One cannot derive from the logic of action (praxeology) that a preference scale must be known by the actor prior to a transaction. It might not be known to the actor until the transaction is under way. One cannot derive from the logic of action whether preference scales are known ahead of time or at the point of the transaction.
A further point is made about the seemingly contradictory statements made earlier. Regarding the first statement, though the ratio of exchange is indeterminate to an outside observer, it does not follow that it is in fact indeterminate. Some economists believe that all preference scales are fixed at the time a transaction takes place. In this view even the actor may not know his own preference scale prior to the transaction. Again, though, one cannot determine whether this is the case from the logic of action. The logic of action cannot tell us anything about how preference scales are formed or when they are actually know. All we can know is that an exchange took place at a given ratio when it does.
Dr. Gordon has argued the Austrian Economists case that value is subjective. This notion of value contradicts the theories of classical economists (Adam Smith, David Ricardo), who argued value was based on the cost of production. Karl Marx, who created ‘scientific socialism’, based his theories upon the classical economist’s notion of value. Dr. Gordon turns to the basis of Marx’s system and shows why it is wrong.
Marx described the idea that prices are determined by individual preferences as ‘vulgar economics.’ According to him, the point of science is to discover the underlying laws that govern behavior, and in this case the laws underlying the behavior of prices. Marx, however, did agree with a kernel of the theory he attacked. He acknowledged that to be valued goods must have some utility. Thus he agreed that mud pies, which are not useful, would not be valuable no matter how long one spent making them.
Marx believed that goods did not only possess value solely based on their utility. He believed this because he recognized that such a value, being subjective, could not be measured. If one could not measure value objectively then it could not serve as a basis for developing any sort of science.
To remedy the problem, Marx held that goods not only had use value, but also exchange value. Besides valuing a good for a ‘use’ one also values a good based on what one could gain by exchanging it. Furthermore, one can measure the exchange value of a good by simply noting what other goods could be obtained for it. Having established a property of a good’s value that one could measure Marx argued one could begin developing a science from it.
The first problem with Marx’s idea of exchange value is that the actors exchanging goods do not view their values as equal. Their values are unequal; the value of the good exchanged is valued less than the good for which the exchange is made. Marx responded to this criticism saying that this shows the utility values are not equal, but the exchange values are equal.
The idea that some sort of exchange value exists on its own apart from any use value the good has is problematical. It implies that there is an exchange value that exists completely separate from a ‘use’ value. In fact, a good is valued in exchange precisely because it is valued for its use somewhere else.
Marx might suggest Gordon is just attached to a subjective value theory. So be it; Marx must still show how exchange value exists separately from use value. Anticipating this Marx also responded that there must be an exchange value which can be measured otherwise there can be no scientific basis for why goods exchange the way they do. There must be some underlying feature of value that makes goods identical. According to Marx this feature was labor. Two goods exchange because the labor used to produce them is identical.
Eugen von Bohm-Bawerk criticized Marx’s labor theory in his works Capital and Interest and Karl Marx and the Close of His System. For the sake of argument, von Bohm-Bawerk acknowledged that there was such a thing as exchange value. Given that, why should labor aside from all other factors be the basis of this value? Furthermore, there are many goods in which labor is but a fraction of the total value of a good. The value of wine, for example, depends more upon its aging than the amount of grape picking.
Another problem with labor was its heterogeneity. Different people are more efficient at making certain goods than others. Should the products they make, though identical, be valued differently then?
Marx had a response to this last criticism. He said that the labor to make a product is based on the ‘socially necessary’ labor needed to produce it. Bohm Bawerk argued that to avoid an arbitrary definition of ‘socially necessary’ labor Marx must use market prices as the means for establishing what is ‘socially necessary’. Marx therefore reasoned in a circle; the market price of a good should be based on the value of labor used to make it, the amount of the labor used to produce a good is based on the socially necessary labor needed to produce it, and the socially necessary labor needed to produce the good is based on market prices. Marx was proving that market prices should be used to determine market prices.
Furthermore, how did Marx’s theory explain how different types of labor, i.e. brain surgery vs. house painting, could be compared? Marx again responded they could be compared using ‘socially necessary’ labor. Again, this demanded the use of market prices.
Marx faced another problem. As he himself admitted, his theory did not in fact explain prices as they existed on the market. That is, goods did not exchange at their labor prices on the market. Nevertheless, he insisted, his theory did explain how actual market prices come about and what “the ‘laws of motion’ of capitalism really are”. Bohm Bawerk, using arguments beyond the scope presented so far, again show Marx to be wrong. Even without referring to Bohm Bawerk’s argument however, all Marx’s theory showed was that two goods exchanged because their exchange values were equal. There is no underlying law of motion.
Sunday, March 29, 2009
Introduction to Economic Reasoning - Chapter 4: Demand and Supply
Dr. Gordon now turns to the laws of demand and supply; the concepts people most often identify with economics.
Gordon begins simply. Two actors have what the other wants. The first actor has apples and wants an orange. The second actor has oranges and wants an apple. In such a situation, we can expect an exchange to take place. One cannot determine, however, the ratio of apples to oranges at which the exchange will take place. True, each actor prefers one good to the other good. Still, it does not follow that the exchange will take place at this ratio. An exchange could take place at a ratio of 1 apple for 2 oranges or 2 apples for 10 oranges. Such ratios are consistent with the preference of 1 apple to 1 orange. Just because an actor prefers one apple to an orange doesn’t mean he has to settle for one apple for an orange. The same applies to the other actor.
A ratio cannot be established without recognizing marginal utility. As an actor acquires more apples, each additional apple will be worth less to him. As he gives up more oranges, each orange he still has will be worth more to him (he prefers apples to oranges, but he still values oranges. They are not worthless to him). A given preference scale for each actor, in this case apples and oranges, helps establish a range of prices at which an exchange will take place.
For example assume the following preference scales:
You have 4 oranges. Your preference scale is 2 apples, 1 orange, 2 oranges, 1 apple
I have 4 apples. My preference scale is 2 oranges, 2 apples, 1 orange, 1 apple
Say you demand 2 apples for 1 orange. According to my preference scale, I value 2 apples more than 1 orange, so I would not trade apples for oranges at this price.
