# CH9

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```					1.(a)S d  –6000  4000r  0.8Y.

(b)       When Y  10,000,
r  0.05.

When Y  10,200,
r  .03.
(c) When G  2400, desired saving becomes S d  –6400  4000r  0.8Y. S d is now 400 less
for any given r and Y.

Setting S d  I d, we get
8000r  8800 – 0.8Y.

Similarly, using the equation that goods supplied equals goods demanded gives the
same anwer.
At Y  10,000, r  0.10. The market-clearing real interest rate increases from 0.05 to
0.10. Thus the IS curve shifts up and to the right from IS1 to IS2 in Figure 9.19.

Figure 9.19
2.(a)        Setting MS=MD:
r  –0.02  (Y/100,000).

When Y  8000, r  0.06.
When Y  9000, r  0.07.
These points are plotted as line LMa in Figure 9.20.

Figure 9.20

(b) M  6600,
r  –0.05  (Y/100,000).

When Y  8000, r  0.03.
When Y  9000, r  0.04.
The LM curve is shifted down and to the right from LMa to LMb in Figure 9.20, since
the same level of Y gives a lower r at equilibrium.
(c)Setting MS=MD:
r  – 0.03  (Y/100,000).

When Y  8000, r  0.05.
When Y  9000, r  0.06.
The LM curve is shifted down and to the right from LMa to LMc in Figure 9.20, since
there is a higher real interest rate for every given level of output. The LM curve
shifts down and to the right by one percentage point (the increase in  e ) because for
any given Y, the same nominal interest rate clears the asset market. With an
unchanged nominal interest rate, the increase in  e is matched by an equal decrease
in r.

3.   (a) Similar to quesiton2: use S d  Y – C d – G and S d  I d   for the IS curve
so Y  (960  2.5G) – 2500r.
When G  196, this is Y  1450 – 2500r.
the LM curve: Setting money demand equal to money supply so Y  19,780/P  50 
500 r.
With full-employment output of 1000 solving for r gives r  0.18.
Using Y  1000 and r  0.18 solving for P gives P  23. Plugging these results into
the consumption and investment equations gives C  694 and I  110.
(b) With G  216, r  .20, P  23.27, C  684, and I  100.

4.   (a) First, look at labor market equilibrium.
Labor supply is NS  55  10(1 – t)w. Labor demand (ND) comes from the equation
w  5A – (0.005A  ND). Substituting the latter equation into the former, and
equating labor supply and labor demand gives N  100. Using this in either the labor
supply or labor demand equation then gives w  9. Using N in the production
function gives Y  950.
(b) Next, look at goods market equilibrium and the IS curve.
S d  Y – C d – G and S d  I d gives
So r  (542.5  G)/450 – 0.004/3Y.
When G  50, this is r  1.317 – 0.004/3 Y.
With full-employment output of 950, r  0.05. C  654 and I  246.
(c) Next, look at asset market equilibrium and the LM curve.
Setting money demand equal to money supply r r  [0.5Y – (5  9150/P)]/250. With
Y  950 and r  0.05, solving for P gives P  20.
(d) With G  72.5, r  1.367 – 0.004/3 Y. With Y  950, r  .10, P  20.56, C  644, I 
233.5. The real wage, employment, and output are unaffected by the change.

