c 2009 Je rey A. Miron

Transcription

1 Lecture : Euilibrium c Je rey A. Miron Outline. Introduction. upply. Market Euilibrium. pecial Cases. Inverse emand and upply Curves. Comparative tatics. Taxes. The Incidence of a Tax. The eadweight Loss from Taxation. Pareto E ciency Introduction o far, we have constructed individual demand curves by using information about preferences, prices, and income. We have also seen that we can add up these individual demand curves to get market demand curves In this lecture, we use the market demand curves to determine the euilibrium market price. This will involve two core principles of economics: optimization and euilibrium. Until now, we have only focused on optimization; we will apply this principle again when we examine rms. Before moving on to that, however, it is useful to consider some aspects of euilibrium analysis. To do so, we need to look brie y at supply.

2 upply We have already seen examples of supply, such as consumers being net suppliers of the goods they own. We have also seen labor supply decisions. In these examples, the supply curve measures how much the consumer is willing to supply of a certain good at each possible market price. This is in fact the de nition of supply: for each p, we determine how much of the good will be supplied, (p). We derive this formally later. For now we accept this intuitive de nition to develop other insights. Market Euilibrium uppose we have a number of consumers of a good. We can obtain a market demand curve by adding up their individual demand curves. Likewise, if we have a number of suppliers, we can obtain the market supply curve by adding up their individual supply curves. For now we assume all individual suppliers and demanders take prices as given and determine their best response given those market prices. This is known as a competitive market. No individual agent can determine the market price; rather, the actions of all agents together determine the market price. The euilibrium price is the price such that the supply of goods euals the demand. Geometrically this is where the demand and supply curves cross. To state this more explicitly, let (p) be the market demand curve and (p) be the market supply curve. Then the euilibrium price solves (p ) = (p ) Why is this an euilibrium? An euilibrium is a situation where all agents are doing the best they can and every agent s actions are consistent with

3 everyone else s actions. The price that solves the euation above satis es these conditions. At any other price, by contrast, someone would have an incentive to change behavior. If, for example, the price were greater than the euilibrium price, the uantity demanded would be less than the uantity supplied. The sellers would therefore have unsold inventories and want to cut back on production. pecial Cases Two special cases of market demand and supply curves deserve mention because they arise freuently and are also useful for understanding more general cases. The rst special case is where supply is perfectly inelastic (totally unresponsive to price). In that case the supply curve is vertical, as in the graph below, and changes in demand only a ect price, not uantity:

4 Graph: Perfectly Inelastic upply p p* * The second special case is where supply is perfectly elastic (in nitely responsive to price). In that case the supply curve is horizontal, as in the graph below, and changes in demand only a ect uantity, not price:

5 Graph: Perfectly Elastic upply p p* * Note that we could also consider perfectly inelastic or perfectly elastic demand curves. Inverse emand and upply Curves As discussed earlier in the context of an individual demand curve, we normally think of these as telling us the uantity demanded at a given price. In many instances, however, it is more convenient to consider the inverse individual demand curve as telling us the price at which the consumer will demand a given uantity. We can readily extend the concept of an inverse demand curve to a market demand curve: it tells us the price at which the overall market will demand a given uantity of a good. These same concepts can be applied to supply curves. An individual inverse supply curve tells us the price at which an individual supplier will

6 supply a given number of units of a good. A market inverse supply curve tells us the price at which the overall market will supply a given number of units of a good. Consider the following linear example, which appears freuently throughout the rest of the course. Assume (p) = a bp (p) = c + dp where (p) tells us the number of units demanded by the market at price p and (p) tells us the number of units supplied by the market at price p. The coe cients a, b, c, and d are parameters. The euilibrium price is the one that euates the uantity demanded and the uantity supplied: (p) = a bp = c + dp = (p) and the solution is p = a c d + b ubstituting this back into the demand or supply curve then yields the euilibrium uantity: = ad + bc b + d We could instead have solved this using the inverse demand and supply curves. To get these, write = a bp = c + dp and solve these for p to get P (p) = (a=b) (=b)

7 P (p) = (c=d) + (=d) We then set the two euations for price eual and solve for. This expression for can then be inserted in either the inverse demand curve or the inverse supply curve to get a solution for p. The two solutions are the same as those derived above using demand and supply curves themselves. Comparative tatics The key thing we want to do with the supply-demand framework is derive comparative static results. This means we consider the e ect of a change in something other than price or uantity (e.g., consumer income or input prices or taxes or other policies) and then determine how euilibrium price and uantity change as the result of a change in the exogenous factor. For example, consider the e ect of drug prohibition on the euilibrium price and uantity of drugs. Prohibition imposes penalties on consumers for purchasing drugs (arrest, incarceration, nes), so this should shift the demand curve inward. Prohibition also imposes costs on suppliers (paying bribes, transporting goods in secret), and this shifts the supply curve up. This means that drug prohibition should reduce the euilibrium uantity consumed relative to a legal market and have an ambiguous e ect on price, as illustrated below:

8 Graph: hifting upply and emand Curves p ' p* ' ' * Taxes A key comparative static of interest is the e ect of a tax on the euilibrium price and uantity of the taxed good. We can think about imposing and collecting this tax in two ways. The rst imposes this tax on consumers, which means that everyone who buys the good pays t dollars in addition to the price (the seller collects this tax and passes it along to the government). The e ect of imposing the tax in this way is to shift the demand curve down by exactly t. The explanation is that if consumers demand units of the good at a price of p, they should demand exactly the same number of units at a price of p t, since once the tax is added in the e ective price is till p. We can illustrate this as follows:

