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(i) According to the Ramsey model, what is the impact of a "fiscal stimulus" on investment, consumption and output if the stimulus is financed with lump-sum taxes? What if it is financed with a tax on capital income? (ii) Chinese households have been enjoying very fast growth in their incomea trend that is expected to continue for a while. According to consumption smoothing, would you expect China to run current-account deficits, or current-account surpluses? (iii) Describe what conditional convergence means in the data? Can both the Solow and Ramsey models help us explain this feature of the data? u (c) = c c2 save more as his future income becomes more uncertain? Question 2 (40% of the grade; you should allocate about 30min.) Consider the Ramsey model (where savings is endogenous). For simplicity, suppose there is neither any technological change nor any population growth. However, there is a government that might subsidy savings. Let R denote the subsidy. Suppose now that the government decides to subsidizes savings, going from a zero subsidy low = 0 to a positive subsidy high > 0. This change is unanticipated but, once it occurs, it is expected to last for ever. Suppose further that before this change the economy was resting at the steady state corresponding to zero subsidy. (i) What is the long-run impact of this change on the steady-state levels of per-hear capital (k), output (y), and consumption (c) are affected by this change?

The US Congress periodically experiments with schemes designed to reduce child care costs for working parents, especially those with low earnings. 1. Compare and contrast the labor supply implications of the following programs: (i) A "child allowance," i.e., an annual lump-sum tax credit for anyone with children (ii) A "child allowance" for working women with incomes below the poverty line. The credit phases out at higher incomes. (iii) Subsidized daycare-center-provided care for the children of working women (iv) Subsidized daycare-center-provided care for all children Use the model of home production outlined in class, where child care can be purchased or produced at home. Analyze the labor supply consequences of each scheme with a graph. Assume that women who work in the market must obtain child care from day care centers while they are on the job. 2. Recent years have seen a large increase in the number of welfare recipients (primarily unmarried women with children) entering the labor market. But some social critics believe that mother-provided child care is better for child development than day care provided outside the home. Which policy of the four specified in question 1 seems likely to reduce home production of child care the least? Justify your answer with a graph and a clear explanation of the economic assumptions required to nail this down. C. Data Analysis An extract from the March 2008 CPS is posted on the Stellar course web page. This data set contains information on working-age women. The variables included are labor force status, hours/week, age, race, marital status, years of schooling, number of own children under age 6, number of own children under age 18, and family unearned income. 1. Using the information provided with the data, construct dummies for employment status and labor force participation, high school and college graduation status, nonwhite race, non-married status, and number of children 6-18. Report descriptive statistics for all variables in your extract. Check your data for implausible or missing values. 2. Run a regressions of LFP and log(hours/week) on age, age-squared, the race dummy, dummies for high school and college graduation status, number of children under 6, number of children aged 6-18, the non-married dummy, and unearned income. Are the results of this regression roughly consistent with the time-allocation model discussed in class? Why or why not? MIT OpenCourseWare http://ocw.mit.edu 14.64 Labor Economics and Public Policy Fall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms

1. (15 Minutes - 20 Points) Answer each of the following subquestions BRIEFLY. (a) (5 points) In my second lecture I defined a solution concept called "pure strategy iterated strict dominance." In my fifth lecture I defined a more powerful version of iterated strict dominance. What was the difference betweeen them and why was the game below a useful example? L C R U M D 10, 9 10, 6 10, 10 -5, 9 15, 10 11, 12 -35, 10 10, 7 15, 5 (b) (5 points) Find all pure strategy Nash equilibria of the game below. X Y Z A B C 4, 3 5, 2 5, 1 1, 7 6, 6 4, 3 2, 3 7, 3 5, 3 (c) (5 points) In class I discussed the general discrete choice model of price competition between N firms: the firms choose prices p1, . . . , pn and each consumer i decides to purchase from the firm j for which vpj +Eij is largest. Describe briefly what happens to equilibrium prices as the number of firms N goes to infinity both for uniformly distributed Eij and under general distributions. (d) (5 points) Describe precisely an example of a game that has no pure or mixed strategy Nash equilibrium. Describe as well as you can a theorem that provides conditions under which a game with an infinite number of pure stategies must have a Nash equilibrium. What conditions of your theorem are violated in your example? 1 2. (25 Minutes - 30 Points) When my daughter Anna was 3 years old, she liked to play Rock-Paper-Scissors. However, she faced a difficulty - three year olds find it hard to make "scissors" with their fingers. Suppose that we capture this problem by treating her playing Rock-Paper-Scissors against her older sister using the asymmetric 3 3 game shown below (with Anna as player 1). R P S R P S 0, 0 -1, 1 1, -1 1, -1 0, 0 -1, 1 1 c, 1 1 c, -1 c, 0 (a) (13 Points) Consider first the version of this game where c > 1. (You can think of this as a model for the extreme situation where Anna is physically incapable of playing scissors.) Find a mixed-strategy Nash Equilibrium of this game. (b) (3 points) What is Anna's expected payoff in the equilibrium you found in part (a)? (c) (14 points) Consider now the version of this game with 0 < c < 1. Find a mixed strategy Nash equilibrium of this game in which both players play every strategy with positive probability. 2 3. (15 Minutes - 22 Points) Two students are deciding how long to spend studying for 14.12 on the night before the exam. Let ei be the fraction of the available time student i devotes to studying with 0 ei 1. Assume that the students' utilities are u1(e1, e2) = log(1 + 3e1 e2) e1 u2(e1, e2) = log(1 + 3e2 e1) e2 (A story for this would be that the first term reflects the benefits they get from learning and getting a good grade, whereas the second reflects the opportunity cost of time. The negative effect of e2 on student 1's utility could reflect that student 1 will get a lower grade if student 2 studies more and does better on the exam.) (a) (5 points) What is player 1's best response to a choice of e2 by player 2. (b) (13 points) Find a pure strategy Nash equilibrium of the game where players 1 and 2 choose e1 and e2 simultaneously. (c) (4 points) Is this game solvable by iterated strict dominance? How do you know this? 3 4. (25 Minutes - 28 Points) Suppose Prof. Ellison decides to run a classroom experiment to teach about mixed strategy equilibrium (and make some money). He chooses two students from the class. Each student is required to write down an integer from 1 to 100 inclusive. The rules of the game are that the student who writes down the smaller number must pay Prof. Ellison that number of dollars. The student who writes down the larger number pays nothing. If both students write down the same number assume that both pay. Assume that both students are risk-neutral and self-interested so that this game can be represented as S1 = S2 = {1, 2, . . . , 100} with s if s s u1(s1, s2) = 1 1 2 0 if s1 > s2 s2 if s2 s1 u2(s1, s2) = 0 if s2 > s1 (a) (3 points) Are any strategies in this game strictly dominated? (b) (7 points) This game has two pure strategy Nash equilibria. What are they? (c) (3 points) Discuss briefly why you should expect given what I told you in part (b) that this game would also have a mixed strategy Nash equilibrium. (d) (15 points) Find a symmetric mixed strategy Nash equilibrium of this game