In essence, though an actor may prefer one good to another, one cannot determine the potential ratios of exchange at which the actor may trade until one knows how much the actor values the good vs. the other good. Even with knowing the preference scale of two actors, one may only know a range of ratios (prices) at which goods will trade for each other, not necessarily a single ratio (price).
Consider, now, when other actors enter the market. According to their preferences they may more readily trade their goods for other goods. As trading between these different actors occurs, exchange ratios become known to other actors, who will also trade depending on their preference scales. As such, a competition will develop between the actors for goods and eventually these goods will exchange at a single price. This process is known as the law of one price.
During this process certain actors may observe different prices established between different sets of other actors. They may take advantage of these different prices and buy from actors willing to sell at a lower price and sell to other actors who are willing to buy at a higher price. Such actors are able to secure what is called an arbitrage profit. As this activity becomes known to other actors these arbitrage profits become more difficult to secure. The activity of arbitrage actually tends to speed up the establishment of a single price.
Gordon next asks us to look at the determination of prices in more detail. In doing so, he will introduce us to supply and demand curves. Before he begins he reiterates two principles (1) we prefer more of a good to less of a good (2) as you acquire more units of a good, you will put them to less valuable uses (law of marginal utility).
Given a preference scale, one can determine how much of a good an actor wants at a given price. For example for 4 apples you want 1 orange. For 3 apples, you want 2 oranges. For 2 apples you want 1 orange. This is a demand schedule for oranges. Such demand schedules, even made up ones, are based on preference scales and must follow rules 1 and 2 above. For example, a demand schedule cannot imply that you would value oranges more and more as you give up more apples for them. For each additional orange you gain, you value oranges more, and for each additional apple you give up, you value apples less. Essentially, the more oranges you acquire under this demand schedule, the more apples you are willing to give up for them. This violates the law of marginal utility.
Dr. Gordon cautions, however, that inconsistent preferences (as opposed preference scales inconsistent with the law of marginal utility) at the same price are not logically contradictory. A person can prefer 5 oranges over 25 apples, but also prefer 16 apples over 5 oranges. Even so, inconsistent preferences are generally not, well, preferred.
The law of demand follows from the last two paragraphs. At a lower price, an actor will demand more of a good.
Typically, the law of demand is illustrated by a demand curve. Discrete points defined by the coordinates of price (on the vertical axis) and quantity (on the horizontal axis) are connected by a downward sloping curve. One must realize however, that there is not necessarily a relationship between quantity and price between the discrete points used to draw the lines. Though points on these lines imply it, one may not be able to determine from the graph the price someone would pay for an orange plus a very small amount of another orange.
The law of supply also follows from principles (1) and (2) above. The law of supply says that the higher the price, the greater the quantity supplied. If one is offered more apples for oranges, one will be willing to supply more oranges.
The law of supply is also typically illustrated with a curve. As opposed to the downward slope of the demand curve the supply curve has an upward slope. The same warning about what demand curves can tell one about prices also applies to supply curves.
Both demand and supply curves can indicate how responsive quantities are to prices. More vertical demand and supply curves are called elastic. They indicate that even large price changes have little effect on the quantity of goods supplied.
One can overlay the demand and supply curves on the same chart. Where they intersect establishes where the demand for the good equals the quantity supplied. At higher prices, suppliers supply more of a good than is demanded, and must lower their prices to sell their stock. At lower prices, more goods are demanded than are supplied, and demanders will bid up the price.
Where the curves intersect establishes the equilibrium or market clearing price.
The demand and supply curves discussed so far apply to individuals. These curves can be combined with others to establish demand and supply curves for a group. The intersection point of these curves is the result of the law of one price, discussed earlier. The law is actually the result of a competitive process, not a mysterious force. Because we know that prices will converge to ‘one price’ as established by the law, we can treat a group of individuals as a single buyer and seller with their corresponding demand curves. Note that there is no preference scales for the group as there are for individuals. The price established by the demand and supply curves of the group, however, will closely match that of the marginal buyer and seller.
On a final note, Dr. Gordon highlights a common fallacy to be avoided. If the quantity of a good supplied increases and prices fall, a change in the quantity demanded of a good has occurred and the price has moved along the demand curve. On the other hand, should the quantity of a good increase along with the price of the good, the demand curve has shifted. Do not confuse movement along a curve with a shift of the curve.
If you remember one thing from this chapter, remember that prices are subjective. Individuals determine the prices of goods.
Gordon begins simply. Two actors have what the other wants. The first actor has apples and wants an orange. The second actor has oranges and wants an apple. In such a situation, we can expect an exchange to take place. One cannot determine, however, the ratio of apples to oranges at which the exchange will take place. True, each actor prefers one good to the other good. Still, it does not follow that the exchange will take place at this ratio. An exchange could take place at a ratio of 1 apple for 2 oranges or 2 apples for 10 oranges. Such ratios are consistent with the preference of 1 apple to 1 orange. Just because an actor prefers one apple to an orange doesn’t mean he has to settle for one apple for an orange. The same applies to the other actor.
A ratio cannot be established without recognizing marginal utility. As an actor acquires more apples, each additional apple will be worth less to him. As he gives up more oranges, each orange he still has will be worth more to him (he prefers apples to oranges, but he still values oranges. They are not worthless to him). A given preference scale for each actor, in this case apples and oranges, helps establish a range of prices at which an exchange will take place.
For example assume the following preference scales:
You have 4 oranges. Your preference scale is 2 apples, 1 orange, 2 oranges, 1 apple
I have 4 apples. My preference scale is 2 oranges, 2 apples, 1 orange, 1 apple
Say you demand 2 apples for 1 orange. According to my preference scale, I value 2 apples more than 1 orange, so I would not trade apples for oranges at this price.
In essence, though an actor may prefer one good to another, one cannot determine the potential ratios of exchange at which the actor may trade until one knows how much the actor values the good vs. the other good. Even with knowing the preference scale of two actors, one may only know a range of ratios (prices) at which goods will trade for each other, not necessarily a single ratio (price).
Consider, now, when other actors enter the market. According to their preferences they may more readily trade their goods for other goods. As trading between these different actors occurs, exchange ratios become known to other actors, who will also trade depending on their preference scales. As such, a competition will develop between the actors for goods and eventually these goods will exchange at a single price. This process is known as the law of one price.
