Download Foundations of Economics for International Business Selected

Foundations of Economics for International Business
Selected Solutions to Homework Assignment 5
INSTRUCTOR: XIN TANG
Department of World Economics
Economics and Management School
Wuhan University
Fall 2015
Due at December 10th, 2015 (Thursday)
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MULTIPLE CHOICES: 40%
Instructions: Choose the one alternative that best completes the statement or answers the question. If you
think any of the problem is not clear, state specifically with argument on where you think is not clear,
explain and justify your answer.
1. If the number of employed workers equals 200 million and the number of unemployed workers
percent (rounded to the nearest percent).
equals 20 million, the unemployment rate equals
(A) 0
(B) 9
(C) 10
(D) 20
2. If the steady-state rate of unemployment equals 0.10 and the fraction of employed workers who lose
their jobs each month (the rate of job separation) is 0.02, then the fraction of unemployed workers
who find jobs each month (the rate of job findings) must be:
(A) 0.02.
(B) 0.08.
(C) 0.10.
(D) 0.18.
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3. Which of the following is an example of frictional unemployment?
(A) Dave searches for a new job after voluntarily moving to San Diego.
(B) Elaine is willing to work for less than the minimum wage, but employers cannot hire her.
(C) Bill is qualified and would like to be an airline pilot, but airlines do not find it profitable to hire
him at the wage established by the airline pilot’s union.
(D) Joan is willing to work at the going wage, but there are no jobs available.
4. The version of Okun’s law studied in Chapter 9 assumes that, with no change in unemployment,
real GDP normally grows by 3 percent over a year. If the unemployment rate rose by 2 percentage
points over a year, Okun’s law predicts that real GDP would:
(A) decrease by 1 percent.
(B) decrease by 2 percent.
(C) decrease by 3 percent.
(D) increase by 1 percent.
5. Measures of average workweeks and of suppliers’ deliveries (vendor performance) are included in
future economic
the index of leading indicators, because shorter workweeks tend to indicate
activity, and slower deliveries tend to indicate
future economic activity.
(A) stronger; stronger
(B) stronger; weaker
(C) weaker; stronger
(D) weaker; weaker
6. Monetary neutrality, the irrelevance of the money supply in determining values of
is generally thought to be a property of the economy in the long-run.
variables,
(A) real
(B) nominal
(C) real and nominal
(D) neither real nor nominal
7. If an aggregate demand curve is drawn with real GDP (Y ) along the horizontal axis and the price
level (P ) along the vertical axis, using the quantity theory of money as a theory of aggregate demand,
this curve slopes
to the right and gets
as it moves farther to the right.
(A) downward; steeper
(B) downward; flatter
(C) upward; steeper
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(D) upward; flatter
8. According to the quantity theory of money, if output is higher,
and for fixed M this means
P.
real balances are required,
(A) higher; lower
(B) lower; higher
(C) higher; higher
(D) lower; lower
9. The price level decreases and output increases in the transition from the short run to the long run
when the short-run equilibrium is
the natural rate of output in the short run.
(A) above
(B) below
(C) equal to
(D) either above or below
10. Assume that the economy starts from long-run equilibrium. If the Federal Reserve increases the
money supply, then
increase(s) in the short run and
increase(s) in the long run.
(A) prices; output
(B) output; prices
(C) output; output
(D) prices; prices
Figure 1: Shift in Aggregate Demand
11. Refer to Figure 1, in this graph, initially the economy is at point E, with price P0 and output Y .
Aggregate demand is given by curve AD0 , and S RAS and LRAS represent, respectively, short-run
and long-run aggregate supply. Now assume that the aggregate demand curve shifts so that it is
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represented by AD1 . The economy moves first to point
.
and then, in the long run, to point
(A) A; D
(B) D; A
(C) C; B
(D) B; C
Figure 2: Supply Shock
12. Refer to Figure 2, in this graph, assume that the economy starts at point A and there is a favorable supply shock that does not last forever. In this situation, point
represents short-run
equilibrium and point
represents long-run equilibrium.
