Econ 102 Winter 2007 Midterm II with Solutions

Econ 102 Winter 2007 Midterm II with Solutions - Econ 102...

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Unformatted text preview: Econ 102 Mark L.J. Wright Macroeconomic Theory In] wright©econ.ucla.edu Winter 2007 Bunche 9284 Second Midterm Exam Date: Thursday lst March, 2007 Instructions 9390715339"? 10. Answer each part of the exam in a separate blue book. Write your name, student number, TA section and the part attemptei on the front page of each blue book that you use. Write your answers in permanent ink. Answers submitted in pencil, or in erasable ink, are not eligible for regrade requests. You have 75 minutes to answer this exam. The exam has four (4) pages. Please check that you have all pages. There are seventy five (75) points worth of questions. Answer all questions. This is a “closed book” exam. You may not consult your notes or textbooks during the exam. No calculators are to be used on the exam. You may not talk to any other student while completing the exam. Exam answers are to be completed, and handed in, individually. Professor Wright will be available to answer questions during the first t: :11 minutes of the exam. If y0u are confused about a question on the exam after the first ten mi nutes, explain why you are confused in your answer, state what you think is necessary to resove your confusion, and then proceed to answer the question accordingly. Part A (Short Answer Questions) (24 points total) Evaluate each of the following statements. State whether they are true, lalse or uncertain, and give a short explanation of your reasoning. No points will be awarded witho it an explanation. 1. In the New Grewth model, the 10ng run growth rate of output is independent of the savings rate. (8 points) 2. The less sensitive is investment to changes in the real interest rate, the flatter is the IS curve. (8 points) i 3. The less sensitive is money demand to changes in income, the flatter is the LM curve. (8 points) Part B (Long Answer Question on the Labor Market) (26 points) As in problem set three, consider a model of the labor market in which L is 1 he number of workers in labor force, E the number of employed workers, and U the number unemployed. Assume that fraction 5 of the employed lose their jobs every period, while a fraction f of the unemployed find a new job every period. Assume that the labor force grows at a rate we per per .od so that L'H'l = + 71') Lt! Assume that all new entrants to the labor force (that is, the new nLt people w no join the labor force each period) begin unemployed. 1. Find an expression for the level of unemployment U¢+1 tomorrow as a iunction of the level of unemployment today Ut. (4 points) 2. Derive an expression for the steady state level of the unemployment ra1e u. (6 points) 3. Suppose that the government reintroduces the draft so that the number of people entering the labor force each period falls (that is, n falls). What happens to the stead y state unemployment rate? (8 points) 4. Suppose that the government raises unemployment benefits. What happens to the steady state unemployment rate? (8 points) Part C (Long Answer Question on the IS—LM Model) (25 points total) Suppose that terrorist attack and destroy the New York Stock Exchange Suppose that the effect of this terrorist attack is to make people lose confidence in the financial s {stem and hold more money. That is, money demand increaSes. For simplicity suppose that it increases by a constant amount AM“l which is the same for all interest rate and income levels. Suppers: also that the attack has no direct effect on any other aspect of the economy. 1. Show that the increase in money demand shifts the the LM curve to th( left (or equivalently, that it shifts the LM curve upwards) (6 points) ‘ ‘ mutate t0 t: 2. What factors determine the size of the horizontal shift in the LM curve" (3 points) “A QOM 3. What factors determine the size of the vertical shift in the LM curve? (3 points) Wiggly 4. What is the effect of the increase in money demand on the equilibrium in the IS—LM model? How does the size of the change in output depend upon the sensitivity Wd to changes in interest rates? lfi points) '\ use 5. Suppose that the government responds to this in money demand by increasing the money supply. How large would the increase in the money supply havu to be, relative to the increase in money demand, for the liege] of output to be uncha gill? points) Suggested Answer of 2nd Midterm Econ 102 Winter 2007 Mar. 6th 2007 Part A (Total 24pt) 1. (Bpt) False: The saving rate affects the growth rate (recall the case that t as marginal productivity of capital on capital per effective labor is censtant). 