During this process certain actors may observe different prices established between different sets of other actors. They may take advantage of these different prices and buy from actors willing to sell at a lower price and sell to other actors who are willing to buy at a higher price. Such actors are able to secure what is called an arbitrage profit. As this activity becomes known to other actors these arbitrage profits become more difficult to secure. The activity of arbitrage actually tends to speed up the establishment of a single price.
Gordon next asks us to look at the determination of prices in more detail. In doing so, he will introduce us to supply and demand curves. Before he begins he reiterates two principles (1) we prefer more of a good to less of a good (2) as you acquire more units of a good, you will put them to less valuable uses (law of marginal utility).
Given a preference scale, one can determine how much of a good an actor wants at a given price. For example for 4 apples you want 1 orange. For 3 apples, you want 2 oranges. For 2 apples you want 1 orange. This is a demand schedule for oranges. Such demand schedules, even made up ones, are based on preference scales and must follow rules 1 and 2 above. For example, a demand schedule cannot imply that you would value oranges more and more as you give up more apples for them. For each additional orange you gain, you value oranges more, and for each additional apple you give up, you value apples less. Essentially, the more oranges you acquire under this demand schedule, the more apples you are willing to give up for them. This violates the law of marginal utility.
Dr. Gordon cautions, however, that inconsistent preferences (as opposed preference scales inconsistent with the law of marginal utility) at the same price are not logically contradictory. A person can prefer 5 oranges over 25 apples, but also prefer 16 apples over 5 oranges. Even so, inconsistent preferences are generally not, well, preferred.
The law of demand follows from the last two paragraphs. At a lower price, an actor will demand more of a good.
Typically, the law of demand is illustrated by a demand curve. Discrete points defined by the coordinates of price (on the vertical axis) and quantity (on the horizontal axis) are connected by a downward sloping curve. One must realize however, that there is not necessarily a relationship between quantity and price between the discrete points used to draw the lines. Though points on these lines imply it, one may not be able to determine from the graph the price someone would pay for an orange plus a very small amount of another orange.
The law of supply also follows from principles (1) and (2) above. The law of supply says that the higher the price, the greater the quantity supplied. If one is offered more apples for oranges, one will be willing to supply more oranges.
The law of supply is also typically illustrated with a curve. As opposed to the downward slope of the demand curve the supply curve has an upward slope. The same warning about what demand curves can tell one about prices also applies to supply curves.
Both demand and supply curves can indicate how responsive quantities are to prices. More vertical demand and supply curves are called elastic. They indicate that even large price changes have little effect on the quantity of goods supplied.
One can overlay the demand and supply curves on the same chart. Where they intersect establishes where the demand for the good equals the quantity supplied. At higher prices, suppliers supply more of a good than is demanded, and must lower their prices to sell their stock. At lower prices, more goods are demanded than are supplied, and demanders will bid up the price.
Where the curves intersect establishes the equilibrium or market clearing price.
The demand and supply curves discussed so far apply to individuals. These curves can be combined with others to establish demand and supply curves for a group. The intersection point of these curves is the result of the law of one price, discussed earlier. The law is actually the result of a competitive process, not a mysterious force. Because we know that prices will converge to ‘one price’ as established by the law, we can treat a group of individuals as a single buyer and seller with their corresponding demand curves. Note that there is no preference scales for the group as there are for individuals. The price established by the demand and supply curves of the group, however, will closely match that of the marginal buyer and seller.
On a final note, Dr. Gordon highlights a common fallacy to be avoided. If the quantity of a good supplied increases and prices fall, a change in the quantity demanded of a good has occurred and the price has moved along the demand curve. On the other hand, should the quantity of a good increase along with the price of the good, the demand curve has shifted. Do not confuse movement along a curve with a shift of the curve.
If you remember one thing from this chapter, remember that prices are subjective. Individuals determine the prices of goods.
Sunday, March 22, 2009
Introduction to Economic Reasoning - Chapter 3: Action and Preference Part II
Given a value scale, an actor will choose his most highly preferred goal. How do we know this? It follows from the action axiom. Given a choice, a person will would rather choose the goal they prefer the most.
Some object to the idea that we always choose our highest preference. They say that that people choose less preferred over more highly preferred goals all the time. For example, a student who will be rewarded for getting an ‘A’ does not cheat if given the chance. This proves highly preferred goals are not necessarily chosen. In fact, however, this action actually shows that the student prefers not cheating more than getting an ‘A’.
Still others then criticize the above response. That “one’s highest preference is what one chooses” is tautological and therefore trivial. We learn nothing from this statement as the terms ‘choose’ and ‘preference’ are synonyms for one another.
In response Gordon clarifies the definition not as ‘one prefers what one has chosen’, but ‘one chooses what one most highly prefers’. He also notes that just because a statement is tautological does not make it trivial.
In fact, the notion of preference leads to the deduction of one the most important theories of economics, the theory of marginal utility.
Gordon illustrates the theory using an example. Imagine you have five preferences for using an orange. You happen to have one orange. Which preference will you use the orange to fulfill? Common sense dictates you will use the orange to fulfill your most highly valued preference. If you have two oranges, you will use them to fulfill your highest preference and next highest preference. An important implication is uncovered, however, if one starts with five oranges. Should you lose your third orange, will you forgo fulfilling your third highest preference? No, you will use your last orange to fulfill that preference. The implication arrives; one uses the last available unit (marginal unit) of a good to fulfill one’s least highly valued preference.
Some challenge the theory of marginal utility saying that it cannot help us in understanding cases of indifference. For example, what happens if I value the second and third preferences for orange use exactly the same. What will I do with the second orange? Burdian, a scholastic, famously illustrated the supposed implication of ranking preferences without considering indifference. He imagined a donkey that starves to death because it cannot decide which of two identical bales of hay to eat first. Rothbard, however, criticized this example. It implies that only two preferences exist (to eat the first bale of hay, to eat the second bale of hay) when actually there are three (eat the first, eat the second, starve to death). There is no indifference when it comes to eating a bale of hay in this case.
Indifference is not important in economics because it cannot be demonstrated in action. Economics is not concerned with how one might chooses between preferences one is indifferent about. Furthermore, the strength of one preference versus another is not important, only their ranking.
