Download Macroeconomic Principles Problem Set 3 Answer Key

Macroeconomic Principles
Problem Set 3 Answer Key-Weeks 5, 6 and 7
1. Chapter 11, Problem 3, Page 323 (assume T=0)
Y
C
IP
7000
6100
400
8000
6900
400
9000
7700
400
10000
8500
400
11000
9300
400
12000
10100
400
13000
10900
400
G
1000
1000
1000
1000
1000
1000
1000
NX
500
500
500
500
500
500
500
a. What is the marginal propensity to consume implicit in these data?
Slope of AE line=mpc=change in C/change in Y=800/1000=0.8
b. What is the numerical value of the expenditure multiplier for this economy?
Expenditure Multiplier=1/(1-mpc)=1/(1-0.8)=5
c. What is the equilibrium level of real GDP?
Y*=12000
d. Suppose that government purchases decreased from 1000 to 400 at each level of income.
What would happen to equilibrium GDP?
Change in GDP=1/(1-mpc) x (change in G)=5 x (-600)=-3000
New Y**=Y*-3000=9000
2. Chapter 11, Problem 9, page 325
Calculate the change in real GDP that would result in each of the following cases, assuming
there are no automatic stabilizers or destabilizers.
a. Planned investment spending rises by $100 billion, and the MPC is 0.9.
Use expenditure multiplier: change in GDP=1/(1-0.9) x 100 billion=$1,000 billion.
b. Autonomous consumption spending decreases by $50 billion, and the MPC is 0.7.
Change in GDP=1/(1-0.7) x (-50 billion)=1/0.3 x (-50)=-$166.67 billion
c. Government purchases rise by $40 billion, while at the same time investment spending falls
by $10 billion. The MPC is 0.6.
Change in GDP=1/(1-0.6) x (40-10)=1/0.4 x (30)=$75 billion
3. Chapter 12, Problem 2, page 350.
Calculate the change in real GDP that would result in each of the following cases, assuming
there are no automatic stabilizers or destabilizers and the MPC=0.8.
a. Taxes fall by $30 billion.
Tax multiplier: change in GDP = -mpc/(1-mpc) x (change in Taxes)
Change in GDP=-0.8/(1-0.8) x (-30) = $120 billion
b. Government spending and taxes both rise by $30 billion.
Change in GDP Taxes: -0.8/(1-0.8) x (30)=-$120 billion
Change in GDP G: 1/(1-0.8) x (30)=$150 billion
Total Change in GDP=$150 billion - $120 billion=$30 billion
c. Government spending and taxes both fall by $30 billion.
Change in GDP Taxes: -0.8/(1-0.8) x (-30)=$120 billion
Change in GDP G: 1/(1-0.8) x (-30)=-$150 billion
Total Change in GDP=$120 billion - $150 billion=-$30 billion
4. Chapter 12, Problem 5, page 350
You are running for reelection as president of the nation of Utopia. Your opponents have
criticized you for allowing the national debt to grow by almost 50 percent over the last 4 years.
Use the following statistics, measured in millions of dollars, to defend yourself to Utopia’s
voters.
National Debt :
Year 1=$152
Year 4=$200
Nominal GDP:
Year 1=$3,042
Year 4=$4,098
Price index:
Year 1=45
Year 4=72
Debt/GDP Year 1=152/3042=0.05
Debt/GDP Year 4=200/4098=0.049
Real GDP Year 1=3042/45=67.6
Real GDP Year 4=4098/72=56.9
Debt/GDP ratio decreased, which is good for the economy. However, the price level increase is
responsible for a significant increase in nominal GDP. The real GDP between year 1 and year 4
decreased, which may be of concern for voters.
5. You are given the following information about an economy.
Nominal Debt in 2005: $100,000
Nominal Debt in 2012: $400,000
Nominal GDP: $500,000
Nominal GDP: $1,000,000
a. What is the debt-to-GDP ratio in 2005? In 2012? Explain why the government should be more
worried about the debt-to-GDP ratio than the nominal size of the debt?
Debt/GDP
2005: 100,000/500,000=0.20
2012: 400,000/1,000,000=0.40
Debt/GDP is a measure of the ability of the government to pay back the debt. What is
considered a large debt to one country, may be small to another, larger country. The debt/GDP
ratio allows for comparison of debt situations across countries, recognizing that the income of
countries can differ dramatically.
b. The government of Xavier must pay yearly interest on the debt. The interest rate is 10%.
