5. True or false? In a two good model if one good is an inferior good the other good must be a luxury good.
15.5. True. The weighted average of the income elasticities must be 1, so if one good has a negative income elasticity, the other good must have an elasticity greater than 1 to get the average to be 1.
16 Equilibrium
1. What is the e?ect of a subsidy in a market with a horizontal supply curve? With a vertical supply curve?
16.1. The entire subsidy gets passed along to the consumers if the supply curve is ?at, but the subsidy is totally received by the producers when the supply curve is vertical.
2. Suppose that the demand curve is vertical while the supply curve slopes upward. If a tax is imposed in this market who ends up paying it?
16.2. The consumer.
3. Suppose that all consumers view red pencils and blue pencils as perfect substitutes. Suppose that the supply curve for red pencils is upward sloping. Let the price of red pencils and blue pencils be ???? and ????. What would happen if the government put a tax only on red pencils? 16.3. In this case the demand curve for red pencils is horizontal at the
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price ????, since that is the most that they would be willing to pay for a red pencil. Thus, if a tax is imposed on red pencils, consumers will end up paying ???? for them, so the entire amount of the tax will end up being borne by the producers (if any red pencils are sold at all—it could be that the tax would induce the producer to get out of the red pencil business).
4. The United States imports about half of its petroleum needs. Suppose that the rest of the oil producers are willing to supply as much oil as the United States wants at a constant price of $25 a barrel. What would happen to the price of domestic oil if a tax of $5 a barrel were placed on foreign oil?
16.4. Here the supply curve of foreign oil is ?at at $25. Thus the price to the consumers must rise by the $5 amount of the tax, so that the net price to the consumers becomes $30. Since foreign oil and domestic oil are perfect substitutes as far as the consumers are concerned, the domestic producers will sell their oil for $30 as well and get a windfall gain of $5 per barrel.
5. Suppose that the supply curve is vertical. What is the deadweight loss of a tax in this market?
16.5. Zero. The deadweight loss measures the value of lost output. Since the same amount is supplied before and after the tax, there is no
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deadweight loss. Put another way: the suppliers are paying the entire amount of the tax, and everything they pay goes to the government. The amount that the suppliers would pay to avoid the tax is simply the tax revenue the government receives, so there is no excess burden of the tax.
6. Consider the tax treatment of borrowing and lending described in the text. How much revenue does this tax system raise if borrowers and lenders are in the same tax bracket? 16.6. Zero revenue.
7. Does such a tax system raise a positive or negative amount of revenue when ????
16.7. It raises negative revenue, since in this case we have a net subsidy of borrowing.
17 Auctions
1. Consider an auction of antique quilts to collectors. Is this a private-value or a common-value auction?
17.1. Since the collectors likely have their own values for the quilts, and don’t particularly care about the other bidders’ values, it is a private-value auction.
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2. Suppose that there are only two bidders with values of $8 and $10 for an item with a bid increment of $1. What should the reservation price be in a pro?t-maximizing English auction?
17.2. Following the analysis in the text, there are four equally likely con?gurations of bidders: (8,8), (8,10), (10,8), and (10,10). With zero reservation price, the optimal bids will be (8,9,9,10), resulting in expected pro?t of $9. The only candidate for a reservation price is $10, which yields expected pro?t of 30/4 = $7 .50. Hence zero is a pro?t-maximizing reservation price in this auction.
3. Suppose that we have two copies of Intermediate Microeconomics to sell to three (enthusiastic) students. How can we use a sealed-bid auction that will guarantee that the bidders with the two highest values get the books?
17.3. Have each person write down a value, then award the two books to the students with the two highest values, but just charge them the bid of the third highest student.
4. Consider the Ucom example in the text. Was the auction design e?cient? Did it maximize pro?ts?
17.4. It was e?cient in the sense that it awarded the license to the ?rm that valued it most highly. But it took a year for this to happen, which is
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ine?cient. A Vickrey auction or an English auction would have achieved the same result more quickly.
5. A game theorist ?lls a jar with pennies and auctions it o? on the ?rst day of class using an English auction. Is this a private-value or a common-value auction? Do you think the winning bidder usually makes a pro?t?
17.5. This is a common-value auction since the value of the prize is the same to all bidders. Normally, the winning bidder overestimates the number of pennies in the jar, illustrating the winner’s curse.
18 Technology
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1. Consider the production function f(x1, ????)= x1 x2. Does this exhibit
constant, increasing, or decreasing returns to scale? 18.1. Increasing returns to scale.
2. Consider the production function f(x1,x2)=4 ???? ????. Does this exhibit constant, increasing, or decreasing returns to scale? 18.2. Decreasing returns to scale.
????3. The Cobb-Douglas production function is given by f(x1,x2)=A???? ????.
??/??
??/??
It turns out that the type of returns to scale of this function will depend on the magnitude of a + b. Which values of a + b will be associated with
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