Econ 210, Final, Fall 2015.

Transcription

1 Econ 210, Final, Fall Prof. Guse, W & L University Instructions. You have 3 hours to complete the exam. You will answer questions worth a total of 90 points. Please write all of your responses on the exam itself in the space provided. If you need additional space, there is a blank sheet included at the end. You may refer only to your own handwritten, cheat sheet. Calculators and all other references materials are not allowed. If a question asks for a numeric quantity you may leave your answer in expression form for full credit. (For example, would be perfectly acceptable in place of 2.) Be sure to label any diagrams you draw, to show your work and to explain your reasoning. Finally, take note that questions are printed on BOTH sides of each page. You may keep your cheat sheet. Thank you and good luck! Name: Pledge: 1

2 PLEASE DO NOT WRITE ON THIS PAGE. 2

3 1. (9 Points) Consider the insurance problem we discussed in class. maxπ b v(ω b +(1 γ)k)+(1 π b )v(ω g γk) k where k is the amount of insurance, γ is the price of the insurance per dollar of bad-state payout, ω b andω b aretheendowmentsinthegoodandbadstate, π b isprobabilitythatthebad state will occur and v is the Bernoulli utility in the consumer s Von-Neumann Morgenstern expected utility function. In the context of this problem... (a) (3 points) Define fair (a.k.a. actuarially fair) insurance (b) (3 points) Define what it would mean to be fully insured. (i.e. how much insurance is that?) (c) (3 points) State (but don t prove) the full insurance principle. 2. (3 Points) The payoffs to the row and column players in the game Battle of the Sexes are shown below. For example, when both players choose O, the row player receives 1 and the column player receives 2. Identify all of the pure strategy Nash equilibria in this game, if any exist. O F O 1,2 0,0 F 0,0 2,1 3

4 3. (3 Points) In general, when there is perfect certainty about demand for pollution, regulating that pollutant with either a tax or a system of tradable permits have roughly equivalent efficiency properties. However, as shown by Martin Weitzman, if there is uncertainty about demand, then a tax will be more efficient than tradable permits when (a) the marginal damage curve is relatively flat. (b) the marginal damage curve is relatively steep. (c) the total damage to human health caused by the pollution is large. (d) the total damage to human health caused by the pollution is small. (e) monitoring costs are large. (f) monitoring costs are small. 4. (3 Points) Circle all that apply. For a price change, the Slutsky-compensated budget line always (a) goes through the endowment and is parallel to the horizontal axis (b) goes through the endowment and is parallel to the old budget line (c) goes through the endowment and is parallel to the new budget line (d) goes through the original choice and is parallel to the horizontal axis (e) goes through the original choice and is parallel to the old budget line (f) goes through the original choice and is parallel to the new budget line. (g) intersects the wage-compensated supply curve 5. (6 Points) In the Spence model the we covered in class, e*(h) and e*(l) represent the efficient levels of education for the high and low types while w*(h)=y(h, e*(h)) and w*(l)=y(l, e*(l)) represent the competitive wages paid to each type in the case of perfect information ( equal to the respective types productive outputs evaluated at their efficient education levels). Meanwhile c(l,e) and c(h,e) are functions that describe the cost experienced by each type of worker of obtaining education level e. Using these definitions, write down an inequality that defines the envy case. 4

5 6. (6 Points) V is Alice s maximum willingness to pay for the object being sold in a second price auction. Let Z be the highest bid among all bidders who are not Alice. Consider a strategy for Alice of submitting a bid B < V. Explain why this isn t a good idea compared to bidding V. (Hint. You should layout and briefly analyze 3 cases) 7. (9 Points) The following bids represent net willingness to pay for a public good in a Groves- Clarke mechanism where the question is should the project be built or not. Bidder Net WTP Bids A -20 B -10 C 15 D 35 (a) (3 Points) Will the project go through? (b) (3 Points) Which bidder or bidders, if anyone, owe a Clarke Tax? (c) (3 Points) For each bidder that owes a non-zero Clarke tax, how much do they owe? 5

6 8. (15 Points) First-price sealed bid auction. Assume there are 2 bidders. Each bidder i has a true value (maximum willingness to pay), v i distributed uniformly on [0,1]. Each bidder knows her own value but does not know the values of the other bidders in the game. Show that there is an equilibrium in linear strategies. In other words, if player 2 employs a strategy with the form b 2 (v 2 ) = a 2 v 2, derive player 1 s best response and show that it also has the linear form. 6

7 9. (15 Points) Madison Cheese makes cheddar out of labor (l) and capital (k). The following production function represents their technology ( f(x l,x k ) = 3log min{x l, x ) k 3 }+1 Let w l and w k be the constant prices of labor and capital face by this firm. Derive the factor demands for labor and capital. 7

8 10. (21 Points) Consider a system of income taxation and support in which every adult receives gauranteed income of G each week and pays proportion t (0,1) of all of their earnings in taxes. Suppose that every adult i has preferences for consumption (c) and leisure (l) described by the following utility function u i (x l,x c ) = x α i l x 1 α i c Note that each individual i has its own α, though you should assume that every α i (0,1). Also each individual has access to a job that pays wage w i > 0 per hour. Also assume that a worker can choose to work any amount of hours in a week between 0 and 100. (Equivalently, they can choose the quantity of leisure, x l, to be any number between 0 and 100). Hence, to be clear, the total consumption of individual i under this system would be x c = G+w i (1 t)(100 x l ) (a) (20 Points) Using the methods we learned in class, derive an expression involving α i, t and w i that represents the threshhold level of G above which worker i would prefer to stay home and not work at all. Diagrams may be helpful. (b) (1 Point - Almost purely for the fun of it bonus question) Suppose that the joint density of α and w in the population is given by f(α,w). Write down an expression for the labor force participation rate involving f, G and t. Interpret your expression. 8

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