Gordon returns to Burdian’s Ass. He addresses the objection that it doesn’t matter whether the donkey wishes to avoid starving to death. The donkey must choose between two identical bales of hay and if a perfectly rational agent cannot do so. Gordon answers such a notion of perfect rationality is problematic. If perfectly rational, why should the donkey waste time reasoning as to how to choose a hay bale in order to avoid starvation?
Returning to the theory of marginal utility, Gordon seeks to address a frequent misconception. Restating the theory, as more units of good are acquired, an actor will apply each additional unit to the satisfaction of a subsequently less highly valued preference. Some economists (Gossen) seek to explain this process as the ‘satiation of wants.’ The ‘satiation of wants’ is a psychological theory may or may not be true, but it has no bearing on the science of economics. It is not deduced from action nor is it an axiomatic principle. Marginal utility says only that people apply units of a good to their most highly valued preference first, and so on down their preference scale. It is deduced solely form the action axiom and is not an attempt to explain why actors act in this way.
Gordon further claims that refuting the notion of choosing the most highly ranked preference based on psychological theory is unfounded. For example, an established psychological principle that a second bite of ice cream may be more pleasurable than the principle that an actor chooses their highest preference. Even if the psychological theory were true, this principle of action still stands. Preference scales need not consist of the single use of a good. Each preference could involve more than one good put to more than one use as well as different uses for different goods. Thus, two ice cream bites can be a single preference leaving the preference principle in tact.
The use actor’s see for goods, then, determines how goods are comprised in value scales. The uses actor’s see for goods is subjective. This does not mean the goods themselves are subjective as some ‘radical subjectivists’ claim. Goods have objective qualitative and quantitative attributes unlike the uses to which actors dedicate them.
In the real world an actor can satisfy their many different preferences with many different goods. Marginal utility recognizes this. Actors rank many different goods based on their assessment of how well these goods satisfy their many different preferences. As an actor acquires more goods, he will dedicate them to satisfy progressively less valued preferences.
Marginal utility applies not only to single actors, but also to actors involved in exchange. Exchanges can be either voluntary or involuntary (involving force or fraud). Economics mainly concerns the former.
Actors voluntarily exchange goods because each expects to benefit. They value the goods they exchange in reverse order. This valuation is the basis for prices.
Some object to the idea that we always choose our highest preference. They say that that people choose less preferred over more highly preferred goals all the time. For example, a student who will be rewarded for getting an ‘A’ does not cheat if given the chance. This proves highly preferred goals are not necessarily chosen. In fact, however, this action actually shows that the student prefers not cheating more than getting an ‘A’.
Still others then criticize the above response. That “one’s highest preference is what one chooses” is tautological and therefore trivial. We learn nothing from this statement as the terms ‘choose’ and ‘preference’ are synonyms for one another.
In response Gordon clarifies the definition not as ‘one prefers what one has chosen’, but ‘one chooses what one most highly prefers’. He also notes that just because a statement is tautological does not make it trivial.
In fact, the notion of preference leads to the deduction of one the most important theories of economics, the theory of marginal utility.
Gordon illustrates the theory using an example. Imagine you have five preferences for using an orange. You happen to have one orange. Which preference will you use the orange to fulfill? Common sense dictates you will use the orange to fulfill your most highly valued preference. If you have two oranges, you will use them to fulfill your highest preference and next highest preference. An important implication is uncovered, however, if one starts with five oranges. Should you lose your third orange, will you forgo fulfilling your third highest preference? No, you will use your last orange to fulfill that preference. The implication arrives; one uses the last available unit (marginal unit) of a good to fulfill one’s least highly valued preference.
Some challenge the theory of marginal utility saying that it cannot help us in understanding cases of indifference. For example, what happens if I value the second and third preferences for orange use exactly the same. What will I do with the second orange? Burdian, a scholastic, famously illustrated the supposed implication of ranking preferences without considering indifference. He imagined a donkey that starves to death because it cannot decide which of two identical bales of hay to eat first. Rothbard, however, criticized this example. It implies that only two preferences exist (to eat the first bale of hay, to eat the second bale of hay) when actually there are three (eat the first, eat the second, starve to death). There is no indifference when it comes to eating a bale of hay in this case.
Indifference is not important in economics because it cannot be demonstrated in action. Economics is not concerned with how one might chooses between preferences one is indifferent about. Furthermore, the strength of one preference versus another is not important, only their ranking.
Gordon returns to Burdian’s Ass. He addresses the objection that it doesn’t matter whether the donkey wishes to avoid starving to death. The donkey must choose between two identical bales of hay and if a perfectly rational agent cannot do so. Gordon answers such a notion of perfect rationality is problematic. If perfectly rational, why should the donkey waste time reasoning as to how to choose a hay bale in order to avoid starvation?
Returning to the theory of marginal utility, Gordon seeks to address a frequent misconception. Restating the theory, as more units of good are acquired, an actor will apply each additional unit to the satisfaction of a subsequently less highly valued preference. Some economists (Gossen) seek to explain this process as the ‘satiation of wants.’ The ‘satiation of wants’ is a psychological theory may or may not be true, but it has no bearing on the science of economics. It is not deduced from action nor is it an axiomatic principle. Marginal utility says only that people apply units of a good to their most highly valued preference first, and so on down their preference scale. It is deduced solely form the action axiom and is not an attempt to explain why actors act in this way.
Gordon further claims that refuting the notion of choosing the most highly ranked preference based on psychological theory is unfounded. For example, an established psychological principle that a second bite of ice cream may be more pleasurable than the principle that an actor chooses their highest preference. Even if the psychological theory were true, this principle of action still stands. Preference scales need not consist of the single use of a good. Each preference could involve more than one good put to more than one use as well as different uses for different goods. Thus, two ice cream bites can be a single preference leaving the preference principle in tact.
The use actor’s see for goods, then, determines how goods are comprised in value scales. The uses actor’s see for goods is subjective. This does not mean the goods themselves are subjective as some ‘radical subjectivists’ claim. Goods have objective qualitative and quantitative attributes unlike the uses to which actors dedicate them.
In the real world an actor can satisfy their many different preferences with many different goods. Marginal utility recognizes this. Actors rank many different goods based on their assessment of how well these goods satisfy their many different preferences. As an actor acquires more goods, he will dedicate them to satisfy progressively less valued preferences.
