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Unformatted text preview: Intermediate Microeconomics, Winter 2008 Problem Set No 21 Solutions Q1. Taxes . What is the problem of taxation? Suppose a government wants to provide defense to its citizens and needs to raise a fixed amount of money by taxing labor. Consider the World of Truth: If the government could perfectly observe everything (preferences, amount of labor provided), argue that the gov- ernment might be able to raise taxes without inducing distortions. Why does this change if preferences are not observable? Can you compare the problem of finding the right tax to the problem of a monopolist finding the right price? Taxing any activity that a person undertakes creates a distortion. For ex- ample, if we impose an income tax, people have more incentives to stay at home and consume leisure. To raise revenue in the least distortionary way possible, we would like to create tax liabilities that are customized for each individuals preferences. We can do this if we know everything about every individual. If the government could base tax liabilities on a persons valuation of a public good or other immutable attributes rather than their activities, then taxes may not be distortionary at all. This is akin to a monopolist extracting surplus from dif- ferent types of consumers - every consumer gets her own price custom designed for her preferences. The problem comes in when we do not observe peoples types. In the mo- nopolists case, in order to provide incentives to high types to buy the expensive product, we lose potential surplus that we could have collected. The same thing applies to taxes. If we want to collect the most taxes from those whose behavior is distorted least by the tax, we have to give them incentives (i.e. lower their taxes or increase the taxes of others) to act in the way we need them to act. Q2. Adverse Selection . Reconsider the used car example from the lecture. The probability of the used car having low quality is L . a) Can you find the optimal price offer by the buyer as a function of L ? Recall that the buyer has to consider only two prices, c H and c L . So, you will have to calculate for which value of L the buyer wants to make an offer that the car seller always accepts ( p = c H ) and for which value of L the buyer wants to make an offer such that the seller accepts only of he has a low valuation for the car ( p = c L ). From lecture, c L = 8 , c H = 16 , v h = 20 , and v L = 10 . If the probability of low quality is L , the buyer will offer the price p = 16 if and only if Expected utility if offer p=16 Expected utility if offer p=8 L * (10) + (1- L ) * (20)- 16 L * (10- 8) 4 12 L 1 3 L 1 So if 1 3 or fewer cars are low quality, then the buyer will offer p = 16 . Note that we are implicitly assuming that the buyer is risk neutral in this model....
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This note was uploaded on 12/10/2011 for the course ECON 401 taught by Professor Burbidge,john during the Winter '08 term at Waterloo.
- Winter '08