2. (Spot) False: The less sensitive is investment to changes in the real inte1 est rate, the steeper is the IS—curve. This can be explained by using the following diagrams: :2) | newness alnsmsmuu use (23‘ 1 assumes :>Sunsntive cause 3. (8131:) True: Suppose the money demand function takes the following form: igzlo—lgr—t-lyY The smaller ly implies the less sensitive money demand with respect to the she: age in income. Note that We can obtain LM-curve as follows: I l *— — . r = + fl” —- I‘ll—“g where M 13 money Supply Hence, smaller by giVes flatter LM-curve. Part B (Total 26pt} 1. (4pt): The level of unemployment U¢+1 tomorrow is as follows: Ut+1: BE: 4* "- + nLt 1 2. (Gpt): Recall the dynamics of Lt: Lt+1 : (1 + n) Lt By using the two expressions above, we can derive the difference equation for u iemployment rate ut E gt: 14‘”! A mi, _ a E; +g1—nv.+nL. Le+1 — Ill-+71 L: U 1 U L ‘ _ 8 _ 8 — t n :5 1“3+1 "’ (+1441 Le (1+niL. + l-I-n Lt + {Twin ‘ _ s a 1— n imm— m—mutJrifitim'tm =>(1+n)u:+1=s—sut+(1—f)ue+n Then impose the steady state condition: u¢+1 2 ti: 5 u. (1+n)u:s—sut+(l~f)u+n :>(s+f+n)u=s+n . u _ 5i” " _ s+f+n 3. (Spt): We have already established the steady state unemployment level am this economy. Suppose it falls because of the draft system: 0+1; . . 2—1 < u 1"; s+f+nl — Who 1 Hence, the steady state unemployment rate decreaSes due to the introduction cf the draft system. 4. (Spt): The effect of the higher unemployment benefit increases the unemployment rate. An increase in unemployment benefit reduces the opportunity cost of being unemployed, which possibly generates the following two effects: increase the separation rate (3 T) and (ii) decrease the job finding rate(f i), which lead to higher unemployment rate. Part C (Total 25pt) 1. (fipt): Suppose we have the following LM—curve: _ _ _ l. _| %=to—lgr+lyY<~—>r:+ifY-T?%¢>Y=i§;rwg;l+§;% Assume that the "increase of demand" comes from higher lo. If Io increases, the LM—curve shifts upward by «it-in or equivalently horizontally by “1-31. This movement in a. short-run equ librium can be explained by using the following diagrams: 2. (3pt): Recall the LM—curve: Here we assumed the money demand increases because of the higher lg. [n this case, the size of 1y determines the size of the horizontal shift in the LM—curve as well as the size of the change in lo. 3. (3pt): Use the same results: Here we assumed the money demand increases because of the higher lo. In t 1is case, the size of l.- deter. mines the size of the vertical shift in the LM—curve as well as the size of the cha nge in lo. 4. (6pt): The upward shift of LM-curve generates the decline of Y and the rise of 1‘ (see the diagram below). Note that the equilibrium moves along IS-cnrve. Hence, the size of the c hange in output depends on the slope of IS-curve. The less sensitive is investment to changes in the real int: erest rate, the steeper is the IS-curve. Hence, the less sensitive is investment to changes in the real interest r rte, the smaller the decline of output is. 4— ’ (s. Equitbdum my“: 5. (Tpt): We are asked to compute the required increase in the money supply to offset the decline of output generated by the increase in money demand. Assume we are in the sh01t~run. Only way to retrieve the original equilibrium is to shift back the LM-curve to the original position. Recall the LM—curve: .: r _7~? r—f}+fY up In order to offset the effect of A la, A If needs to satisfy the following equation ...
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This note was uploaded on 03/12/2008 for the course ECON 102 taught by Professor Serra during the Winter '08 term at UCLA.

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Econ 102 Winter 2007 Midterm II with Solutions - Econ 102...

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