5.       The IS curve is found by setting Setting S d  I d.

Desired saving is S d 
Y – C d – G  Y – [1275  0.5(Y –T) – 200r] – G. gives Y – [1275  0.5(Y – T) –
200r] – G  900 –200r, or Y  4350 – 800r  2G – T. The LM curve is M/P  L  0.5Y
– 200i  0.5Y – 200(r   )  0.5Y – 200r.
(a) T  G  450, M  9000. The IS curve gives Y  4800 – 800r. The LM curve gives
9000/P  0.5Y – 200r. To find the aggregate demand curve,
LM: 9000/P  0.5Y – 200r. Multiplying by 4 gives 36,000/P  2Y – 800r.
Rearranging gives 800r  2Y – 36,000/P.
IS: Y  4800 – 800r. Rearranging gives 800r  4800 – Y. Setting the right-hand sides
of these two equations to each other (since both equal 800r) gives: 2Y – (36,000/P) 
4800 – Y, or 3Y  4800  (36,000/P), or Y  1600  (12,000/P); this is the AD curve.
With Y  4600 at full employment, the AD curve gives 4600  1600  (12,000/P), or
P  4. From the IS curve Y  4800 – 800r, so 4600  4800 – 800r, or 800r  200, so
r  0.25. Consumption is C  1275  0.5(Y – T) – 200r  1275  0.5(4600 – 450) –
(200 × 0.25)  3300. Investment is I  900 – 200r  900 – (200 × 0.25)  850.
(b) Following the same steps as above, with M  4500 the aggregate demand curve AD:
Y  1600  (6000/P). With Y  4600, this gives P  2. Nothing has changed in the IS
equation, so it still gives r  0.25. And nothing has changed in either the
consumption or investment equations, so we still get C  3300 and I  850. Money is
neutral here, as no real variables are affected and the price level changes in
proportion to the money supply.
(c) T  G  330, M  9000. The IS curve is Y  4350 – 800r  2G – T  4350 – 800r 
(2  330) – 330  4680 – 800r.
LM: 36,000/P  2Y – 800r, or 800r  2Y – 36,000/P.
IS: Y  4680 – 800r, or 800r  4680 – Y.
AD: 2Y – (36,000/P)  4680 – Y, or (36,000/P)  4680  3Y, or Y  1560 
(12,000/P).
With Y  4600 at full employment, the AD curve gives 4600  1560  (12,000/P), or
P  3.95. From the IS curve, Y  4680 – 800r, so 4600  4680 – 800r, or 800r  80,
so r  0.10. Consumption is C  1275  0.5(Y – T) – 200r  1275  0.5(4600 – 330)
– (200  0.10)  3390. Investment is I  900 – 200r  900 – (200  0.10)  880.

6. (a) A  2, f1  5, f2  0.005, n0  55, nw  10, c0  300, cY  0.8, cr  200, t0  20, t  0.5,
i0  258.5,
ir  250, l0  0, lY  0.5, lr  250.
(b) These values are all calculated directly, using the equations in the Appendix. They
should match the results in Numerical Problem 4, above.

(c) See the answer to part b.

Analytical Problems

1. (a) The increase in desired investment shifts the IS curve up and to the right, as shown in
Figure 9.21. The price level rises, shifting the LM curve up and to the left to restore
equilibrium. Since the real interest rate rises, consumption declines. In summary, there
is no change in the real wage, employment, or output; there is a rise in the real interest
rate, the price level, and investment; and there is a decline in consumption.

Figure 9.21
(b) The rise in expected inflation shifts the LM curve down and to the right, as shown in
Figure 9.22. The price level rises, shifting the LM curve up and to the left to restore
equilibrium. Since the real interest rate is unchanged, consumption and investment are
unchanged. In summary, there is no change in the real wage, employment, output, the
real interest rate, consumption, or investment; and there is a rise in the price level.

Figure 9.22

(c) The increase in labor supply is shown as a shift in the labor supply curve in Figure
9.23 (a).
This leads to a decline in the real wage rate and an increase in employment. The rise
in employment causes an increase in output, shifting the FE line to the right in
Figure 9.23 (b).
To restore equilibrium, the price level must decline, shifting the LM curve down and
to the right. Since output increases and the real interest rate declines, consumption
and investment increase.
In summary, the real wage, the real interest rate, and the price level decline; and
employment, output, consumption, and investment rise.
Figure 9.23

(d) The reduction in the demand for money gives results identical to those in part (b).
2.   The increase in the price of oil reduces the marginal product of labor, causing the labor
demand curve to shift to the left from ND1 to ND2 in Figure 9.24. Since households’
expected future incomes decline, labor supply increases, shifting the labor supply curve
from NS1 to NS2 (but by assumption, the shift to the left in labor demand is larger than
the shift to the right in labor supply). At equilibrium, there is a reduced real wage and
lower employment. The productivity shock results in a shift to the left of the
full-employment line from FE1 to FE2 in Figure 9.25, as both employment and
productivity decline. Because the shock is permanent, it reduces future output and
reduces the future marginal product of capital, both of which result in a downward shift
of the IS curve. The new equilibrium is located at the intersection of the new IS curve
and the new FE line. If, as shown in the figure, this intersection lies above and to the left
of the original LM curve, the price level will increase and shift the LM curve upward
(from LM1 to LM2) to pass through the new equilibrium point. The result is an increase
in the price level, but an ambiguous effect on the real interest rate. Since output is lower,
consumption is lower. Since the effect on the real interest rate is ambiguous, the effect
on saving and investment are ambiguous as well, though the fall in the future marginal
product of capital would tend to reduce investment.

