Homework 5-
1. Write down and interpret the following equations (without looking at your notes):
(a) GDP accounting equation (expenditure approach);
(b) National income accounting equation for Sprivate;
(c) National income accounting equation for Spublic;
(d) National income accounting equation for NS = Stotal = S;
(e) The most general equilibrium condition for the loanable funds market (you need to know this).
2. Use the Classical Model and the following information to answer this problem.
Classical Model:
Y = C + SP + T - TR
Y = C + I + G + (X - M)
KI = M - X
SG = T - TR - G
NS = SP + SG = Y - C - G
I = Y - C - G + KI
Leakages = Injections in Equilibrium or SP + T - TR + M = I + G + X
Note: in the table below iR is the real interest rate and in the problem it is expressed as a decimal: e.g. if the real interest rate is 20%, then iR enters the mathematical expression as .2.
|
Country
|
GDP
|
C
|
G
|
T - TR
|
M-X
|
SP
|
I
|
|
A
|
$5,000
|
3,500
|
700
|
300
|
-400
|
1000+2000 iR
|
800-4000 iR
|
a. Calculate the equilibrium real interest rate for country A.
b. Calculate the value of net exports for country A.
c. Calculate the supply of loanable funds and the demand for loanable funds in country A. Does the market for loanable funds clear in this country? That is, does the supply of loanable funds equal the demand for loanable funds?
d. Calculate NS + KI for each country and compare this sum with the value of investment. Use the classical model to prove the equality: NS + KI = I.
3. Use the following information about an economy and the Keynesian Model to answer the following questions. Assume that government spending and planned investment are constant at 1,675 and the net export level is originally fixed and has a value of -500.
|
Real GDP
|
C
|
Iplanned
|
G
|
T - TR
|
NX
|
AE
|
Unplanned change in inventories
|
|
8,000
|
6,200
|
1,675
|
1,675
|
1,600
|
-500
|
|
|
|
9,000
|
6,800
|
1,675
|
1,675
|
1,800
|
-500
|
|
|
|
10,000
|
7,400
|
1,675
|
1,675
|
2,000
|
-500
|
|
|
|
11,000
|
8,000
|
1,675
|
1,675
|
2,200
|
-500
|
|
|
|
12,000
|
8,600
|
1,675
|
1,675
|
2,400
|
-500
|
|
|
a. Given the above information, what is the marginal propensity to consume? Hint: you will want to find disposable income in order to calculate the marginal propensity to consumer: remember that the marginal propensity to consume = the change in consumption divided by the change in disposable income.
b. Given the above information, what is the level of autonomous consumption?
c. Given the above information, what is the macroeconomic equilibrium GDP? {Hint: once you have your consumption function from parts (a) and (c) you should be able to calculate this value.]
d. Suppose that planned investment spending is equal to 1,675 in this country and this level of planned investment spending does not change, no matter what the level of income is. If the current level of aggregate expenditure is equal to 13250, describe how this economy will respond to this level of aggregate expenditure given the model developed. In your answer comment on what is happening to unplanned investment spending, inventories, and the level of real GDP. Explain your answer fully.
e. Given the above information, what is the multiplier in this problem?
f. In order to increase real GDP, the government can choose to increase the government spending or decrease the tax revenue. Which policy is more effective in increasing real GDP?
4. This problem considers short-run and Long-run effects using the aggregate demand and aggregate supply model.
a. What factors shift the aggregate demand and aggregate supply curves?
b. Consider the following events:
i. Major fraud in the financial markets is uncovered by investigators and this leads to widespread concern about the integrity of all financial market transactions
ii. After a battle, many oil refineries were destroyed. This caused the price of oil to increase drastically.
iii. Recently, the department of mechanical engineering at the University of Wisconsin-Madison invents a high-tech product which greatly increases productivity. In your answer you will want to consider that if productivity increases and this increases the ability to produce output in the economy in the long run, then this increase in output will also affect aggregate demand. In your answer also remember that in the long run population increases.
For each of these events, determine:
- if the event causes a shift in the short run aggregate supply (SRAS) curve or the long run aggregate supply (LRAS) curve for the United States
- if the event is followed by an inflationary gap or a recessionary gap
- the long run adjustment process that occurs as a result of the event
5. Let:
C = consumption, I = investment spending, G = government spending, Tx = tax revenue, Y = national income, MS = money supply, MD = money demand (LP), i = interest rate.
Assume for a given closed economy:
(i) consumers spend $400 billion plus 90% of after-tax income, or C = 400 + 0.9(Y - Tx),
(ii) investment demand varies inversely with the interest rate, such that I = 700 - 2000i, (that is, if the interest rate is 10%, investors want to invest $700 billion minus 10% of $2,000 billion, or $500 billion in total),
(iii) currently government spending and taxes are both equal to $200 billion, or G = G- = 200, Tx = Tx- = 200,
(iv) the total money demand or liquidity preference schedule for this economy is an inverse function of the rate of interest and is given by the equation MD = 800 - 1000i, (that is, if the interest rate is 10%, the demand for money will be $800 billion minus 10% of $1,000 billion, or $700 billion in total),
(v) the required reserve ratio for banks in this economy is 15%. No bank holds excess reserves, and everybody keeps their money in the bank. The total of reserves in the banks is $90 billion.
a. What is the total money supply? (HINT: begin with (v) above.)
b. What is the equilibrium interest rate? (HINT: it is the result of supply of and demand for money.)
c. What is the equilibrium level of national income?
d. The economy is in a slump and the head of the central bank wants to increase the equilibrium level of national income to $10,000 billion using open market operations. Should she (the head of the central bank) buy or sell bonds to achieve this goal? How much in bonds (give a dollar figure) should she buy or sell? Assume that there are no other changes in the model except for this open market operation. Hint: you know how much aggregate output needs to be, but you will need to figure out what the interest rate must be in order for aggregate output to be at this level. Once you have the interest rate then you will need to calculate the implied money supply that results in this equilibrium interest rate.