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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—tlyY The smaller ly implies the less sensitive money demand with respect to the she: age in income. Note that We
can obtain LMcurve as follows: I l *— — .
r = + fl” — I‘ll—“g where M 13 money Supply Hence, smaller by giVes flatter LMcurve. 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. + lIn 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:+ifYT?%¢>Y=i§;rwg;l+§;% Assume that the "increase of demand" comes from higher lo. If Io increases, the LM—curve shifts upward
by «itin or equivalently horizontally by “131. This movement in a. shortrun 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 LMcurve generates the decline of Y and the rise of 1‘ (see the diagram
below). Note that the equilibrium moves along IScnrve. Hence, the size of the c hange in output depends on
the slope of IScurve. The less sensitive is investment to changes in the real int: erest rate, the steeper is the IScurve. 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 LMcurve 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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 Winter '08
 Serra
 Economics, Macroeconomics, Inflation, Unemployment, money demand

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