Marginal utility applies not only to single actors, but also to actors involved in exchange. Exchanges can be either voluntary or involuntary (involving force or fraud). Economics mainly concerns the former.
Actors voluntarily exchange goods because each expects to benefit. They value the goods they exchange in reverse order. This valuation is the basis for prices.
Monday, March 16, 2009
Economic Reasoning - Chapter 2 - Action and Preference
Having covered deductive logic, Dr. Gordon turns to the foundation of economic science. The foundation, he argues, is the action axiom; man acts.
Action is conscious, purposeful behavior directed towards a goal. Action does not require physical movement. For example, one can remain seated to vote against a proposal. Still, most actions involve physical movement.
How does one know the axiom is true? According to Gordon we know it’s true because it is common sense.
That economics is based on an axiom understood to be common sense makes it different from the natural sciences. These sciences rely on controlled experimentation and observation because we do not know the underlying structure of natural phenomena; we must guess at it based on observation. On the other hand we, being acting humans, can understand what action is without having to experiment or observe.
Many economists reject the notion that one can develop economic science using deduction. Premises cannot be accepted because they are self-evident. One must work backwards starting with observable reality and formulating premises that explain it. If these premises predict an outcome that is eventually observed, then they are sound.
Having established the action axiom as true, Dr. Gordon next discusses what must follow from it. What first follows is that action is directed toward obtaining something. If we already possessed that which we wish to obtain, we would not act. The actions we employ to obtain something (our goal or purpose) involve means.
The structure of action involves the use of means to achieve a goal. From his one must acknowledge the goal will not come about without action. More precisely, one must not believe that one can obtain a desired goal no matter what action one takes. This must be distinguished from the idea that one cannot be certain of achieving a goal despite the action one takes. This is a much more powerful statement. It suggests a completely uncertain future. According to Gordon, it is also false. If you wish to reach a point across the room, and you know that if you walk there you will reach it, then the future is not uncertain. The forgoing distinction is subtle, but important. Some economists claim the future is “radically uncertain” and that actors can know very little about the outcome of their actions. If economics were the study of ignorant actors, it would not be of much use.
Dr. Gordon also states a corollary to action; one of ‘inaction’. One must not believe a goal will not be achieved no matter what one does. An actor will not act to achieve what they believe is impossible.
Next Gordon discusses the subjects of preference and utility. When one acts to fulfill a goal, one prefers this goal to some other goal. Some economists claim that one prefers one goal to another because it maximizes their utility, or increases there satisfaction. This notion adds nothing to the understanding of action; that is one acts to fulfill a goal one prefers versus another goal. In fact, acting to increase satisfaction suggests that actors are motivated to fulfill their goals based on the pleasure or pain they derive (or do not derive) from them. This is a psychological theory known as hedonism.
It is here that Dr. Gordon clarifies what economists mean by utility and welfare. These terms refer to the fact that an actor prefers one goal to another, not to any sensations these goals might elicit. The idea that people seek pleasure and avoid pain is known as hedonism. Reference to ‘hedonism’ is concerned with how or why people act. Whether it is true or not, hedonism has no place in economics. Economics is concerned only with the implication of actions.
Action not only involves choosing the best means to achieve a goal, but also choosing from various goals. Note that these facts do not follow from the action axiom. The axiom could apply to a single goal with a single means to achieve it. That economics is a science deduced from action, however, does not mean one cannot introduce other principles that are not derived from the axiom. Thus, Gordon argues the above principles can be introduced to derive a science of economics. Like the action axiom, they are common sense principles and require no explanation. (Dr. Gordon does note that there are economists who argue that these new axioms can be derived from the action axiom).
Gordon has now introduced 3 axiomatic principles as the basis of economic science (1) Man acts (2) Man has a variety of goals from which to choose (3) Man has variety of means from which to choose to achieve a goal.
Man has different goals; which does he choose? He chooses his most highly preferred goal. This goal is subjectively ranked against other goals, not measured. (Measurement implies an account of satisfaction and suggests hedonism). As the economist Lionel Robbins noted, utility, welfare, or satisfaction, in the sense Gordon specifies is like love. It is expressed as a comparison, not measured. In the next chapter Gordon addresses the status of preference; whether it is axiomatic or deduced from the principles noted above.
Action is conscious, purposeful behavior directed towards a goal. Action does not require physical movement. For example, one can remain seated to vote against a proposal. Still, most actions involve physical movement.
How does one know the axiom is true? According to Gordon we know it’s true because it is common sense.
That economics is based on an axiom understood to be common sense makes it different from the natural sciences. These sciences rely on controlled experimentation and observation because we do not know the underlying structure of natural phenomena; we must guess at it based on observation. On the other hand we, being acting humans, can understand what action is without having to experiment or observe.
Many economists reject the notion that one can develop economic science using deduction. Premises cannot be accepted because they are self-evident. One must work backwards starting with observable reality and formulating premises that explain it. If these premises predict an outcome that is eventually observed, then they are sound.
Having established the action axiom as true, Dr. Gordon next discusses what must follow from it. What first follows is that action is directed toward obtaining something. If we already possessed that which we wish to obtain, we would not act. The actions we employ to obtain something (our goal or purpose) involve means.
The structure of action involves the use of means to achieve a goal. From his one must acknowledge the goal will not come about without action. More precisely, one must not believe that one can obtain a desired goal no matter what action one takes. This must be distinguished from the idea that one cannot be certain of achieving a goal despite the action one takes. This is a much more powerful statement. It suggests a completely uncertain future. According to Gordon, it is also false. If you wish to reach a point across the room, and you know that if you walk there you will reach it, then the future is not uncertain. The forgoing distinction is subtle, but important. Some economists claim the future is “radically uncertain” and that actors can know very little about the outcome of their actions. If economics were the study of ignorant actors, it would not be of much use.
Dr. Gordon also states a corollary to action; one of ‘inaction’. One must not believe a goal will not be achieved no matter what one does. An actor will not act to achieve what they believe is impossible.