Figure 9.24

Figure 9.25
The result is different from that of a temporary supply shock; when the shock is
temporary there is no impact on future output or the marginal product of capital, so the
IS curve does not shift. In that case the price level increases to shift the LM curve up and
to the left from LM1 to LM2 in Figure 9.26 to restore equilibrium. In that case, the real
interest rate unambiguously increases. Under a permanent shock, the IS curve shifts
down and to the left, so the rise in the real interest rate is less than in the case of a
temporary shock, and the real interest rate can even decline.

Figure 9.26

3. (a) The decrease in expected inflation increases real money demand, shifting the LM
curve up, as shown in Figure 9.27. The real interest rate rises and output declines.

Figure 9.27
(b) The increase in desired consumption shifts the IS curve up and to the right, as shown
in
Figure 9.28. This causes the real interest rate and output to rise.

Figure 9.28

(c) The increase in government purchases shifts the IS curve up and to the right, with
the same result as in part (b). (The FE line also shifts, as the increase in government
expenditures reduces people’s wealth and leads them to increase labor supply, but
this shift will not affect the short-run equilibrium, as the economy will be off the FE
line.)
(d) If Ricardian equivalence holds, the increase in taxes has no effect on either the IS or
LM curves, so there is no change in either the real interest rate or output. If Ricardian
equivalence doesn’t hold, so that the increase in taxes reduces consumption
spending, the IS curve shifts down and to the left, as shown in Figure 9.29. Both the
real interest rate and output decline.

Figure 9.29

(e) An increase in the expected future marginal productivity of capital shifts the IS curve
up and to the right, with the same result as in part (b).
4.   The change in Eq. (9.B.10) has no effect on employment, the real wage, or output. The
only effect this has is on the term IS, which is now IS  [1 – (1 – t)cY – iY]/(cr  ir). The
real interest rate and price level are still determined by Eqs. (9.B.22) and (9.B.23),
respectively.

5.   The change in the money demand function affects only the equation determining the
price level,
Eq. (9.B.23). It is now

P  M/[l0  lY Y – lr(IS – IS Y   e – im)]
CH10
Numerical Problems

1.   (a) Labor supply is given by the equation NS  45  0.1w. Before the shock, labor
demand is determined by the equation w  1.0(100 – N). Setting labor supply equal
to labor demand by substituting the labor demand equation into the labor supply
equation gives N  45  0.1 w  45  [0.1  1.0(100 – N)]  45  10 – 0.1N, or 1.1 N
 55, so N  50. Then w  1.0(100 – N)  50. Output is Y  1.0[(100  50) – (0.5 
502)]  3750.
After the shock, repeating the above steps gives N  45  0.1 w  45  [0.1 
1.1(100 – N)] 
45  11 – 0.11N, or 1.11 N  56, so N  50.45. Then w  1.1(100 – N)  54.505.
Output is Y  1.1[(100  50.45) – (0.5  50.452)]  4150.
(b) Now NS  10  0.8w. Before the shock, N  10  0.8 w  10  [0.8  1.0(100 –
N)]  10  80 – 0.8N, or 1.8 N  90, so N  50. Then w  1.0(100 – N)  50. Output
is Y  1.0[(100  50) –
(0.5  502)]  3750.
After the shock, N  10  0.8 w  10  [0.8  1.1(100 – N)]  10  88 – 0.88N, or
1.88 N  98,
so N  52.13. Then w  1.1(100 – N)  52.66. Output is Y  1.1[(100  52.13) – (0.5
 52.132)]  4240.
(c) If the real wage is only slightly procyclical, then a flat labor supply curve, as in
part (b) is necessary, rather than a steep labor supply curve as in part (a). Figure 10.4
illustrates the difference in slopes of the two labor supply curves. When labor
demand increases from ND1 to ND2, the real wage rises a lot (from w1a to w2a) with a
steep labor supply curve, but the real wage rises only a little bit (from w1b to w2b) if
the labor supply curve is fairly flat. A calibrated RBC model would fit the facts
better if the labor supply curve were fairly flat, that is, labor supply is sensitive to the
real wage, as in part (b).

