Econ 1 - Problem Set 9 With Solutions

Problem Set 9 This problem set is completely optional, and it is just designed to give you the opportunity to practice more before the exams. Do not hand in your answers; no points will be awarded. 1. For each of the following factors, discuss whether it would change the natural rate of unemployment, why, and how. Make sure your explanations encompass all factors, even those that do not change the natural rate of unemployment. (a) Real GDP increases due to higher government spending. (b) Changes in atmospheric conditions disable all long distance real-time communication (for example, phone, internet) permanently. (c) Technology stops improving, reducing the creation and destruction of economic sectors. 2. Suppose President Bush is concerned about the size of the U.S. trade deficit and convinces Congress to increase tariffs on imports, while he manages to convince other countries not to retaliate and increase their tariffs on U.S. products. (a) What will be the short and long run effects of this policy on real GDP, inflation, real interest rate, consumption, investment, and net exports? Use three graphs (AD/IA, Keynesian cross/expenditure line, and monetary policy rule) to show your answer and explain verbally. (b) Now use the spending allocation model to analyze the long run effects of the higher tariffs on imports. Explain verbally and graphically. (c) Is your long run analysis using the AD/IA model in part (a) consistent with your long run analysis using the SAM model in part (b)? Point out any similarities and differences in your conclusions to parts (a) and (b). 3. American consumers spend much more of their income than consumers in most other countries, spurred on in part by the wide availability of credit. Congress, hoping to inspire higher savings rates, passes a law limiting each American to one credit card. Assuming the rule has the desired effect of increasing saving rates, what effect will this have on the economy? Give your answer, both graphically and in words (a brief explanation will suffice), according to each of the following three models: (a) Use the Spending Allocation Model (SAM) to show the long run effects of the change in policy. Be sure to show and explain what happens to each component share of the economy and what happens to interest rates. (b) Use the Expenditure Model (the “Keynesian Cross”) to show short run effects. Assume that autonomous consumption does not change. Be sure to explain and demonstrate what happens to output and spending.

(c) Use the AD/IA model to show short and long run effects. Make sure your analysis includes the effects on GDP, inflation, interest rate (real and nominal), C, I, G, and X. Taylor, fourth edition, chapter 24, problems 3, 4, 5, 6, and 7. Taylor, fourth edition, chapter 25, problems 5, 6, and 7.

Problem Set 9 Solutions Economics 1 Fall 2005 Question 1 Remember that natural unemployment is the unemployment rate that exists when real GDP is equal to potential GDP. Cyclical unemployment, on the other hand, is unemployment due to deviations from potential GDP during recessions and booms. Natural unemployment consists of frictional unemployment (arising from normal turnover in the labor market) and structural unemployment (arising from structural problems). (a) If real GDP increases due to higher government spending, then real GDP has departed from potential GDP. This therefore lowers the cyclical unemployment rate but does not affect natural unemployment. (b) We would expect the destruction of long-distance communication capabilities to increase frictional unemployment as it would make it harder for people changing occupations to find new jobs and harder for new entrants in the labor markets to locate jobs. This change would therefore increase the natural rate of unemployment. (c) Since the lack of technological improvement is said to reduce the creation and destruction of economic sectors, this would decrease structural unemployment because there would be fewer changes in demand for different types of labor and skills in different sectors. Therefore we would expect this change to decrease the natural rate of unemployment. Question 2 a) Initially, the economy is in equilibrium, as shown on the graphs below. Monetary Policy Rule

AD-IA Inflation

Potential GDP

R

MPR

Keynesian Cross

Spending

45o line Exp0(At Ro)

R0

IA0 AD0 Y0

Real GDP

Inflation

INF0

Real GDP

Y0

When President Bush increases tariffs on imports, this decreases imports. Since other countries do not retaliate, exports do not change. Since net exports (X) = exports – imports, the overall result is in an increase in net exports. Thus, the expenditure line shifts up, which causes the aggregate demand curve to shift out. Monetary Policy Rule

AD-IA

Keynesian Cross

Potential GDP R

Inflation

MPR

Spending

45o line ExpSR(At R0) Exp0(At R0)

R0

IA0 AD1

AD0 Y0

YSR

Real GDP

INF0

Inflation

Y0

YSR

Real GDP

1

In the SR. Real GDP increases and inflation stays constant. Nothing changes in the monetary policy rule graph because inflation is constant and the Federal Reserve has not changed the monetary policy rule. Thus, real interest rate is constant. Consumption increases because of the increase in real GDP. Investment stays constant. The effect on net exports is a little more complicated. The increase in income tends to increase imports (which decreases net exports) but President Bush’s policy tends to decrease imports (which increases net exports). Overall net exports have increased. Please note that the analysis above disregards the fact that consumption includes both domestic and imported goods. If you do take this information into account, there are two possible approaches: 1) A simple approach would consider that the decrease in imports is exactly matched by a decrease in consumption of imported goods. These effects nullify each other, the expenditure line does not shift, the aggregate demand does not shift, and real GDP is unchanged. 2) A more sophisticated approach would take into account the fact that the tariff on imports would make imported goods relatively more expensive than domestically produced goods (compared to the pre-tariff situation). Thus, consumers would switch some of their purchases away from imported goods and increase their consumption of domestic goods. The net effect would be that the expenditure line shifts up, the aggregate demand shifts to the right, and real GDP increases. * For the purpose of this problem set, any of the three answers will be considered correct. Note, however, that the third answer is the best.