Next Gordon discusses the subjects of preference and utility. When one acts to fulfill a goal, one prefers this goal to some other goal. Some economists claim that one prefers one goal to another because it maximizes their utility, or increases there satisfaction. This notion adds nothing to the understanding of action; that is one acts to fulfill a goal one prefers versus another goal. In fact, acting to increase satisfaction suggests that actors are motivated to fulfill their goals based on the pleasure or pain they derive (or do not derive) from them. This is a psychological theory known as hedonism.
It is here that Dr. Gordon clarifies what economists mean by utility and welfare. These terms refer to the fact that an actor prefers one goal to another, not to any sensations these goals might elicit. The idea that people seek pleasure and avoid pain is known as hedonism. Reference to ‘hedonism’ is concerned with how or why people act. Whether it is true or not, hedonism has no place in economics. Economics is concerned only with the implication of actions.
Action not only involves choosing the best means to achieve a goal, but also choosing from various goals. Note that these facts do not follow from the action axiom. The axiom could apply to a single goal with a single means to achieve it. That economics is a science deduced from action, however, does not mean one cannot introduce other principles that are not derived from the axiom. Thus, Gordon argues the above principles can be introduced to derive a science of economics. Like the action axiom, they are common sense principles and require no explanation. (Dr. Gordon does note that there are economists who argue that these new axioms can be derived from the action axiom).
Gordon has now introduced 3 axiomatic principles as the basis of economic science (1) Man acts (2) Man has a variety of goals from which to choose (3) Man has variety of means from which to choose to achieve a goal.
Man has different goals; which does he choose? He chooses his most highly preferred goal. This goal is subjectively ranked against other goals, not measured. (Measurement implies an account of satisfaction and suggests hedonism). As the economist Lionel Robbins noted, utility, welfare, or satisfaction, in the sense Gordon specifies is like love. It is expressed as a comparison, not measured. In the next chapter Gordon addresses the status of preference; whether it is axiomatic or deduced from the principles noted above.
Tuesday, February 10, 2009
David Gordon - Economic Reasoning Chapter 1 - The Method of Economics
Dr. David Gordon begins his book with the following statement;
"In economics, we operate with deductive logic."
In this first chapter of his book Dr. Gordon explains why deductive logic is a powerful tool, and some of its basic rules.
What makes deductive logic so powerful? Starting from premises one knows to be true, the rules of deductive logic deliver conclusions that must be true.
Dr. Gordon begins with a simple example to illustrate; if all of a class A are part of a class B, and all of a class B are part of a class C, then all of A are part of C.
(It is after this example the reader comes upon the first of Dr. Gordon's 'thought starter's -I'll call them- that are found throughout his book. I appreciate his adding of these questions. They forced me to think more about what I had read. I list these questions at the end of each Chapter and attempt to answer them if Dr. Gordon has not answered them already.)
In the next section he continues the discussion with Aristotle' Laws of Reality (sometimes misnamed the 'Laws of Thought);
Aristotle's Laws of Reality:
1) A=A: The Law of Identity
2) Not (A and not A): The Law of Non-Contradiction
3) A or not A: The Law of Excluded Middle
The first rule, restated, says a thing is what it is. For example; a ball is ball, not something else.
The second rule, restated, says that a thing cannot be a thing and not a thing at the same time. For example, a thing cannot be a ball and not a ball.
The third rule, a bit trickier, says that a thing is either something or not something. For example, a thing is either red or non-red. It cannot be neither, or both.
The next section is on validity. Dr. Gordon now reviews the implications of an argument based on false premises. An argument based on true premises that follows the rules of logic yields a true conclusion every time. What about an argument beginning with false premises? Does it yield a false conclusion if it too, follows the rules? No. It may, but it also may not. Examples are given showing this to be the case.
An argument yields a true conclusion only if its premises are true and it is valid. It is valid if it follows the rules of logic. An argument resting on true premises that does not follow the rules of logic may also yield a false conclusion.
The next section, Deduction Extended, adds the hypothetical syllogism as another argument type. Up to this point Gordon discusses arguments of the type known as the categorical syllogism which has two factual premises and a conclusion. A hypothetical syllogism consists of premises that are not factual and yield non factual conclusions. An argument if X then Y does not say X or Y is a fact, only that if X is a fact then Y is a fact. Hypothetical syllogisms can have one or two premises that yield a conclusion.
Deduction Further Extended discusses the nature of certain premises. All premises are meant as facts, but their factual ‘nature’ fall under two different categories. In the first category, a premise is a fact, but does not necessarily have to be a fact. The statement ‘A communist is a two-headed monster’ does not say a communist must be a two headed monster; a communist could be something else.
Under the other category, a premise is necessarily a fact. That is, it cannot be anything else but what it is. The statement ‘No one can be their own father’ is a necessarily true statement. It must be the fact that no one can be their own father. Propositions of this nature are very important in economics.
Furthermore a categorical syllogism containing premises that are not necessarily true can yield a conclusion that it also not necessarily true even though the conclusion must necessarily follow from the premises. (If the premises are true, then the conclusion is true. This is not the same as saying that the conclusion must be true).
On the other hand, it is possible for premises that are not necessarily true to yield conclusions that are necessarily true. For example, some fathers are football players, all football players are males, from which it follows some fathers are males; the conclusion is necessarily true, though the premises are not.
(Note that some logicians argue the following; all X are Y means if X, then Y, which does not mean X exists. At the same time, they maintain that some X is Y means that there is at least one X that is Y, which implies the existence of X. This was discussed in Logic and Scientific Method by Cohen).
A final extension of deduction is that not all deductive arguments are syllogistic. For example, one can deduce all fathead socialists are fatheaded subversives from all socialists are fatheads alone. This inference is especially important in Austrian Economic Theory as several non syllogistic inferences are drawn from the concept of action, which is central to Austrian Theory.
In the final section of economics vs. mathematics, Dr Gordon explains economics, like math, is a deductive science. Yet, he continues, it is unlike math in that one cannot just ‘fill in the blanks’ and operate mechanically. For example, the immediate inference all Russian socialists are Russian subversives does not necessarily follow from all socialists are subversives. The Russian socialists could be Bulgarian subversives; wanting to overthrow the Bulgarian government, but not their own. Immediate inference, then, requires judgment as opposed to simple mechanical operations like 2x=10, x=? in mathematics.
Chapter 1 Questions;
p.4
1. Can something be both red and not red?
No. A thing is either red or it is not. It cannot be both at the same time. If a thing is red, then it is not not-red. If a thing is not-red, then it cannot be red.