(A) B; C
(B) B; A
(C) E; D
(D) E; A
13. Starting from long-run equilibrium, without policy intervention, the long-run impact of an adverse
supply shock is that prices will:
(A) be permanently higher and output will be restored to the natural rate.
(B) return to the old level and output will be restored to the natural rate.
(C) be permanently higher and output will be permanently lower.
(D) return to the old level, but output will be permanently lower.
14. If Fed A cares only about keeping the price level stable and Fed B cares only about keeping output
at its natural level, then in response to an exogenous decrease in the velocity of money:
(A) both Fed A and Fed B should increase the quantity of money.
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(B) Fed A should increase the quantity of money whereas Fed B should keep it stable.
(C) Fed A should keep the quantity of money stable whereas Fed B should increase it.
(D) both Fed A and Fed B should keep the quantity of money stable.
Figure 3: Keynesian Cross
15. Refer to Figure 3, in this graph, the equilibrium levels of income and expenditure are:
(A) Y1 and P E1 .
(B) Y2 and P E2 .
(C) Y3 and P E3 .
(D) Y3 and P E4 .
16. Refer to Figure 3, in this graph, if firms are producing at level Y1 , then inventories will
inducing firms to
production.
(A) rise; increase
(B) rise; decrease
(C) fall; increase
(D) fall; decrease
17. In the Keynesian-cross model, if the M P C equals 0.75, then a $1 billion increase in government
spending increases planned expenditures by
and increases the equilibrium level of income
by
.
(A) $1 billion; more than $1 billion
(B) $0.75 billion; more than $0.75 billion
(C) $0.75 billion; $0.75 billion
(D) $1 billion; $1 billion
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18. According to the Keynesian-cross analysis, if M P C stands for marginal propensity to consume, then
a rise in taxes of ∆T will:
(A) decrease equilibrium income by ∆T .
(B) decrease equilibrium income by ∆T /(1 − M P C ).
(C) decrease equilibrium income by (∆T )(M P C )/(1 − M P C ).
(D) not affect equilibrium income at all.
Figure 4: Market for Real Money Balances
19. Refer to Figure 4, in this graph, the equilibrium levels of interest rates and real money balances are:
(A) r1 and M1 /P1
(B) r2 and M2 /P2
(C) r3 and M2 /P2
(D) r3 and M3 /P3
20. Refer to Figure 4, in this graph, Based on the graph, if the interest rate is r1 , then people will
bonds and the interest rate will
.
(A) sell; rise
(B) sell; fall
(C) buy; rise
(D) buy; fall
21. According to the theory of liquidity preference, tightening the money supply will
nominal
interest rates in the short run, and according to the Fisher effect, tightening the money supply will
nominal interest rates in the long run.
(A) increase; increase
(B) increase; decrease
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(C) decrease; decrease
(D) decrease; increase
22. The IS curve provides combinations of interest rates and income that satisfy equilibrium in the
market for
, and the LM curve provides combinations of interest rates and income that satisfy
.
equilibrium in the market for
(A) saving and investment; planned spending
(B) real-money balances; loanable funds
(C) goods and services; real money balances
(D) real-money balances; goods and services
23. According to the Keynesian-cross analysis, if the marginal propensity to consume is 0.6, and government expenditures and autonomous taxes are both increased by 100, equilibrium income will rise
by:
(A) 0.
(B) 100.
(C) 150.
(D) 250.
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SHORT ANSWERS AND NUMERICAL PROBLEMS: 60%
Remember you have to show the detailed calculation, reason, induction or any other necessary process of
your solution.
1. (10%) Suppose that the labor force is normalized to unity, let U represent the unemployment rate,
s the exogenous job arrival rate and σ the exogenous separation rate.
(a) Suppose the labor market steady-state is defined by the unemployment rate that balances the
flow in and out of the unemployment pool, characterize the unemployment rate U as a function
of s and σ. (3%)
(b) Suppose that the unemployment rate does not begin at this level, show that unemployment
will evolve over time and reach this steady state. (Hint: Express the change in the number
of unemployed workers as a function of s, σ and U . Then show if unemployment is above the
natural rate, unemployment falls and if unemployment is below the natural rate, unemployment
rises. You may wish to refer to a similar problem of the numerical example in Solow Model, p.
