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Final

# 2012-1 Final Solutions.pdf

3 Pages
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School
Simon Fraser University
Department
Economics
Course
ECON 302
Professor
Luba Patterson
Semester
Winter

Description
2012-1 Final Solutions A1. 4, 5. Type A values each of the first 4 units at more than the cost, so they should consume at least 4. After that, the benefit is nil, while the cost is positive, so the quantity should be exactly 4. Similarly, type B’s quantity should be exactly 5. A2. In the first best, the monopoly chooses the efficient allocation to maximize the surplus because it can take all the surplus. Thus it makes 4*(4-1) = 12 from type A and 5*(5-1) = 20 from type B. A3. subject to IR means “individual rationality”, and IC means “incentive compatibility.” A4. Because , and together imply , which can be eliminated. This means that must be binding, because otherwise the firm can raise . Therefore, , which implies as long as because increases with . This in turn implies that must bind because otherwise the firm can raise . A5. The firm’s maximization problem becomes: or subject to . By inspection (or economic intuition), the firm must pick and , so the problem becomes: , or , subject to , , and . It’s easy to see that must be as high as possible, so . The same goes for when is positive, so when . Otherwise, must be as low as possible, so when . (If , the firm is indifferent between all from 0 to 4.) Thus when , and . From , we get , and then from , we get . When , and . Then , and from , we get . A6. In the model from class, the low type’s second-best quantity is always lower than its first- best quantity. That is not the case here when . The reason is that the marginal value of the good is not continuous (it drops from 4 to 0), so it is not equal to the marginal cost (1) at the first-best quantity. This means that when the firm decreases from 4, the loss in profit is first-order rather than second-order. Thus, when there are enough customers of type A, the firm is unwilling to do so. A7. Type A always gets 0 surplus ( always binds), so it has no reason to perform the task. Type B would like to pool with type A, because if the fraction of type A in the pool is above ¼, type B gets positive surplus. Since type A never performs the task, type B also won’t – if it does, it would incur a cost and not gain any surplus. Thus the only equilibrium is a pooling equilibrium where no one performs the task. Obviously, k>c or c>k doesn’t matter! B1. . Certainty equivalent is 2 \$11.4 , or \$129.96. Thus you need to offer your friend at least \$29.96. B2. In the first best, Dean is employed (his value to the firm is \$200,000 and he only costs \$19,600), but exerts no effort (effort is useless, but the firm would have to pay him more if it requires effort). The first best is achievable: the firm pays Dean a fixed \$19,600. B3. The efficient allocation is for all the good cars to go to the buyers, and for all the bad cars to stay with the sellers. This can never happen regardless of p: the price must be above \$6,000 for the good cars to sell, but then the owners of bad cars would sell as well. B4. FALSE (or UNCERTAIN): While it’s true that the appropriate size of a carbon tax is hard to determine, if the right size were known, then the efficient allocation of emissions will be achieved. With regulation, even if the r
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