Figure 10.4
2.    The IS curve gives Y  C  I  G  600  0.5(Y – T) – 50r  450 – 50r  G  1050
– 100r  0.5Y – 0.5T  G, or 0.5Y  1050 – 100r – 0.5T  G, or Y  2100 – 200r – T
 2G. The LM curve gives M/P  L  0.5Y – 100i  0.5Y – 100(r   )  0.5Y –
100(r  0.05)  0.5Y – 100r – 5.
(a) M  4320, G  T  150. The IS curve is Y  2100 – 200r – T  2G  2100 – 200r –
150  (2  150)  2250 – 200r. Output must be at its full-employment level of 2210.
From the IS curve, 2210  2250 – 200r, or 200r  40, so r  0.20. Using this in the LM
curve to find the price level gives M/P  0.5Y – 100r – 5, or 4320/P  (0.5  2210) –
(100  0.20) – 5, so P  4320/(1105 – 20 – 5)  4320/1080  4. Then consumption is C
 600  0.5(Y – T) – 50r  600  0.5(2210 – 150) – (50  0.20)  600  1030 – 10 
1620. Investment is I  450 – 50r  450 – (50  0.20)  440.
(b) When M increases to 4752, nothing in the IS curve is affected, so Y and r are
the same as in part (a), as are C and I. The LM curve becomes 4752/P  1080, or P 
4.4. No real variables are affected, and the price level rises 10% just as the money
supply did, so money is neutral.
(c) When G  T  190, the IS curve shifts. It becomes Y  2100 – 200r – T  2G 
2100 – 200r –
190  (2  190)  2290 – 200r. With Y  2210, this gives 2210  2290 – 200r, or
200r  80,
so r  0.40. From the LM curve, 4320/P  0.5Y – 100r – 5  (0.5  2210) – (100 
0.40) – 5 
1105 – 40 – 5  1060, so P  4320/1060  4.075. C  600  0.5(Y – T) – 50r  600 
0.5(2210 – 190) – (50  0.40)  600  1010 – 20  1590. I  450 – 50r  450 – (50 
0.40)  430. Fiscal policy is not neutral since the change in policy has real effects on
the interest rate, consumption, and investment.