213) (7%)
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2. (10%) An economy begins in long-run equilibrium, and then a change in government regulations
allows banks to start paying interest on checking accounts. Recall that the money stock is the sum
of currency and demand deposits, including checking accounts, so this regulatory change makes
holding money more attractive.
(a) How does this change affect the demand for money? (2%)
(b) What happens to the velocity of money? (2%)
(c) If the Fed keeps the money supply constant, what will happen to output and prices in the short
run and in the long run? (2%)
(d) If the goal of the Fed is to stabilize the price level, should the Fed keep the money supply constant
in response to this regulatory change? If not, what should it do and why? (2%)
(e) If the goal of the Fed is to stabilize output, how would your answer to the last question change?
(2%)
3. (20%) In the Keynesian cross, assume that the consumption function is given by
C = 2000 + 0.75(Y − T )
Planned investment is 100; government purchases and taxes are both 100.
(a) Graph planned expenditure as a function of income. (6%)
(b) What is the equilibrium level of income? (6%)
(c) If government purchases increase to 125, what is the new equilibrium income? (4%)
(d) What level of government purchases is needed to achieve an income of 1600? (4%)
4. (20%) Suppose that the money demand function is
(M /P )d = 1000 − 100r
where r is the interest rate in percent. The money supply M is 1000 and the price level P is 2.
(a) Graph the supply and demand for real money balances. (6%)
(b) What is the equilibrium interest rate? (6%)
(c) Assume that the price level is fixe. What happens to the equilibrium interest rate if the supply
of money is raised from 1000 to 1200? (4%)
(d) If the Fed wishes to raise the interest rate to 7 percent, what money supply should it set? (4%)
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SOLUTIONS
Multiple Choices:
1–5 B D A A C
6–10 A B A B B
11–15 C D B A B
16–20 C A C B D
21–23 B C B.
Numerical:
1. (a) U =
σ
(σ+s)
(b) To show that the unemployment rate evolves over time to the steady-state rate, let’s begin by
defining how the number of people unemployed changes over time. The change in the number
of unemployed equals the number of people losing jobs (σ E) minus the number finding jobs
(s U ). In equation form, we can express this as:
Ut +1 − Ut = ∆Ut +1 = σ E t − s Ut .
Recall from the text that 1 = E t + Ut , or E t = 1 − Ut , where L is the total labor force (we
normalized L to unity). Substituting for E t in the above equation, we find:
∆Ut +1 = σ(1 − Ut ) − s Ut .
Rearranging terms on the right-hand side of the equation above, we end up with line 1 below.
Now take line 1 below, multiply the right-hand side by (σ + s)/(σ + s) and rearrange terms to
end up with line 2 below:
∆Ut +1 = σ − (σ + s)Ut
= (σ + s)[σ/(σ + s) − Ut ].
The first point to note about this equation is that in steady state, when the unemployment rate
equals its natural rate, the left-hand side of this expression equals zero. This tells us that, as we
found in the text, the natural rate of unemployment U n equals σ/(σ + s). We can now rewrite
the above expression, substituting U n for σ/(σ + s), to get an equation that is easier to interpret:
∆Ut +1 = (σ + s)(U n − Ut ).
This expression shows the following:
• If Ut > U n (that is, the unemployment rate is above its natural rate), then ∆Ut +1 is negative:
the unemployment rate falls.
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• If Ut < U n (that is, the unemployment rate is below its natural rate), then ∆Ut +1 is positive:
the unemployment rate rises.
This process continues until the unemployment rate U reaches the steady-state rate U n .
2. (a) Interest-bearing checking accounts make holding money more attractive. This increases the
demand for money.
(b) The increase in money demand is equivalent to a decrease in the velocity of money. Recall the
quantity equation M /P = kY , where k = 1/V . For this equation to hold, an increase in real
money balances for a given amount of output means that k must increase; that is, velocity falls.
Because interest on checking accounts encourages people to hold money, dollars circulate less
frequently.