2. Some philosophers have denied that these laws are always true. Marxists say, e.g., that everything is constantly changing; therefore, the Law of Identity isn’t true. Why is this objection based on a misunderstanding of the Law of Identity?
Saying that everything is constantly changing and that therefore the Law of Identity (a thing is what it is) is not true is a misunderstanding because the Law does not say anything about change. The Law says a thing is what is, not that a thing cannot be something else at some future point in time. For example, a caterpillar is a caterpillar, and not something else, until it becomes a chrysalis.
Also, what about the Law of Identity as it applies to the word ‘change?’ Change is what it is, it cannot be something else.
Questions p. 8
1. Diagram the argument just given. Show why the conclusion does not follow.
2. Give examples of (a) valid arguments w/ true premises (b) valid arguments w/ at least one false premise (c) invalid arguments with at least one false premise (d) invalid arguments with true premises. Must any of these types always lead to a false conclusion?
a. All dogs are mammals
All mammals are warm-blooded
All dogs are warm blooded
b. All dogs are domesticated mammals
All domesticated mammals are warm-blooded
All dogs are warm blooded
c. Some dogs are trained reptiles
Some trained reptiles are 4-legged
Some dogs are 4-legged
d. Some dogs are trained mammals
Some trained mammals are large
Some dogs are large
As one can see, none of the above arguments leads to a false conclusion, so none of the argument types need lead to a false conclusion. (Valid arguments with true premises always yield a true conclusion. False conclusions derived from valid arguments must have at least one false premise).
Pg 9.
1. Show, using diagrams, that the argument about Mises is valid.
2. Give examples of a valid argument with a false conclusion that has (a) one false premise and one true premise; (b) two false premises
a. All dogs are mammals.
All mammals are cats.
All dogs are cats.
b. All dogs are cats
All cats are fish
All dogs are fish
3. Suppose you have an invalid argument with a false conclusion. What can you tell about the premises?
You cannot tell anything from an invalid argument. The premises may be true or false. A false conclusion implies a false premise only if the argument is valid.
p. 10
1. Give examples of syllogisms with (a) one and (b) two hypothetical syllogisms
a. If money grew on trees then we would encourage CO2 emissions
b. If money grew on trees then we would encourage CO2 emissions
If we would encourage CO2 emissions then Al Gore would have to find a new job
2. Can you convert a hypothetical premise into a categorical one?
(With help from Cohen)
Hypothetical: If A then B
Categorical version of Hypothetical: All A that exist are B
p. 13
1. How can you find out if a statement is necessarily true?
A statement is necessarily true if by denying it you contradict the nature of the meaning of the subject.
2. If a statement is necessarily true, do you need to test it to find out whether it is true?
You do not need to test a necessarily true statement to determine its truth. You can tell if it’s true by deduction.
p. 14
1. How do we know the rules of mathematics are correct?
I answer first by noting that we cannot expect the rules of mathematics to be correct based on experimentation. We expect 2+2=4 all the time, not only under certain conditions, or until some experiment, test or observation proves that 2+2 could equal 5. The rules of mathematics are logically deduced based on propositions that we understand to be self evident.
2. Would it be a good idea to use symbolic logic in economics, if economics relies on immediate inferences?
It is not a good idea to use symbolic logic in economics because of its reliance on immediate inferences. Immediate inference requires evaluating the terms involved in order to determine if the inference is valid.
3. Is it always best to begin by “defining your terms”? Why or why not?
I argue it is always best to begin by defining your terms. The terms you use must be understood clearly in order to ensure your premises, conclusions and arguments are sound.
Note that certain terms must be assumed to be commonly understood; otherwise one would have to define the terms used to define your terms, and so on, ad infinitum.
4. Deduction only tells us what we already “know.” How might a supporter of the deductive approach reply?
Deduction does not tell us what we already know. The application of deduction uncovers the implication and relationship between certain propositions and conclusions. It tells us what must follow if we assume certain things to be true, or false. Though these relationships have always existed, we only come to know them through the application of deductive logic.
"In economics, we operate with deductive logic."
In this first chapter of his book Dr. Gordon explains why deductive logic is a powerful tool, and some of its basic rules.
What makes deductive logic so powerful? Starting from premises one knows to be true, the rules of deductive logic deliver conclusions that must be true.
Dr. Gordon begins with a simple example to illustrate; if all of a class A are part of a class B, and all of a class B are part of a class C, then all of A are part of C.
(It is after this example the reader comes upon the first of Dr. Gordon's 'thought starter's -I'll call them- that are found throughout his book. I appreciate his adding of these questions. They forced me to think more about what I had read. I list these questions at the end of each Chapter and attempt to answer them if Dr. Gordon has not answered them already.)
In the next section he continues the discussion with Aristotle' Laws of Reality (sometimes misnamed the 'Laws of Thought);
Aristotle's Laws of Reality:
1) A=A: The Law of Identity
2) Not (A and not A): The Law of Non-Contradiction
3) A or not A: The Law of Excluded Middle
The first rule, restated, says a thing is what it is. For example; a ball is ball, not something else.
The second rule, restated, says that a thing cannot be a thing and not a thing at the same time. For example, a thing cannot be a ball and not a ball.
The third rule, a bit trickier, says that a thing is either something or not something. For example, a thing is either red or non-red. It cannot be neither, or both.
The next section is on validity. Dr. Gordon now reviews the implications of an argument based on false premises. An argument based on true premises that follows the rules of logic yields a true conclusion every time. What about an argument beginning with false premises? Does it yield a false conclusion if it too, follows the rules? No. It may, but it also may not. Examples are given showing this to be the case.
An argument yields a true conclusion only if its premises are true and it is valid. It is valid if it follows the rules of logic. An argument resting on true premises that does not follow the rules of logic may also yield a false conclusion.
The next section, Deduction Extended, adds the hypothetical syllogism as another argument type. Up to this point Gordon discusses arguments of the type known as the categorical syllogism which has two factual premises and a conclusion. A hypothetical syllogism consists of premises that are not factual and yield non factual conclusions. An argument if X then Y does not say X or Y is a fact, only that if X is a fact then Y is a fact. Hypothetical syllogisms can have one or two premises that yield a conclusion.
