Answers – Problem Set 4 by wuyunyi

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```									                         Answers – Problem Set 4
(s04aps4mt – 3/26/04)

Problem 1a.        See the diagrams illustrated on the page that follows.

Problem 1b.        See the diagrams illustrated two and three pages hence.

Problem 1c.       As shown three pages hence, no change in the demand side equilibrium
value or real GDP emerges as a result of this external disturbance and the ensuing monetary
adjustment. Since we observe no change in demand side equilibrium real GDP, we must
also observe no change in the position of the demand side equilibrium locus, the aggregate
demand curve. Thus, in the diagrams illustrated four pages hence, no repercussions occur.

Problem 1d.         As we travel from the original equilibrium at (Y0,r0,e0) to the new
equilibrium at (Y0,r1,e0), we can assess the behavior of each component of planned
expenditures as follows

Consumption: Y = 0  YD = 0  C = 0
Planned Investment: r  Ip= 0 (here planned investment is interest-insensitive)
Government Purchases: G = 0 (here no action is taken by fiscal policymakers)
Net Exports: Y = 0  NX = 0 and e = 0  NX = 0

In sum, we witness no change in any of the four components of planned expenditures

Problem 1e.         The capital outflow induced by rising foreign interest rates generates an
excess supply disequilibrium in the foreign exchange market. To eliminate this
disequilibrium and maintain the fixed exchange rate, the home central bank intervenes in the
foreign exchange market by conducting official reserve transactions designed to increase the
demand for the home currency. To do this, Saint Helena’s central bank buys Saint Helena
Pounds and sells Saint Pierre Francs. As it buys up the home currency, it contracts the
domestic money supply because fewer Saint Helena Pounds remain in circulation. And as it
sells the foreign currency, it draws down its holdings of Saint Pierre Francs in particular and
therefore decreases Saint Helena’s holdings of international currency reserves in general.

Problem 1f.     The velocity of money can be expressed as the ratio of nominal GDP to
      PY 
the nominal money supply  V  s  or as the ratio of real GDP to the real money supply
      M 
        
        
 V  Y  . In Saint Helena, we witness Y = 0 and P = 0 as a result of this external
     Ms 
        
      P 

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disturbance and the ensuing monetary adjustment. Consequently, nominal GDP (PY)
remains unchanged. But the monetary adjustment necessary to maintain the fixed exchange
rate contracts Saint Helena’s nominal money supply (Ms < 0), as noted above. So if
nominal GDP remains constant while the nominal money supply decreases, the velocity of
PY
money increases:          V  . To reaffirm this result, observe that if the nominal money
Ms 
supply decreases while prices remain unchanged, the real money supply decreases and the
Ms        Y
velocity of money increases: M s        s  V  .
P      M

P

Y
Problem 1g.       Labor productivity equals output-per-worker:       . Since Saint Helena
N
experiences no change in real GDP (Y = 0) and no change in employment (N = 0) as a
result of this external disturbance and the ensuing monetary adjustment, Saint Helena
observes no change in its labor productivity. As shown on the preceding page, labor
Y
productivity remains constant at 0 .
N0

Problem 2a.       See the diagrams illustrated on the page that follows.

Problem 2b.        See the diagrams illustrated two pages hence.

Problem 2c.      Since prices rise due to this adverse supply side disturbance, the real
Ms
money supply decreases in Vanuatu: P            . The demand side and foreign exchange
P
market consequences of this real money supply contraction are illustrated three and four
pages hence.

Problem 2d.       Since income falls in Vanuatu, tax revenues decrease as well, and this
causes the government budget deficit in Vanuatu to rise: Y↓  t0Y↓  R↓  BD↑.

Problem 2e.        The real exchange rate (e) equals the nominal exchange rate (e’) times the
e' P
home price level (P) over the foreign price level (Pf): e       . Since the Vanuatu Vatu
Pf
appreciates against the Fiji Dollar, we observe an increase in the value of the nominal
exchange rate: e’↑. And since Vanuatu experiences price inflation, we also observe an
increase in the home price level: P↑. Both of these changes push the real exchange rate
higher: e’↑  e↑ and P↑  e↑. Thus, the real exchange rate increases unambiguously in
this scenario.

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Problem 2f.        In Vanuatu, we witness Y < 0 and P > 0 as a result of this adverse
supply side disturbance and the ensuing monetary adjustment. Consequently, nominal GDP
(PY) behaves ambiguously. We observe no change in the nominal money supply (Ms = 0).
But if nominal GDP behaves ambiguously while the nominal money supply remains
PY
constant, the velocity of money V  s displays ambiguity overall.
M

Looking at velocity as the ratio of real GDP to the real money supply, we notice that the
drop in Vanuatu’s real GDP combines with the drop in Vanuatu’s real money supply to
Y
reaffirm the ambiguity of velocity’s behavior:         V? .
Ms

P
Problem 2g. The decrease in the marginal product of labor caused by the contraction
in the capital stock (K↓  MPN↓) makes workers look less attractive to profit-maximizing
firms, and the resulting decrease in the demand for labor puts downward pressure on
employment (MPN↓  N↓). But the decrease in the real wage caused by the price inflation
        W 
 P         makes workers look more attractive to profit-maximizing firms, and the
        P 
resulting increase in the quantity of labor demanded puts upward pressure on employment
W             
  N   . In the diagrams illustrated three pages earlier, the second of these effects
P             
dominates the first, so that employment increases overall.

Since Vanuatu’s real GDP falls (Y < 0) while its employment rises (N > 0), Vanuatu’s
Y                 Y
labor productivity decreases unambiguously: Y   and N   . Moreover,
N                  N
inspection of the slopes of appropriate lines drawn from the origin to the short-run
aggregate production functions illustrated three pages earlier confirms the decrease in labor
Y     Y
productivity: 1  0 .
N1 N 0

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