Homework 4-
1. Use the loanable funds framework for this problem. Suppose that initially in an economy net taxes, T - TR, are equal to $400 while government expenditures are equal to $400. Furthermore, suppose you know that this economy is initially a closed economy. You are told that the demand for loanable funds by businesses is given by the equation
r = 10 - (1/100)LFD
where r is the interest rate expressed as a percent rather than a decimal and LFD is the quantity of loanable funds demanded. You also know that the supply of loanable funds curve (LFS) curve is given by the equation
r = 2 + (1/300) LFS
where LFS is the quantity of loanable funds supplied.
a. Calculate the initial value of government savings, Sg.
b. Calculate the initial value of capital inflows for this economy.
c. Calculate the equilibrium interest rate, the equilibrium level of investment spending, and the equilibrium level of private savings given the above information.
d. Suppose that government spending increases to $500 while net taxes remain at $400. Calculate government saving, Sg. Is the government running a budget deficit, a budget surplus, or a balanced budget?
e. Suppose we model the government's deficit as additional demand for loanable funds at every interest rate. What would the new demand for loanable funds curve equation be given that government spending is now $500 and net taxes are $400. Assume nothing else changes except for the level of government spending.
f. Given the new demand curve you found in (e) calculate the new equilibrium interest rate, the equilibrium level of investment spending, and the equilibrium level of private savings.
2. Use the loanable funds framework for this problem. Suppose that initially in an economy net taxes, T - TR, are equal to $400 while government expenditures are equal to $200. Furthermore, suppose you know that this economy is initially a closed economy. You are told that the demand for loanable funds by businesses is given by the equation
r = 10 - (1/100)LFD
where r is the interest rate expressed as a percent rather than a decimal and LFD is the quantity of loanable funds demanded. You also know that the supply of private savings (Sp) curve is given by the equation
r = 2 + (1/300) Sp
where Sp is the quantity of private savings supplied at any given interest rate.
a. Calculate the initial value of government savings, Sg.
b. Before calculating the equilibrium interest rate, the equilibrium level of investment spending, and the equilibrium level of private savings given the above information make a prediction of the direction of change for each of these variables given the values you found in problem 1c. Provide a verbal explanation justifying your prediction.
c. Calculate the equilibrium interest rate, the equilibrium level of investment spending, and the equilibrium level of private savings given the above information.
Suppose the government enacts a policy that results in higher savings by households at every interest rate. Suppose this policy results in savings increasing by $100 at every interest rate. Write a new equation for the supply of loanable funds curve given this information. In your equation for the supply of loanable funds include Sp as well as Sg: that is, write an equation for the supply of national savings, NS.
d. Given the change in (c), solve for the new equilibrium interest rate, the equilibrium level of investment spending, and the equilibrium level of private savings given the above information.
3. Suppose the loanable funds market is initially in equilibrium in an open economy that is currently operating with a trade deficit and a balanced budget.
a. Draw a graph of the loanable funds market illustrating this initial equilibrium. In your graph be sure to identify Sp, Sg, KI, and I. Also, identify the initial equilibrium interest rate (r1) as well as the equilibrium levels of investment spending (I1) and private savings (Sp1). Label your graph carefully and completely.
b. Now, suppose the government increases its level of government spending while maintaining the same net taxes. Redraw your graph from (a) illustrating this change. In your graph model this change in government spending on the demand side of the loanable funds market. Identify the new equilibrium interest rate (r2) as well as the new equilibrium level of investment spending (I2) and private savings (Sp2). On your graph indicate the amount of investment spending that is "crowded out" by this change in government policy. Provide a verbal explanation of the effect of this government spending change on the loanable funds market.
4. Use the simple Keynesian model to answer this set of questions. Assume that this is a closed economy. Assume TR equals zero and that the aggregate price level is constant. You are provided the following information.
|
Y
|
T
|
C
|
I
|
G
|
Unplanned Inventory Change
|
Direction of Change in Real GDP
|
|
100
|
40
|
|
10
|
20
|
|
|
|
200
|
40
|
|
10
|
20
|
|
|
|
300
|
40
|
308
|
10
|
20
|
|
|
|
400
|
40
|
388
|
10
|
20
|
|
|
|
500
|
40
|
|
10
|
20
|
|
|
a. What is the consumption function with respect to aggregate output, Y, for this economy?
b. Fill in the missing values in the above table.
c. From your work in part (b) give a range for the equilibrium value of real GDP for this economy.
d. Find the equilibrium value for real GDP in this economy.
e. Suppose full employment real GDP equals 640. Calculate three possible options for reaching full employment real GDP:
- Option 1: reach full employment real GDP through a change in government spending.
- Option 2: reach full employment real GDP through a change in lump-sum taxes, T.
- Option 3: reach full employment real GDP through a policy where government spending and lump-sum taxes change by the same amount so that there is no change in the government deficit.
For each option identify what the change in G, the change in T, or the change in T and the change in G must be.
f. Of the three options in part (e) which is the most economical option for reaching full employment real GDP?
5. Use the simple Keynesian model to answer this question. Assume that TR = 0 and that the price level is constant. You are given the following information. (S is private household saving.)
|
Y
|
T
|
C
|
I
|
G
|
X
|
M
|
S
|
|
20
|
20
|
18
|
2
|
6
|
3
|
4
|
|
|
30
|
20
|
|
2
|
6
|
3
|
4
|
-16
|
|
40
|
20
|
|
2
|
6
|
3
|
4
|
|
|
50
|
20
|
|
2
|
6
|
3
|
4
|
|
|
60
|
20
|
|
2
|
6
|
3
|
4
|
|
a. Fill in the missing cells in the above table.
b. Using the information in the above table write an equation for consumption expressed as a function of disposable income, (Y - T). Then write a second equation for consumption as a function of aggregate income, Y.
c. Using the information in the above table write an equation for private household savings expressed as a function of disposable income, (Y - T). Then write a second equation for private household savings as a function of aggregate income, Y.
d. Given the above information, calculate the equilibrium level of real GDP, Y, for this economy.
e. Given the above information, calculate capital inflows (KI), the trade balance, the budget balance, and government saving (Sg) for this economy.
f. Is the following true for this economy in equilibrium?
I = S + Sg + KI
g. Suppose this economy is in equilibrium. Suppose full employment output is equal to 100. Draw a graph of the Keynesian cross to illustrate the current production level as well as the full employment production level. Describe current economic conditions in this economy paying particular attention to the unemployment level in the economy, inventory adjustment, and production levels.
h. Use the information in part (g) for this question. Suppose government leaders tell producers to produce Yfe = 100 even though there have not been any other changes in this economy. What will happen in this economy if producers attempt to produce at Yfe = 100?
i. Given the information in part (g), what must the change in government spending equal in order for this economy to return to the full employment level of output (Yfe = 100) through activist expansionary fiscal policy?
j. Verify that your answer in part (i) results in this economy producing at Yfe.
6. Use the simple Keynesian model to answer this question.
a. Draw a graph representing an economy that is in short-run equilibrium where the economy is in a recession. In your graph make sure you represent Ye and Yfe. Describe in words what would happen if this economy tried to produce at Yfe.
b. Draw a graph representing an economy that is in short-run equilibrium where the economy is in a boom. In your graph make sure you represent Ye and Yfe. Describe in words what would happen if this economy tried to produce at Yfe.