3.    The IS curve is found by setting desired saving equal to desired investment. Desired
saving is S d  Y – C d – G  Y – [250  0.5(Y – T) – 500r] – G. Setting Sd  Id gives
Y – [250  0.5(Y– T) – 500r] – G  250 – 500r, or Y  1000 – 2000r  2G – T. The
LM curve is M/P  L  0.5Y – 500i  0.5Y – 500(r   e)  0.5Y – 500r.
(a) T  G  200, M  7650. The IS curve gives Y  1000 – 2000r  2G – T  1000
– 2000r 
(2  200) – 200  1200 – 2000r. The LM curve gives 7650/P  0.5Y – 500r. To find
the aggregate demand curve, eliminate r in the two equations by multiplying the LM
curve through by 4 and rearrange the resulting equation and the IS curve.
LM: 7650/P  0.5Y – 500r. Multiplying by 4 gives 30,600/P  2Y – 2000r.
Rearranging gives 2000r  2Y – 30,600/P. IS: Y  1200 – 2000r. Rearranging gives
2000r  1200 – Y. Setting the right-hand sides of these two equations to each other
(since both equal 2000r) gives: 2Y – (30,600/P)  1200 – Y, or 3Y  1200 
(30,600/P), or Y  400  (10,200/P); this is the AD curve.
With Y  1000 at full employment, the AD curve gives 1000  400  (10,200/P), or
P  17. From the IS curve Y  1200 – 2000r, so 1000  1200 – 2000r, or 2000r 
200, so r  0.10. Consumption is C  250  0.5(Y – T) – 500r  250  0.5(1000 –
200) – (500  0.10)  600. Investment is I  250 – 500r  250 – (500  0.10)  200.
(b) Following the same steps as above, with M  9000 instead of 7650, gives the
aggregate demand curve AD: Y  400  (12,000/P). With Y  1000, this gives P 
20. Nothing has changed in the IS equation, so it still gives r  0.10. And nothing has
changed in either the consumption or investment equations, so we still get C  600
and I  200. Money is neutral here, as no real variables are affected and the price
level changes in proportion to the money supply.
(c) T  G  300, M  7650. The IS curve is Y  1000 – 2000r  2G – T  1000 –
2000r  (2  300) – 300  1300 – 2000r. IS: Y  1300 – 2000r, or 2000r  1300 – Y.
LM: 30,600/P  2Y – 2000r, or 2000r  2Y – 30,600/P.
AD: 2Y – (30,600/P)  1300 – Y, or (30,600/P)  1300  3Y, or Y  433 1/3 
(10,200/P).
With Y  1000 at full employment, the AD curve gives 1000  433 1/3  (10,200/P),
or P  18. From the IS curve, Y  1300 – 2000r, so 1000  1300 – 2000r, or 2000r 
300, so r  0.15. Consumption is C  250  0.5(Y – T) – 500r  250  0.5(1000 –
300) – (500  0.15)  525. Investment is I  250 – 500r  250 – (500  0.15)  175.

4.    AD: Y  300  30(M/P), AS: Y  500  10(P – Pe), M  400.
(a) P e  60. Setting AD  AS to eliminate Y, we get 300  30(M/P)  500  10(P –
P e ). Plugging in the values of M and P e gives 300  (30  400/P)  500  10(P –
60), or 300  (12,000/P)  500  10P – 600, or 400  (12,000/P)  10P. Multiplying
this equation through by P/10 gives 40P  1200  P 2, or P 2 – 40P – 1200  0. This
can be factored into (P – 60)(P  20)  0. P can’t be negative, so the only solution to
this equation is P  60. At this equilibrium P  P e, so Y  500, and the economy is at
full-employment output.
(b) With an unanticipated increase in the money supply to M  700, the expected
price level is unchanged at Pe  60. The aggregate demand curve is Y  300 
30(M/P)  300  (30  700/P)  300  (21,000/P). The aggregate supply curve is Y
 500  10(P – Pe)  500  10(P – 60)  10P – 100. Setting AD  AS to eliminate Y
gives 300  (21,000/P)  10P – 100, or 400  (21,000/P)  10P, or P – 40 –
(2100/P)  0. Multiplying through by P gives P2 – 40P – 2100  0. This can be
factored as (P – 70)(P  30)  0, which has the positive solution P  70. From the
AD curve, Y  300  (21,000/P)  300  (21,000/70)  600.
(c) When M  700 and is anticipated, P  Pe. Then the AD curve is Y  300 
(21,000/P) and the AS curve is Y  500. Setting AD  AS gives 500  300 
(21,000/P), which has the solution P  105.

5.   (a) To find the Solow residual, use the equation for the production function,
dividing through to solve for A: A  Y/K 0.3N 0.7. Assuming there’s no change in
utilization rates, this is the measured Solow residual. Given that equation, plugging
in the values for Y, K, and N, gives the Solow residual as 1.435 in 2006 and 1.507 in
2007. The growth rate of the Solow residual is [(1.507/1.435) – 1]  100%  5.0%.
(b) With no change in utilization rates, the growth rate of the Solow residual equals
the growth rate of productivity (A), 5.0%.
(c) With a change in utilization rates, the production function is modified, as
shown in Eq. (10.2). Now productivity is measured as A  Y/(uKK) 0.3(uNN) 0.7 but the
Solow residual is still measured as in part (a). Setting uN  1 in year 2006 and 1.03 in
year 2007, we calculate the value of A as 1.435 in 2006 (as in part a), and 1.476 in
2007. This is an increase in productivity of [(1.476/1.435) –1] 100%  2.9%,
significantly less than the 5.0% increase in the Solow residual.
(d) Setting uN  1 in year 2006 and 1.03 in year 2007, and uK  1 in year 2006 and
1.03 in year 2007, we calculate the value of A as 1.435 in 2006 (as in part a), and
1.463 in 2007. This is an increase in productivity of [(1.463/1.435) – 1]  100% 
2.0%, again significantly less than the 5.0% increase in the Solow residual.
This problem illustrates the idea that the measured Solow residual grows faster
than productivity when the utilization rates of capital and labor increase.

