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Unformatted text preview: PART A (40 points) Write your answers to the’multiple—choice questions in the space below.
WRITE LEGLY! 1.___B____ 11.____B______ 21 ____C____ 31. D_______
2 ____C_ 12 _C_____ 22 ___A____ 32 __B_
3. ____D___ 13’._B_____ ‘23.___C____ 33. C__
4. __C___ 14. __A____ 24. ___C______ 34. ___B______
5 ___B_____ 15 _B_____ 25 _C__ 35 __C__
6 _D___ 16. ____A___ 26. ___B__ 36. E____
7 ____C_ 17. ___A___ 27 _B___ 37. ___C__
8 _ __ 18. ;_A_ 28.___E___ 38. __A_______
9 B 19 E 29 C 39 C l
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I PART B
QUESTION 1 The just elected president of Uruguay hires you to advice him on which exchange rate
system to adopt. Uruguay is a small open economy, which takes the interestrate as given
from the international capital markets; A (a) In order to reduce the volatility of the exchange rate, the new government is thinking
of adopting aﬁxed eXchange rate syStem. This decrease in uncertainty could
potentially enhance the confidence of foreign investors when deciding to invest in
Uruguay. As an expert in the small open economy lS—LM model, you know that a
drawback of a fixed exchange rate is that the government loses'control on one of its
policy variables (either G, T orMS) to affect the output level (Y). Y Which is the policy variable that has noeffects on Y under a ﬁxed exchange rate
system? (Hint: Either monetary or fiscal policy). MONETARY POLICY Explain how you reached this conclusion in Panel A (next page), showing the
movement in the IS and LM curves and the resulting equilibrium from this policy.
(Note: in panels A and B, rf is the international interest rate and E0 denotes the initial :
equilibrium). M (b) The president also explains that he plans to reduce the budget deficit in the next years V
by reducing the number of public employees. However, he wants to avoid causing a
recession as a result of this contractionary fiscal policy move. Again, using the small
open economy IS—LM model, you know that one of the exchange rate regimes you
studied in C11 can avoid a recession after a fall in G. ' Which exchange rate system delivers the ineffectiveness of fiscal policy on output? FLEXIBLE EXCHANGE RATE Explain how you reached this conclusion in Panel B, showing the movement in the IS
and curves and the resulting equilibrium from this policy. ‘ ' Would the exchange rate after the decrease in G' have appreciated or depreciated
compared to the initial equilibrium? ‘ DEPRECIATED PANEL A: LMO=LM2 LM1 Real Y GDP 1) money supply increases; 2) LM shifts out (LM2); 3) interest rate falls; 4) outﬂow of V
capital; 5) M falls; 6) LM shifts back; 7) back to initial equilibrium, with lower reserves. PANEL B: ‘
R ‘ LM
ISO=ISZ Real Y GDP 1) G falls; 2) IS curve shifts in (ISI); 3) interest rate falls; 4) outﬂow of capital; 5)
exchange rate depreciates; 5) net exports increase; 6) IS shifts back; 7) back to initial
equilibrium, with a depreciated exchange rate. QUESTION 2 Consider an economy with the follOwing SP relationship
p=pe+0.5 19 +2 where p and p6 are actual and expected rates of inﬂation, l? is the log output ratio (where Y =100*ln[Y/YN] where YN is the natural rate of real output) and z is a supply shock.
Assume that the natural rate of real output growth is zero, so that nominal GDP growth is
the same as excess nominal GDP growth. Also asSUme that inﬂationary expectations pe
adjust according to the following rule: ' ' PEP1
Supply shocks have been absent in the last years and the government has maintained a constant rate nominal GDP growth of 1% (i.e. 2:0 and x=1 in all years up to and
including 1999). The economy is in the steady statein 1999. a) Write the equations for the DG and SP curve and solve for the initial Y and p in 1999.
SP: p=1+0.5 )9 +0 DG: p=1Y+l;1 19:19.1 = 0
pezp1:x:1 b) Suppose that in the year 2000, an unexpected military conﬂict in Asia causes a rise in
government expenditures, increasing x to 3%. Find the year 2000 levels of l; and p. x23; p1=1; f4 = 0
SP: p=1+l9 DG: p=3 )9 Equilibrium: 1+? = 3 )9. So, i? = 2 and p= 1 . Aiwmtz..wwrrw.w. , ., u ,, m A 0) Suppose that, due to presidential elections in the year 2002, the government has as an objective to implement l; to be equal to 0 in the year 2002. (i.e. electors value stability).