In the LR. Because real GDP > potential GDP, inflation begins to rise. As inflation rises, the Federal Reserve raises the real interest rate according to the monetary policy rule, causing a movement along the new aggregate demand curve. This continues until real GDP = potential GDP. In the long run, the higher real interest rate reduces consumption and investment. Net exports, however, have increased. In Summary GDP

SR LR

Inflation Rate

C

I

X

G

up

Real Interest Rate same

same

up

same

up

same

same

Up

up

down

down up

same

2

AD-IA Inflation

Monetary Policy Rule

Potential GDP

R

MPR

Keynesian Cross

Spending

45o line

RLR

ExpSR(At Ro)

IALR IASR

ExpLR(At RLR)

R0

AD1

AD0 YLR

INF0 INFLR

YSR

YLR YSR

Real GDP

b) Long -run effects can also be analyzed with the Spending Allocation (SAM) model. The 1-G/Y net export curve shifts up and to the right, causing an increase in the non-government share curve. This increases the equilibrium interest rate, which causes a decrease in C/Y and I/Y. Since C/Y and I/Y have both decreased, while G/Y has remained constant (by assumption), X/Y must have increased. R

R

R

R

R1 R0

C/YLR C/Y0

C/Y

I/YLR I/Y0

I/Y

X/Y0 X/YLR

X/Y

NG/Y

c) The LR results from the AD-IA model are consistent with the SAM model. C/Y, I/Y have gone down, while X/Y has gone up. The real interest rate has increased. The only difference lies in the fact that the AD-IA model demonstrates that inflation has also increased – a fact not readily apparent from the SAM model. Question 3 a) If the one credit card limit induces higher savings, individuals will spend less of their income and consumption will fall. Using the SAM model, we find that C/Y will shift to the left. In turn, this shifts the non-government share curve downward, and the equilibrium interest rate falls. Hence, we will observe a movement along the I/Y and X/Y curves, increasing their respective shares of GDP. G/Y remains constant (by assumption). (Note that the effect on C/Y might be seen as ambiguous, because there is a shift to the left and then movement along the curve to the right. However, since the interest rate does not affect C/Y very much, we may assume that the net change is a decrease.) 1-G/Y R

R

R

R

R0 R1

C/YLR C/Y0

C/Y

I/Y0 I/YLR

I/Y

X/Y0 X/YLR

X/Y

NG/Y

3

b) The vertical intercept of the consumption line represents what is known as “autonomous consumption,” the part of consumption spending that is independent of income. In this question, we are told that autonomous consumption does not change. However, we would still expect the one credit card limit to decrease the marginal propensity to consume (MPC) where MPC = change in income/change in consumption i.e. the slope of the expenditure line. In the short run, according to the Keynesian Cross model, the expenditure line will have a smaller slope, therefore “rotating” down. The intersection of the expenditure line with the 45-degree line now occurs at a lower level of spending and real GDP. 45o line Spending Exp0 ExpSR (lower MPC)

YSR

Y0

Real GDP

c) In the SR. Higher savings implies less consumption which shifts the AD curve to the left. At this point, real GDP is lower than potential GDP. Prices are “sticky” in the short run and remain constant. Therefore inflation remains unchanged as does the real interest rate. Because nominal interest rate = real interest rate + inflation, the nominal interest rate remains constant as well. As interest rates have not changed, investment stays the same. With lower real GDP, income is down, so net exports will rise because the lower level of income in the United States means that people will import less from abroad (recall that net exports (X) = exports – imports). Government spending is not affected as the assumption is government spending does not depend on income. In the LR. Because real GDP < potential GDP, inflation begins to fall. As inflation falls, the Federal Reserve lowers the real interest rate causing a movement along the new aggregate demand curve. This continues until real GDP = potential GDP. In the long run, the lower real interest rate increases investment and net exports. The effect on consumption is a little more complicated. The lower interest rate tends to increase consumption but if the one credit card policy is permanent, it will tend to decrease consumption. Overall consumption thus decreases. Government spending remains unchanged. In Summary GDP