6.       An example is shown in Figure 10.5. There are several long cycles in output.

Figure 10.5

7.      (a) With an unemployment rate of 5%, there are initially 5 million unemployed and
95 million employed. Since 1% of the employed become unemployed, 95 million 
.01  950,000 move from employment to unemployment each month. Since 19% of
the unemployed become employed, 5 million  .19  950,000 from unemployment
each month. Since the same number move from employed to unemployed as the
number moving from unemployed to employed, the unemployment rate remains 5%
in February and March.
(b) Note: All amounts are in millions.
April: Employed (E) to Unemployed (U): 95  .03  2.85. U to E is 5  .19  .95. So
U  5  2.85 – .95  6.9. The unemployment rate (u)  6.9%.
May: E to U: 93.1  .01  .931. U to E is 6.9  .19  1.311. So U  6.9  .931 –
1.311  6.52 and u  6.52%.
June: E to U: 93.48  .01  .9348. U to E is 6.52  .19  1.2388. So U  6.52 
.9348 – 1.2388  6.216 and u  6.216%.
July: E to U: 93.784  .01  .93784. U to E is 6.216  .19  1.18104. So U  6.216 
.93784 – 1.18104  5.9728 and u  5.9728%.

8.      (a)   IS  2.47,  IS  0.0004, LM  0, LM  0.001, lr  500, b  100.
(b) Y  [2.47  88,950/(P  500)]/(.0004  .001)  (2.47  177.9/P)/.0014
(c) Y  6000  100P – 2915  3085  100P; use this in the AD curve to eliminate
Y.
3085  100P  (2.47  177.9/P)/.0014; multiply through by P and .0014 to get
4.319P  .14P 2  2.47P  177.9, or .14P 2  1.849P – 177.9  0; use quadratic
formula:
P  29.65. Y  3085  100P  6050.
(d) Long run: Y  6000; 6000  (2.47  177.9/P)/.0014, so P  30.

Analytical Problems

1.   (a) The increase in MPK f leaves aggregate supply unchanged, since expected future
labor income and expected future wages are unchanged. But aggregate demand
increases, because firms increase investment, shifting the IS curve up and to the
right. There is no shift in either the LM curve or the FE line.
Figure 10.6(a) shows that the increase in aggregate demand causes no change in
output, since the AS curve is vertical, but the price level increases. Figure 10.6(b)
shows the shift up and to the right of the IS curve from IS 1 to IS 2. To get the
economy to equilibrium, the price level rises so that the LM curve shifts from LM 1
to LM 2. The real interest rate increases as a result. In the labor market, there is no
change in labor demand or supply, so employment and output are unchanged. Since
the real interest rate rises, saving increases and consumption declines. Since
investment equals saving, investment also rises.
Figure 10.6

(b) The misperceptions theory gets a different result. As shown in Figure 10.7, the shift
in the aggregate demand curve from AD1 to AD2 increases both output and the price
level as the economy moves along the short-run aggregate supply curve SRAS. The
difference in this result compared to the result in part (a) comes from producers
misperceiving the change in the price level as a change in relative prices, and
increasing their labor demand and output.
Figure 10.7

2.   (a) In the case of a permanent increase in government purchases, the income effect on
labor supply, which arises because the present value of taxes increases to pay for the
added government spending, is much higher than in the case of a temporary increase
in government spending. So workers increase their labor supply more when the
government spending change is permanent than when it is temporary.
(b) Desired national saving is unaffected by the change in government spending if the
change in consumption is just equal to the change in taxes, so there is no shift in the
saving curve. If investment is also unaffected by the change in government spending,
then the IS curve does not shift.