9 Graph: Imposition of a Tax on Purchases of a Good p() p d p* p s ' * An alternative approach is to impose the tax on sellers of the good. This means that every time a seller sells a unit at price p, the seller must send t dollars to the government. This means the supply curve must shift up by exactly p, since if sellers were originally willing to sell units at price p, they should now be willing to sell units at a price of p + t (they net exactly p after sending t to the government). We can illustrate this as follows:

10 Graph: Imposition of a Tax on the ellers of a Good p() p s p d p* ' * Geometry tells us that these two approaches must yield the same result for the euilibrium price and uantity under the tax. We can also see this another way. We know that in euilibrium the price paid by the demander and the price received by the seller must di er by exactly t, and the uantity demanded must eual the uantity supplied. We can nd this point by inserting a line segment of length t in the diagram as shown below:

11 Graph: The Impact of a Tax p p d p s p d p s = amount of tax * Thus, we do not need to say anything about whether buyers or sellers pay the tax. Indeed, a crucial point is that the side of the market that pays the tax need bear no relation to the side of the market that bears the true economic burden of the tax. The Incidence of a Tax A crucial uestion for economic policy is determining who bears the burden of a particular tax. The naive, non-economist view is that the person who pays out the cash for the tax bears the burden of the tax, but this is incorrect. As we have already seen, we get the same prices for demanders and suppliers net of tax whether we impose the tax on the purchasers or sellers. Thus, the true burden, or incidence, must depend on something else. This something else is the elasticity of supply and demand. The side of the market whose behavior is least responsive to price bears the greater

12 burden of the tax. cases. To see this, it is useful to consider rst the extreme Consider the case of perfectly elastic supply:

13 Graph: The Incidence of Taxation with Perfectly Elastic upply p() p*+t p* t = vertical distance between and ' ' If supply is perfectly elastic, the imposition of a tax raises the cost per unit by t, and this shifts up the supply curve by exactly t. The price rises by the full amount of the tax, so purchasers bear the entire burden. Now, consider the extreme alternative, perfectly inelastic supply:

14 Graph: Incidence of Taxation with Inelastic upply p() t = vertical distance between p* and p* t p* p* t If supply is perfectly inelastic, the imposition of tax has no e ect on the supply curve, so suppliers bear the entire burden of the tax. If the supply curve is not perfectly elastic or perfectly inelastic, these extreme results do not hold, but the general pattern is similar:

15 Graph: Incidence of Taxation with Elastic upply p() p' p* t = vertical distance between and ' ' Graph: Incidence of Taxation with Elastic upply p() p' p* ' t = vertical distance between and '

16 In the top graph, supply is almost perfectly elastic, and purchasers bear most of the burden; in the bottom graph, supply is almost perfectly inelastic, and sellers bear most of the burden. We can conduct the analogous analysis for elastic versus inelastic demand curves (do this for yourself as an exercise). If demand is inelastic, then purchasers bear much of the burden of the tax. If demand is elastic, then suppliers bear much of the burden of the tax. Remember that none of these results about incidence depends on whether we tax demanders or suppliers; the incidence depends only on which side of the market s behavior is relatively elastic. In the general case, both demanders and suppliers bear some burden; but the side whose behavior is least responsive bears the greater share of the burden. This makes intuitive sense; the side of the market that can most easily adjust its behavior in response to a tax will bear the lowest costs of that tax. The eadweight Loss of a Tax The last issue about taxation that we address is the welfare impact. The diagram below shows the e ect of a tax on consumer and producer surplus:

17 Graph: eadweight Loss from Taxation p p d p s A C B p d p s = amount of tax B+ = deadweight loss * Before imposition of the tax, consumer surplus was the area below the demand curve but above price, while producer surplus was the area above the supply curve but below price. After imposition of the tax, consumer surplus shrinks to the smaller triangle above p d and below the demand curve (remember that purchasers pay the price inclusive of the tax, p d ). Also, producer surplus shrinks to the area above the supply curve and below p s (remember that suppliers collect p d from purchasers but only get to keep this amount minus the tax, t; they send the amount t per unit to the government). The area A + C corresponds to the tax revenue collected and sent to the government. This amount is not a loss; someone still gets to consume it. The loss caused by the tax is the triangle corresponding to B +. This is lost consumer plus producer surplus. Over this range, consumers exist who are willing to pay more for the good than it costs to produce it. If

18 these consumers and suppliers could trade without having to pay the tax, both groups would be better o. This loss is known as the deadweight loss from taxation. It is also known as a Harberger triangle, after a famous University of Chicago economist. Pareto E ciency An economic situation is Pareto e cient if there is no way to make any person better o without hurting somebody else. The competitive euilibria that we have been examining are Pareto e - cient, as illustrated below:

19 Graph: The Pareto E ciency of Competition p() p d p d=p s p s willing to buy at price p d willing to sell at price p s * At any output level below the euilibrium level, consumers exist whose willingness to pay exceeds the costs of production, so this is not a pareto e cient allocation. At the euilibrium, however, such a combination of consumers and suppliers no longer exists.