602_MidtermExamSolutions

602_MidtermExamSolutions - Department of Applied Economics...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Department of Applied Economics Johns Hopkins University Economics 602 Macroeconomic Theory and Policy Midterm Exam Suggested Solutions Professor Sanjay Chugh Summer 2010 NAME: 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 do solutions need to 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 one page (double-sided) of notes. You may not use a calculator. Problem 1 / 26 Problem 2 / 20 Problem 3 / 32 Problem 4 / 22 TOTAL / 100
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
1 Problem 1: Two-Period Economy (26 points). Consider a two-period economy (with no government), in which the representative consumer has no control over his income. The lifetime utility function of the representative consumer is ( ) 12 1 2 ,l n ucc c c = + , where ln stands for the natural logarithm (that is not a typo – it is only 1 c that is inside the ln operator). Suppose the following numerical values: the nominal interest rate is 0.05 i = , the nominal price of period-1 consumption is 1 100 P = , the nominal price of period-2 consumption is 2 105 P = , and the consumer begins period 1 with zero net assets. a. (4 points) Is it possible to numerically compute the real interest rate ( r ) between period one and period two? If so, compute it; if not, explain why not. Solution: The inflation rate is easily computed as 2 2 1 105 1 1 0.05 100 P P π =− = = . Them using the exact Fisher equation, 2 11 . 0 5 . 0 5 i r + += = = + , so that 0 r = . b. (14 points) Set up a sequential Lagrangian formulation of the consumer’s problem, in order to answer the following: i) is it possible to numerically compute the consumer’s optimal choice of consumption in period 1? If so, compute it; if not, explain why not. ii) is it possible to numerically compute the consumer’s optimal choice of consumption in period 2? If so, compute it; if not, explain why not. Solution: The sequential Lagrangian for this problem (here cast in real terms, but you could have case it in nominal terms as well) is 11 1 1 2 2 1 2 (, ) [ ] [ ( 1 ) ] uc c y c a y ra c λ +− + + + , where 1 and 2 are the multipliers on the period-1 and period-2 budget constraints. The first- order condition with respect to 1 c is 112 1 0 = , with respect to 2 c is 212 2 0 = , and with respect to 1 a is (1 ) 0 r −+ + = . The third FOC allows us to conclude ) r =+ . Substituting this into the FOC on 1 c gives 2 ( r = + . Next, the FOC on 2 c allows us to obtain 22 1 2 = . Substituting this into the previous expression gives us ( r , or 1 r = + , which of course is the usual consumption- savings optimality condition. Using the given functional form, the consumption-savings optimality condition for this problem can be expressed as 1 1/ 1 1 c r = + , which immediately allows us to conclude 1 1 c r == = + , which completes part i. However, 2 c cannot be computed here because you are given no information regarding income, either in present-value or period-by-period form.
Background image of page 2
2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/08/2011 for the course ECON 602 taught by Professor Chugh during the Spring '11 term at Johns Hopkins.

Page1 / 13

602_MidtermExamSolutions - Department of Applied Economics...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online