A. A consumer chooses between two goods, x1 and x2, with prices p1 and p2 given income y, so as to maximize utility. 1. Graph the consumer's problem in x1 and x2 space. Show the consumer's optimal choice. 2. Give a graphical decomposition of the income and substitution effects of a change in p1 on the demand for x1. B. Assume the consumer's utility function is given by: u(x1, x2) = ln(x1 - 1) + (1-)ln(x2 - 2), where: 0 < < 1, x1 > 1 > 0, x2 > 2 > 0. (This is called a Stone-Geary utility function. The parameters 1 and 2 are sometimes thought of as "subsistence" levels of consumption, below which utility is not defined.) 1. What is the marginal rate of substitution (MRS) for this utility function? 2. Present the first-order conditions for optimal choices of x1 and x2 as a single equation involving the MRS. What is the graphical interpretation of this condition? 3. Derive the uncompensated ("Marshallian") demand function for x1 for this consumer as a function of prices and income. 4. Derive the compensated ("Hicksian") demand function for x1 for this consumer as a function of p1, p2 and a fixed level of utility, u*. Derive the same relationship graphically. What is the connection between the compensated demand function and the substitution effects of question A.2? C. Applied researchers often work with the Cobb-Douglas production function: Q = LK; > 0, > 0, > 0, where L is Labor, K is capital, and Q is the quantity of output. 1. What must be true for this production function to exhibit constant returns to scale? 2. Econometricians have estimated and by fitting the following equation to time series data on measures of output, capital, and labor: LnQt = ln + lnLt + lnKt + t, where t is an error term and t indexes time series observations. (i) Where does this equation come from? (ii) Assuming you have the necessary data, describe two ways to construct a statistical test for constant returns to scale in production. D. Use a graph to explain the relationship between the purchase of insurance and the concept of risk aversion. Why might someone who purchases fire insurance also play the lottery? E. Your uncle gives you a government bond for your Bar Mitzvah that can be given back to the government for 100 dollars in five years. You would rather have cash. How much could you sell the bond for today if the interest rate on FDIC insured savings accounts is fixed at 5 percent (compounded annually)? F. Suppose that the demand for MP3 downloads is a linear function of their price and the annual income of college students. Make up some notation for a demand equation that expresses this model of demand (assume downloads are not free). Use this equation to compute the price-elasticity of demand for MP3 downloads as a function of price and income. G. Do private schools do a better job of preparing students for MIT than public schools? Consider two regressions that address this question, one short and one long. The short regression looks like this: MITGPAi = 0+ 0PRIVATEi + 0i The long regression adds controls for a student's SAT score: MITGPAi = 1 + 1PRIVATEi + 1SATi + 1i (i) Why is the long regression likely to be a better measure of the effect of a private school education on MIT GPA? (ii) Use the omitted variables bias formula to give a precise description of the likely relationship between 0 and 1. MIT OpenCourseWare http://ocw.mit.edu 14.64 Labor Economics and Public Policy Fall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms

BOP Transactions. Identify the correct BOP account for each of the following transactions.

a. A German-based pension fund buys U.S. government 30-year bonds for its investment porte Financial account portfolio investment liabilities

b. Scandinavian Airlines System (SAS) buys jet fuel at Newark Airport for its flight to Copenhagen. Current account: Goods: Exports FOB

C. Hong Kong students pay tuition to the University of California, Berkeley Current account Services credit

d. The US Air Force buys food in South Korea to supply its air crews. Current account Goods Imports

e. A Japanese auto company pays the salaries of its executives working for its US subsidiaries Current account Services credit AUS tounst pays for a restaurant meal in Bangkok.