(c) Figure 10.8 shows the effect of the increase in government purchases on the
economy. The FE line shifts to the right from FE1 to FE2 due to the increase in labor
supply. To restore equilibrium, the price level must decline to shift the LM curve
from LM 1 to LM 2. So output rises and the real interest rate declines.

Figure 10.8

If consumption falls less than the increase in government purchases, the IS curve
shifts up and to the right from IS1 to IS2 in Figure 10.9. As a result of the shift in the
IS curve, the real interest rate and the price level will fall by less than in the case in
which current consumption falls by 100, and in fact, the real interest rate and the
price level may even rise if the IS curve shifts by a lot, as shown in the figure.
Figure 10.9
3.   The temporary increase in government purchases causes an income effect that increases
workers’ labor supply. This results in an increase in the full-employment level of
output from FE1 to FE2 in Figure 10.10. The increase in government purchases also
shifts the IS curve up and to the right from IS1 to IS2, as it reduces national saving.
Assuming that the shift up of the IS curve is so large that it intersects the LM curve to
the right of the FE line, the price level must rise to get back to equilibrium at full
employment, by shifting the LM curve up and to the left from LM1 to LM2. The result
is an increase in output and the real interest rate.

Figure 10.10

Figure 10.11 shows the impact on the labor market. Labor supply shifts from NS1 to NS2,
leading to a decline in the real wage and a rise in employment. Average labor
productivity declines, since employment rises while capital is fixed. Investment declines,
since the real interest rate rises.

Figure 10.11

To summarize, in response to a temporary increase in government purchases, output, the
real interest rate, the price level, and employment rise, while average labor productivity
and investment decline.
(a) The business cycle fact is that employment is procyclical. The model is consistent
with this fact, since employment rises when government purchases rise, causing
output to rise.
(b) The business cycle fact is that the real wage is mildly procyclical. The model is
inconsistent with this fact, since it shows a decline in the real wage when
government purchases rise and output rises.
(c) The business cycle fact is that average labor productivity is procyclical. The model
is inconsistent with this fact, since it shows a decline in average labor productivity
when government purchases rise and output rises.
(d) The business cycle fact is that investment is procyclical. The model is not consistent
with this fact, as investment falls when government purchases rise and output rises.
(e) The business cycle fact is that the price level is procyclical. The model is consistent
with this fact, as the price level rises when government purchases increase and
output increases.

4.   (a) An increase in expected future output increases money demand, so the LM curve
shifts up and to the left. As shown in Figure 10.12, the LM curve shifts from LM1 to
LM2. General equilibrium in the economy can be restored by shifting the LM curve
from LM2 to LM3, which occurs as the price level declines

Figure 10.12

(b) If the Fed wants to stabilize the price level, then it increases the money supply in
response to the increase in money demand, so that the LM curve shifts from LM2 to
LM3 without a decline in the price level. This represents reverse causation, because
the rise in future output causes the current money supply to increase. It might appear
that the rise in the current money supply caused the rise in future output because of
this timing, but in fact the reverse is true.
5.    The temporary wage tax has a small income effect but a large substitution effect, so
labor supply is reduced. As Figure 10.13 shows, this increases the (pretax) real wage rate
and reduces employment. The reduction in employment shifts the FE line from FE1 to
FE2 in Figure 10.14, while the increase in government purchases shifts the IS curve from
IS1 to IS2. To restore equilibrium, where IS, LM, and FE intersect, the price level must
rise, so that the LM curve shifts from LM1 to LM2. The result is an increase in the real
interest rate and a decline in output.