What is the size of the interest payment in 2005? What must the tax rate be in order for tax
revenue to cover the interest payment in 2005?
Interest Payment
2005: 0.10 x 100,000=10,000
Tax rate=10,000/500,000=0.02=2%
c. In 2012, the interest rate is still 10%. What is the size of the interest payment in 2012? What
must the tax rate be in order to cover the interest payment in 2012?
Interest Payment
2012: 0.10 x 400,000=40,000
Tax rate=40,000/1,000,000=0.04=4%
d. If the CPI in 2005 was 240 and the in 2012, the CPI was 250, calculate the real GDP in each
year.
Real GDP 2005: 500,000/240=2083.33
Real GDP 2012: 1,000,000/250=4000
6. Chapter 12, Problem 7, page 351
Are either of the following countries violating the minimal guidelines for responsible
government as outline in the text (and lecture)?
Country A
Year
Debt
GDP
1999
2000
2001
1
2
3
100
110
150
Country B
Year
Debt
GDP
1999
2000
2001
1236
1346
1406
1400
1550
1707
Country A is in trouble. Between 1999 and 2000, the debt grew by 100% but GDP only grew by
10%; from 2000 to 2001, the debt grew again by 50%, but GDP grew only by 36%. In country B,
between 1999 and 2000, the debt grew by about 9% while GDP grew by about 11%; from 2000
to 2001, the debt grew by about 4.5% and GDP grew by about 10%. Country B meets the basic
debt guideline.
7. A bank that represents the entire economy has its balance sheet shown below:
Bank’s Balance Sheet (RRR=0.10)
Assets: what they have/what is owed to them
Liabilities: what they owe
Loans=1350
Deposits=1500
Total reserves=150
Cash in Vault=100
Acct. with FED=50
a. In table.
b.
Bank’s Balance Sheet (RRR=0.10)
Assets: what they have/what is owed to them
Loans=1800
Total reserves=200
Cash in Vault=100
Acct. with FED=100
Liabilities: what they owe
Deposits=2000
8. Chapter 13, Problem 1, Page 384
Suppose the required reserve ratio is 0.2. If an extra $20 billion in reserves is injected into the
banking system through an open market purchase of bonds, by how much will the money supply
increase? Would your answer be different if the required reserve ratio were 0.1?
With the required reserve ratio equal to 0.2, a $20 billion reserve injection can increase the
money supply by a maximum of $20 billion  (1/0.2) = $100 billion. With a required reserve ratio
of 0.1, the money supply can increase by $20 billion  (1/0.1) = $200 billion.
9. Chapter 13, Problem 8, Page 384
Suppose that the money supply is $3.2 trillion. Decision makers at the Federal Reserve decide
that they wish to use open market operations to increase the money supply by $500 billion. If
the required reserve ratio is 0.10, what does the Fed need to do to carry out the planned
increase? What if the required reserve ratio is 0.15?
To find the answer, substitute the desired change in the money supply ($500 billion) and the
money multiplier (10 = 1/0.10) into the equation for the change in the money supply, and solve
for the change in reserves:
$500 billion = 10 x Reserves Reserves = $500 billion/10 = $50 billion
The Fed will need to increase initial deposits by $50 billion. It can do this by buying
government bonds worth $50 billion from the public.
If the required reserve ratio is 0.15 (so that the money multiplier = 1/0.15 = 6.67), the Fed will
need to increase initial deposits by $500 billion/(6.67) = $74.96 billion. It can do this by buying
government bonds worth $74.96 billion from the public.
10. Chapter 13, Problem 9, Page 389
For each of the following situations, determine whether the money supply will increase,
decrease or stay the same.
a. Depositors become concerned about the safety of depository institutions.
Depositors will withdraw reserves, so the money supply will decrease.
b. The Fed lowers the required reserve ratio.
Banks will find themselves with excess reserves, which they will lend out, so the
money supply will increase.
c. The economy enters a recession and banks have a hard time finding credit-worthy
borrowers.
Banks will decrease their lending and accumulate excess reserves; the volume of loans and
deposits will shrink, and the money supply will decrease.
d. The Fed sells $100 million of bonds to First National Bank of Ames, Iowa; banks never
hold excess reserves; and the public doesn't change its cash holdings.
This open market operation will take reserves out of the banking system; the money
supply will decrease.
e. The Fed buys $100 million of bonds of First National Bank of Ames, Iowa, but the interest
rate banks can earn from lending is the same as the interest rate the Fed pays on reserves.
The money multiplier is zero, because new reserves are just held as excess reserves.