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Date Created: 11/02/15
Comprehensive Examination ADVANCED MICRO THEORY 201n3e Ame Urciversity Department of Economics Page 1 of 4 General Instructions: This examination has two Sections, (Microecono mic Analysis II and Micro Political Economy). You must answer both sections; be sure to follow the directions in each part carefully. Each part receives equal weight in the overall grading. Therefore, you should plan to spend an equal amount of time (i.e., about 2 hours) on each s ection, Microeconomic Analysis II and Micro Political Economy, regardless of the number of questions in each. Please make sure that all math is intuitively explained, all diagrams are clearl y labeled, and all answers are responsive to the speciﬁc questions asked. The time limits should sugge st the expected length and depth of your answers. The standard for passing this exam is demonstration of “mastery” of the material. MICRO POLITICAL ECONOMY SECTION (2 hours total) This section has two parts A and B; you must answer both parts and there is some choice in each part. Pay careful attention to the time limits! Part A - Essay Questions – Answer one (1) of the following. (One hour) 1. Bowles offers a theory of class. a. According to this theory, what fundamental economic problem results in the emergence of classes? (note: It is not the distribution of resources, which is the result in this model.) b. What might have determined who ended up in which class position as exchange expanded? c. Outline (mainly in words) Bowles’ explanation of how what happens in credit markets prevents movement by individuals across classes (economic mobility) over time, carefully explaining why the outcomes represent rational decisions by each actor. d. Explain the link between income distribution and efficiency in this theory. 2. Drawing on Bowles, Knight, and Greif, carefully explain a “Bowlesian” theory of underdevelopment and offer relevant examples to support the theory. Part B - Long Answers. Answer one (1) of the following. (One hour) 1. A worker in a capitalist firm has a utility function U = U(w,e), so that expected utility is Page 2 of 4 V = U(w,e) + f(e)V + (1f(e)) Z 1 + i where w = wage rate e = effort per hour by the worker f = probability of retaining one’s job, i.e. the level of supervision in the firm I = interest rate Z = worker’s fall back position, i.e. what s/he would earn if fired a. If we let p = 1, the firm has the production function Q = Q(he), where h = hours hired. Assume the firm maximizes profit and that f is costless to the firm. Use the firm’s first order conditions to calculate h*, w* and e*. Explain the FOCs. b. Explain how w* differs from the standard neoclassical wage. What assumptions of political economists produce the differences in outcomes? What are the economic implications of the differences in outcomes? c. Explain the worker’s optimal level of effort, e*. d. If the wage remained unchanged, show how would e* change if (i) there was an increase in the effectiveness of supervision in the firm? (ii) there was an increase in unemploy- ment benefits? e. Returning now to the original version of the problem (prior to the changes in d.), how does the optimization problem for the workers and the firm change if the firm is a worker-owned firm (cooperative)? What change do we expect in e* and w*? Why? f. Might the technology chosen by the firm change? Explain. 2. Consider a production function Q = qE, a utility function U = C – E (there are only variable inputs of labor effort, E, and the producer consumes the good she produces in amount C) and an economy composed of 3 individuals with the above functions. Two are tenants and the other their landlord, whose income is his own production (governed by the above production function) plus a share, α, of the two tenants’ crops. For each of the tenants, C = (1–α)Q. Let q = 1. a. What is the landlord’s optimal effort level (farming his own land)? b. Assuming that the landlord has the power to determine α, what value would she select? (Give both FOCs and a numerical value.) c. Indicate the levels of utility achieved by all three individuals. d. Since none of the tenants can obtain capital to buy land from the landlord, protests ensue, as a result of which there is a land redistribution (costless!), in which everyone gets one acre of the landlord’s 3 acres, including the former landlord. As a result, how much does each farmer work and what is their level of utility? (Micro Part B continues on the next page) Page 3 of 4 e. Carefully explain this result and its relevance to the Second Fundamental Theorem of Welfare Economics. f. What changes in production technology might you predict would occur as a result of the redistribution? Carefully explain. MICROECONOMIC ANALYSIS II SECTION (2 hours total) This section has two parts, A and B. You must answer both pa rts, and there is some choice in each section. Part A. DO TWO (2) SHORT ANSWER QUESTIONS. All short-answer questions are equally weighted. (Time allotted: 30 minutes each.) 1. Three roommates come across a couch that someone had left near their apartment. They must collectively determine whether or not to take the couch. Suppose a roommate suggests that they simply take a vote of yes or no and base their group couch decision on majority vote. Is this voting rule strategy proof (i.e. does any roommate have any incentive to lie?)? Give an example of a set of values, ▯ ,▯ , and ▯ , the roommates’ ▯ ▯ ▯ respective utilities or disutilities for having the couch, such that where a majority vote rule would lead to a pareto dominated outcome. Identify a strategy proof alternative rule for which the Nash Equilibria under all possible value combinations will lead to pareto optimal payoffs. 2. Recall that the ultimatum game is a two player game where first player 1 makes an offer of ▯▯▯0,▯▯ to player 2. Then next player 2 can choose to either accept or reject player 1’s offer. If player 2 accepts the offer, player 1 receives a payoff of ▯▯▯ and player 2 receives a payoff x. If player 2 rejects the offer, then both players receive 0. What is the Subgame Perfect Nash Equilibrium for this game? When this ultimatum game is conducted in an experimental lab setting, what differences (if any) in behavior would you expect? Please construct a normative utility function for player 2 and an alternative behavioral utility function for player 2. 3. Suppose a theatre seats no more than K people, but there are N > K people interested in watching a movie for a particular showing. Let ▯ ▯▯ ▯▯ ▯▯▯▯ represent the ▯ ▯ ▯ ▯ values of watching the movie for each movie goer. The theatre’s management decides who gets to actually watch the movie by queuing people in the order that they arrive. How would you describe this scenario in terms of an auction? What is the utility function of a potential movie watcher? Assuming that it is costless to examine the line and leave but costly to wait in line to actually watch the movie (i.e. a potential movie goer will not Page 4 of 4 waste time queuing if he/she cannot gain admission to the movie), describe all Nash Equilibria for this game. Part B. DO ONE (1) LONG ANSWER QUESTION. (Time allotted: 1 hour.) 1. Describe Arrow’s Impossibility Theorem or the Gibbard-Satterthwaite Theorem. What are the implications for all social choice functions? How would you apply these theorems (if it all) to real world voting rule construction? For each of a) Plurality, b) Borda , and c) Range Voting - i) describe the voting rule, ii) provide a real world example of where the rule is used, iii) describe preference expression benefits and concerns, and iv) voter strategic implications . Finally using an additional voting rule or using one of the three aforementioned rules, suggest a new real world application for that voting rule and why it would be beneficial as compared to the alternative (under the current system). 2. Suppose that a single seller is selling a single unit of a good to two buyers. There is incomplete information in that the seller and the buyers are not aware of the of the other players’ values. Let the seller’s reservation value be 0. Assume that each buyer’s values are drawn from a random uniform distribution, ▯~▯▯0,▯▯. a. If the seller decides to auction the good via a first price auction, what is his expected profit? [Make sure to show your work]. HINT: first find each buyer’s expected profit maximizing bid as a function of her value and then sum over all the value states. b. If the seller decides to auction the good via a second price auction, what is his expected profit? c. If the seller decides to auction the good via an all pay auction, what is his expected profit? d. Based on these results which auction should the seller choose? If there were more buyers, would this answer change? What would you choose if you were the seller in a real world setting and why?
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