Figure 5: Aggregate Demand and Aggregate Supply
(c) If the Fed keeps the money supply the same, the decrease in velocity shifts the aggregate demand
curve downward, as in Figure 5. In the short run when prices are sticky, the economy moves
from the initial equilibrium, point A, to the short-run equilibrium, point B. The drop in aggregate demand reduces the output of the economy below the natural rate. Over time, the low level
of aggregate demand causes prices and wages to fall. As prices fall, output gradually rises until it
reaches the natural-rate level of output at point C .
(d) The decrease in velocity causes the aggregate demand curve to shift downward. The Fed could
increase the money supply to offset this decrease and thereby return the economy to its original
equilibrium at point A, as in Figure 6. To the extent that the Fed can accurately measure changes
in velocity, it has the ability to reduce or even eliminate the impact of such a demand shock on
output. In particular, when a regulatory change causes money demand to change in a predictable
way, the Fed should make the money supply respond to that change in order to prevent it from
disrupting the economy.
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Figure 6: Aggregate Demand and Aggregate Supply
(e) The decrease in velocity shifts the aggregate demand curve down and to the left. In the short
run, the price level remains the same and the level of output falls below the natural rate. If the
Fed wants to stabilize output and return it to the natural rate, they should increase the money
supply. Note that increasing the money supply in this case will stabilize both output and the
price level so that the answer here is the same as in part (d).
3. (a) Total planned expenditure is
P E = C (Y − T ) + I + G.
Plugging in the consumption function and the values for investment I , government purchases
G, and taxes T given in the question, total planned expenditure PE is
P E = 200 + 0.75(Y − 100) + 100 + 100 = 0.75Y + 325.
This equation is graphed in Figure 7.
(b) To find the equilibrium level of income, combine the planned-expenditure equation derived in
part (a) with the equilibrium condition Y = P E:
Y = 0.75Y + 325
Y = 1, 300.
The equilibrium level of income is 1,300, as indicated in Figure 7.
(c) If government purchases increase to 125, then planned expenditure changes to P E = 0.75Y +350.
Equilibrium income increases to Y = 1, 400. Therefore, an increase in government purchases of
25 (i.e., 125 − 100 = 25) increases income by 100. This is what we expect to find, because the
formula for the government-purchases multiplier is 1/(1 − M P C ), the M P C is 0.75, and the
government-purchases multiplier therefore has a numerical value of 4.
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Figure 7: Planned Expenditure
(d) An income level of 1,600 represents an increase of 300 over the original level of income. The
government-purchases multiplier is 1/(1 − M P C ): the M P C in this example equals 0.75, so the
government-purchases multiplier is 4. This means that government purchases must increase by
75 (to a level of 175) for income to increase by 300.
Figure 8: Money Demand
4. (a) The downward sloping line in Figure 8 represents the money demand function (M /P )d =
1, 000 − 100r . With M = 1, 000 and P = 2, the real money supply (M /P ) s = 500. The real
money supply is independent of the interest rate and is, therefore, represented by the vertical
line in Figure 8.
(b) We can solve for the equilibrium interest rate by setting the supply and demand for real balances
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equal to each other:
500 = 1, 000 − 100r
r = 5.
Therefore, the equilibrium real interest rate equals 5 percent.
(c) If the price level remains fixed at 2 and the supply of money is raised from 1,000 to 1,200, then
the new supply of real balances (M/P)s equals 600. We can solve for the new equilibrium interest
rate by setting the new (M /P ) s equal to (M /P )d :
600 = 1, 000 − 100r
100r = 400
r = 4.
Thus, increasing the money supply from 1,000 to 1,200 causes the equilibrium interest rate to
fall from 5 percent to 4 percent.
(d) To determine at what level the Fed should set the money supply to raise the interest rate to 7
percent, set (M /P ) s equal to (M /P )d :
M /P = 1, 000 − 100r.
Setting the price level at 2 and substituting r = 7, we find:
M /2 = 1, 000 − 100 × 7
M = 600.
For the Fed to raise the interest rate from 5 percent to 7 percent, it must reduce the nominal
money supply from 1,000 to 600.
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