Figure 10.13

Figure 10.14
CH8
Analytical Problems
1. Figure 8.8 illustrates the business cycle. The current NBER method picks peaks and
troughs in the level of aggregate economic activity, which are points on the figure where
the slope of the line is zero. These are shown in Figure 8.8 as P1 (at the peak of the cycle)
and T1 (at the trough of the cycle). However, the older method picks peaks and troughs in
detrended economic activity. This means the peaks and troughs occur at points that are
the farthest away from the trend line, which means those points at which the slope of the
line showing aggregate economic activity is the same as the slope of the trend line. These
points are shown in Figure 8.8 as P2 and T2. Note that the point P2 occurs before P1,
meaning that peaks in detrended economic activity are earlier than peaks in the level of
economic activity. Note also that the point T2 occurs later than T1, which means that
troughs in detrended economic activity are later than troughs in the level of economic
activity. Since under the old method, troughs occur later and peaks occur earlier,
contractions appear to be longer and expansions appear to
be shorter using the pre-1927 method than using the current method. Thus the fact that
after World War II expansions were longer and contractions were shorter than before
World War I is somewhat illusory, since it’s based on two different accounting
mechanisms. If expansions and contractions were in fact equally long in both periods, the
change in accounting method would mean that our official
dating of the business cycle would show longer expansions and shorter contractions after
World War II than before World War I.

Figure 8.8

2.         Expenditure on durable goods is more sensitive to the business cycle than
expenditure on nondurable goods and services, because people can more easily
change the timing of their expenditure on durables. When economic activity is
weak, and people face the danger of losing their jobs, they avoid making durable
goods purchases. Instead, they may drive their cars a little longer before buying
new ones, get the old washing machine repaired instead of buying a new one, and
put off buying new furniture until a new expansion indicates greater income
security. So in a recession, durable purchases decline a lot, but when an expansion
begins, durable purchases pick up substantially. The exception was in the business
cycle that began in March 2001, when very low interest rates supported
expenditures on durable goods.

3.        (a) In symbols, let A  average labor productivity, Y  output, and H  total hours
worked. By definition, A  Y/H, so in growth terms, A/A  Y/Y – H/H. Since all
three are procyclical, they all move in the same direction over the business cycle. If
total hours worked varied more than output in an expansion, then H/H would be
greater than Y/Y, so that A/A would be negative, and average labor productivity
would be countercyclical. So it must be the case that output varies more than total
hours worked in an expansion. A similar argument holds in a contraction.
(b) That average labor productivity is procyclical helps explain why the Okun’s
Law coefficient is 2, not 1. A one-percentage point increase in unemployment is
approximately a one percent fall in employment. Thus, if there were no change in
average labor productivity, we might expect the percentage fall in output to equal the
number of percentage points that the unemployment rate rises. But since average
labor productivity moves in the same direction as output, it magnifies the output
effect of a given amount of unemployment.

4.   Figure 8.9 illustrates the effects of a demand shock. The economy begins in equilibrium
at point A, where the LRAS, SRAS, and AD curves intersect. The demand shock shifts
the aggregate demand curve to the left to AD. In the short run, the equilibrium is at
point B, where AD intersects SRAS. This is a point at which output has declined (a
recession), but the price level is unchanged. Over time, the short-run aggregate supply
curve shifts down to SRAS, restoring long-run equilibrium at point C. At this point,
output is back at its full-employment level and the price level has declined. Thus the
result of a demand shock on the price level is that the price level is unchanged in the
short run and declines in the long run. Since the 1973–1975 recession was one in
which the price level rose sharply, it must not have been due to a demand shock.

Figure 8.9

Figure 8.10 illustrates the effects of a supply shock. The economy begins in equilibrium
at point A, where the LRAS, SRAS, and AD curves intersect. The supply shock shifts
the long-run aggregate supply curve to the left to LRAS. The new equilibrium is at
point B, where AD intersects LRAS. This is a point at which output has declined (a
recession), but the price level has risen. This matches what happened in the
1973–1975 recession. Thus we conclude that the 1973–1975 recession was the result
of a supply shock, not a demand shock.
Figure 8.10

5.       Growth that is “too rapid” most likely refers to a situation in which the aggregate
demand curve has shifted to the right and, in the short run, intersects the SRAS
curve at a level of output that’s greater than the full-employment level of output
(Figure 8.11). This situation is associated with inflation because, in the long run,
prices will rise, shifting the SRAS curve up to intersect with the LRAS and AD
curves. The shock that is implicitly assumed to be hitting the economy is an
aggregate demand shock, since that’s the only shock that increases output in the
short run and inflation in the long run.

Figure 8.11

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