JHU_Fall2013_MidtermExamSolutions(1).pdf - Department of...

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Macroeconomic Theory and Policy – Midterm Exam | © Sanjay K. Chugh 1 Department of Applied Economics Johns Hopkins University Economics 602 Macroeconomic Theory and Policy Midterm Exam Suggested Solutions Professor Sanjay Chugh Fall 2013 NAME: The Exam has a total of four (4) problems and pages numbered (including this cover page) one (1) through seventeen (17). Each problem’s total number of points is shown below. Your solutions should consist of some appropriate combination of mathematical analysis, graphical analysis, logical analysis, and economic intuition, but in no case should solutions be exceptionally long. Your solutions should get straight to the point – solutions with irrelevant discussions and derivations will be penalized.You are to answer all questions in the spaces provided. You may use your class notes, text, and lecture slides as needed; but you are on your honor to neither use any other materials whatsoever nor collaborate with anyone (inside the class or outside the class) in completing the exam. Problem 1 / 20 Problem 2 / 30 Problem 3 / 20 Problem 4 / 30 TOTAL / 100
Macroeconomic Theory and Policy – Midterm Exam | © Sanjay K. Chugh 2 Problem 1: Two-Period Consumption-Savings Framework (20 points). Consider the two-period economy (with zero government spending and zero taxation), in which the representative consumer has no control over his real income (y1in period 1 and y2in period 2). The lifetime utility function of the representative consumer is ()2211,lnlnu c ccc=+. The lifetime budget constraint (in real terms) of the consumer is, as usual, 22110(1)11cycyr arr+=+++++. Suppose the consumer begins period 1 with zero net assets (a0= 0), and as per the notation in Chapters 3 and 4, r denotes the real interest rate. For use below, it is convenient to define the gross real interest rate as R= 1+r(as a point of terminology, “r” is the netreal interest rate). a.(4 points) Set up a lifetimeLagrangian formulation for the representative consumer’s lifetime utility maximization problem. Define any new notation you introduce. Solution: The lifetime Lagrangian is 2212101(111ln)lnycr accycrrλ+++++++, which contains Lagrange multiplier λ.
Macroeconomic Theory and Policy – Midterm Exam | © Sanjay K. Chugh 3 Problem 1 continued b.(6 points) Based on the Lagrangian from part a, compute the first-order conditions with respect to c1and c2. Then,use these first-order conditions to derive the consumption-savings optimality condition for the given utility function. NOTE: Your final expression of the consumption-savings optimality condition should be presented in terms of the ratio 21cc. Furthermore, in obtaining the representation of the consumption-savings optimality condition, you should express any (1+r) terms that appear as R instead (if you have not already done so).

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