Deduction Further Extended discusses the nature of certain premises. All premises are meant as facts, but their factual ‘nature’ fall under two different categories. In the first category, a premise is a fact, but does not necessarily have to be a fact. The statement ‘A communist is a two-headed monster’ does not say a communist must be a two headed monster; a communist could be something else.
Under the other category, a premise is necessarily a fact. That is, it cannot be anything else but what it is. The statement ‘No one can be their own father’ is a necessarily true statement. It must be the fact that no one can be their own father. Propositions of this nature are very important in economics.
Furthermore a categorical syllogism containing premises that are not necessarily true can yield a conclusion that it also not necessarily true even though the conclusion must necessarily follow from the premises. (If the premises are true, then the conclusion is true. This is not the same as saying that the conclusion must be true).
On the other hand, it is possible for premises that are not necessarily true to yield conclusions that are necessarily true. For example, some fathers are football players, all football players are males, from which it follows some fathers are males; the conclusion is necessarily true, though the premises are not.
(Note that some logicians argue the following; all X are Y means if X, then Y, which does not mean X exists. At the same time, they maintain that some X is Y means that there is at least one X that is Y, which implies the existence of X. This was discussed in Logic and Scientific Method by Cohen).
A final extension of deduction is that not all deductive arguments are syllogistic. For example, one can deduce all fathead socialists are fatheaded subversives from all socialists are fatheads alone. This inference is especially important in Austrian Economic Theory as several non syllogistic inferences are drawn from the concept of action, which is central to Austrian Theory.
In the final section of economics vs. mathematics, Dr Gordon explains economics, like math, is a deductive science. Yet, he continues, it is unlike math in that one cannot just ‘fill in the blanks’ and operate mechanically. For example, the immediate inference all Russian socialists are Russian subversives does not necessarily follow from all socialists are subversives. The Russian socialists could be Bulgarian subversives; wanting to overthrow the Bulgarian government, but not their own. Immediate inference, then, requires judgment as opposed to simple mechanical operations like 2x=10, x=? in mathematics.
Chapter 1 Questions;
p.4
1. Can something be both red and not red?
No. A thing is either red or it is not. It cannot be both at the same time. If a thing is red, then it is not not-red. If a thing is not-red, then it cannot be red.
2. Some philosophers have denied that these laws are always true. Marxists say, e.g., that everything is constantly changing; therefore, the Law of Identity isn’t true. Why is this objection based on a misunderstanding of the Law of Identity?
Saying that everything is constantly changing and that therefore the Law of Identity (a thing is what it is) is not true is a misunderstanding because the Law does not say anything about change. The Law says a thing is what is, not that a thing cannot be something else at some future point in time. For example, a caterpillar is a caterpillar, and not something else, until it becomes a chrysalis.
Also, what about the Law of Identity as it applies to the word ‘change?’ Change is what it is, it cannot be something else.
Questions p. 8
1. Diagram the argument just given. Show why the conclusion does not follow.
2. Give examples of (a) valid arguments w/ true premises (b) valid arguments w/ at least one false premise (c) invalid arguments with at least one false premise (d) invalid arguments with true premises. Must any of these types always lead to a false conclusion?
a. All dogs are mammals
All mammals are warm-blooded
All dogs are warm blooded
b. All dogs are domesticated mammals
All domesticated mammals are warm-blooded
All dogs are warm blooded
c. Some dogs are trained reptiles
Some trained reptiles are 4-legged
Some dogs are 4-legged
d. Some dogs are trained mammals
Some trained mammals are large
Some dogs are large
As one can see, none of the above arguments leads to a false conclusion, so none of the argument types need lead to a false conclusion. (Valid arguments with true premises always yield a true conclusion. False conclusions derived from valid arguments must have at least one false premise).
Pg 9.
1. Show, using diagrams, that the argument about Mises is valid.
2. Give examples of a valid argument with a false conclusion that has (a) one false premise and one true premise; (b) two false premises
a. All dogs are mammals.
All mammals are cats.
All dogs are cats.
b. All dogs are cats
All cats are fish
All dogs are fish
3. Suppose you have an invalid argument with a false conclusion. What can you tell about the premises?
You cannot tell anything from an invalid argument. The premises may be true or false. A false conclusion implies a false premise only if the argument is valid.
p. 10
1. Give examples of syllogisms with (a) one and (b) two hypothetical syllogisms
a. If money grew on trees then we would encourage CO2 emissions
b. If money grew on trees then we would encourage CO2 emissions
If we would encourage CO2 emissions then Al Gore would have to find a new job
2. Can you convert a hypothetical premise into a categorical one?
(With help from Cohen)
Hypothetical: If A then B
Categorical version of Hypothetical: All A that exist are B
p. 13
1. How can you find out if a statement is necessarily true?
A statement is necessarily true if by denying it you contradict the nature of the meaning of the subject.
2. If a statement is necessarily true, do you need to test it to find out whether it is true?
You do not need to test a necessarily true statement to determine its truth. You can tell if it’s true by deduction.
p. 14
1. How do we know the rules of mathematics are correct?
I answer first by noting that we cannot expect the rules of mathematics to be correct based on experimentation. We expect 2+2=4 all the time, not only under certain conditions, or until some experiment, test or observation proves that 2+2 could equal 5. The rules of mathematics are logically deduced based on propositions that we understand to be self evident.
2. Would it be a good idea to use symbolic logic in economics, if economics relies on immediate inferences?
It is not a good idea to use symbolic logic in economics because of its reliance on immediate inferences. Immediate inference requires evaluating the terms involved in order to determine if the inference is valid.
3. Is it always best to begin by “defining your terms”? Why or why not?
I argue it is always best to begin by defining your terms. The terms you use must be understood clearly in order to ensure your premises, conclusions and arguments are sound.
Note that certain terms must be assumed to be commonly understood; otherwise one would have to define the terms used to define your terms, and so on, ad infinitum.
4. Deduction only tells us what we already “know.” How might a supporter of the deductive approach reply?
Deduction does not tell us what we already know. The application of deduction uncovers the implication and relationship between certain propositions and conclusions. It tells us what must follow if we assume certain things to be true, or false. Though these relationships have always existed, we only come to know them through the application of deductive logic.
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