In order to achieve this objective, the government has to announce a constant level of x
for the years 2001 and 2002. The government expects no shocks during these 2 years.
What is the level of x that should be chosen? Start of 2001: Y‘_1=2 and p.1=1. Given x: SP: p: 1 + ll} DG: p=xl?+2 So,1+ l7”: x—fI—Z, or sz/Z +1 /f‘2 ; and p :2 x/2 +1.5 Start of 2002: 17' _1= x/2 +1/2 and p_1= x/2 +1.5 Given x: A SP: p: x/2 +1.5 + Y
DG: p=x )9 + x/2 + 1/2 We want l?=0.
So, p = x/2 +1.5 and p: 1.5 x + 0.5 So, x=1 and p = 2. QUESTION 3 Consider an economy with positive labor—augmenting technological progress.
The production function for the economy is given by: Y=F(K, XN), where X grows at a rate x>0 and N grows at rate n=0 (there is no population growth) and
F is a constant returns to scale production function. The economy is initially in steady state, where the values of the capital stock and
effective labor are K0 and XoNo, respectively. The savings rate 3 is constant, and the
depreciation rate is equal to zero. a) What is the steady state condition that K0, N0 and Xomust satisfy?
Solution 1: Analytical Scale the production function by NX. . The capital accumulation equation here is = sY 2 SF (K , XN) For the capital per unit of effective labor, we have dKA__dAK dX
i I. __1_ M __1_ M_Zt_£ _Sf .15. _x_1_<.
dt XN' N A2 .N‘ X X X XN XN In the steady state fl— —K— 20,80 sf £— _ 2 xi.
dt XN XN XN Solution 2: By Analogy ’  We know that in the model with disembodied technological change (i.e. Y=XF(K, N) ), and nonzero population growth rate It the steady state relationship is given by K ,_ Ii;
sf(7V—]—nN Note that in our case we have Y=F(K,XN) and the effective labor (that is, XN) grows at a
rate x, since the population is constant (selfcheck question: what would be the growth
rate were it not constant ?). After scaling by effective labor, we have exactiy the same functional form as we had in
 the model in class, just x takes place of n, and the place of N. So the steady state relationship is
K r K L
Sf[ XN) x XN . ( ) Yo/(XoNo) Y1/(XoN1) b) What is thergrowth rate of per capita output in the steady state? As we see that the steady state level of capital per unit of effective labor is given by (1),
that is, it is constant. Therefore, Y/(XN) = f(K/XN) is also constant.
Then, per capita output Y/N = X*(_Y/(XN))=X*Const, which grows at exactly the rate x. Now suppose there is a onetime increase in the number of workers due to
immigration '(N goes up, and stays at the new level afterwards). c) (i) At the time the increase occurs, does output per unit of effective labor rise, fall or.
stay the same? Why? When N1>N0, K0/(X0No))> Ko/(XoNl) (that is, the capital does not jump) and
f(Ko/(X0No))> f(Ko/(X0N1)) because f is an increasing function, so ,
Y0/(X0N0) > Y1/(X0N1), and the output per unit of effective labor falls (see picture below) (ii) Is there any further change in output per unit of effective labor after the change (if
any) in output per unit of effective labor at the time the new workers appear? If so, does
output per unit of effective labor rise or fall? Why? * .x K/(XN) f(K/(XN)) s f(K/(XN)) Ko/(XoNo) Ko/(XoN 1) K/(XN) After the jump, the savings will be at point B in the graph above. Since none of the rates
change, none of the lines shift. That’s above the xK/(XN) line, so net change in capital
per unit of effective labor will be positive. It Will increase until we are again at the point
A, that'is, at the old steady state. d) In the steady state corresponding to the new level of N, is output per unit of effective
labor higher, lower or the same as it was before the increase in N? Why? Since we are again in the old steady state, output per unit of effective labor is exactly the
same as it was before. ' e) In the steady state corresponding to the new level of N, is per capita output higher,
lower or the same as it was before the increase in N? (AsSume that the adjustment
process took some time). ' Since we are in the old steady state again, we know that the output per unit of effective
labor is exactly the same as it was before, that is, ' Y1 _ Yo,
X1N1‘.X0No
It is easy to see that
‘ ULJELE’L
,Nl X0 0 Since x is positive, and the adjustment process took time, X will have grown by some '
amount during that time, so thatX1>X0, or X1/X0>1, and therefore, Y1/N1>Y0/No, that is,
per capita output after the adjustment Will be higher than before. ...
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 Spring '08
 GORDON
 Macroeconomics, Exchange Rate, Monetary Policy, gross domestic product, per capita

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