SR LR

Nominal Inflation Interest Rate Rate same same

C

I

X

G

Down

Real Interest Rate same

down

same

up

same

Same

down

down

down

up

up

same

down

4

Inflation

Potential GDP

IASR

SR

IALR

LR

AD0 AD1

YSR

YLR

Real GDP

Taylor Chapter 24, Problem 3 on Page 625. If the real interest rate in the United States rises, international investors will be more inclined to put funds in dollar-denominated assets as they can earn more from doing so. Thus, they will shift their funds from Tokyo to New York in order to take advantage of the higher interest rate. As funds are shifted to the United States, the demand for dollars increases. This increased demand puts upward pressure on the dollar exchange rate, and causes the dollar to appreciate against the yen. A higher dollar exchange rate will tend to make goods imported into the United States more attractive because it makes these foreign goods cheaper, and make exported goods less attractive to other countries since it makes American goods more expensive. With more imports and fewer exports, U.S. net exports will fall. Taylor Chapter 24, Problem 4 on Page 625. If the Fed shifts from rule 1 to rule 2, higher real interest rates decrease aggregate spending and thus shift the AD curve to the left. The Fed might change its policy to end a prolonged episode of high inflation expectations or perhaps to aggressively anticipate future inflation. Alternatively, the Fed may simply become more hawkish in its policy toward inflation. The change will decrease real GDP. Alternative Policy Rules Interest Rate 12

Rule 2

10

Rule 1

8 6 4 2 0 0

2

4

6

8 Inflation 5

Taylor Chapter 24, Problem 5 on Page 625. a) The rates are 0 in the United States and 1 percent in Europe, respectively.

b) Both rules have nominal interest rates rising by more than inflation so that the real interest rate will rise. The slope of the policy rule for the ECB is 0.2, compared to 0.5 for the Fed. So, the Fed is more aggressive in terms of raising real rates – and hence has a lower tolerance for inflation – than the ECB. Taylor Chapter 24, Problem 6 on Page 625. a)

b) The average rate of inflation is 3 percent, since the real GDP deviation from trend is zero in the long run. c) The central bank permanently increases the money supply by 2 percent, and so inflation permanently increases by 2 percent.

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Taylor Chapter 24, Problem 7 on Page 625. (a) For the United States, net exports fall so that the expenditure line shifts down. (b) AD shifts to the left, and real GDP decreases. In the diagram below, EXP0 is the old expenditure line and EXP1 is the new expenditure line, while AD0 is the old aggregate demand curve and AD1 is the new aggregate demand curve. Keynesian Cross

AD-IA

Spending

Inflation

Potential GDP

45o line EXP0

IASR

SR EXP1

IALR

LR AD0 AD1

YSR

Y0

Real GDP

Real GDP

Taylor Chapter 25, Problem 5 on Page 644. a) As the figure in part b) shows, the current deviation from potential GDP is 2 percent. b) Inflation will be 3 percent at potential GDP of $5,000 billion. The adjustment occurs because the GDP deviation from potential is 2 percent. This puts upward pressure on wages and prices that increases the rate of inflation. This will occur because as contracts are renewed, they will reflect altered expectations about inflation so that gradually the inflation rate will increase until it reaches 3 percent. Potential GDP 6

Inflation (percent)

5 4 3

IA

2 1

AD line

0 -5%

-4%

-3%

-2%

-1%

0%

1%

2%

3%

4%

5%

Deviation of Real GDP from Potential GDP (percent)

7

Taylor Chapter 25, Problem 6 on Page 644. a) The Fed policy rule shifts to the left; it slows the growth of money to a rate compatible with 2 rather than 3 percent inflation. This goal is accomplished by the open market sale of government securities, which reduces liquidity in the financial system. b) The scenario starts from potential GDP of $5,000 billion and inflation at 3 percent. The decrease in the growth of money shifts the AD line from AD0 to AD1. In the short run, the shift in the AD line results in a negative deviation of real GDP from potential of 2 percent, since AD1 has real GDP equal to $4,900 billion at inflation of 3 percent. Potential GDP 6

Inflation (percent)

5 4 3

IA0

2

IA1

1

AD1

AD0

0 -8%

-6%

-4%

-2%

0%

2%

4%

6%

Deviation of Real GDP from Potential GDP (percent)

c) The negative deviation from potential in part b) reduces income through the multiplier. In the short run, consumption spending falls, net exports spending rises, and investment spending remains the same. The lower inflation target takes effect in the medium run as real interest rates decline so that investment spending increases. In the long run, the decline in inflation and real interest rate increases C, X, and I spending until potential GDP is reached. Taylor Chapter 25, Problem 7 on Page 644. a) In the short run GDP is below potential at SR. The Fed is assumed to raise interest rates, consistent with the description in the text. b) This is portrayed in Text Figure 25.6. Real GDP may fall and inflation may increase, but only temporarily. See the discussion of temporary shifts in the inflation adjustment line on page 637.

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