Homework 4-

1. Use the loanable funds framework for this problem. Suppose that in an economy net taxes, T - TR, are equal to $500 while government expenditures are equal to $500. 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 = 20 - (1/500)I

where r is the interest rate expressed as a percent rather than a decimal and I is investment spending by businesses. You also know that the supply of private savings curve is given by the equation

r = (1/1500)Sp

where Sp is the quantity of private savings.

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 at every interest rate private savings increases by $1500. Holding everything else constant, calculate the new equilibrium interest rate, the new equilibrium level of investment spending, and the new equilibrium level of private saving.

e. Suppose that the loanable funds market is described as it was initially (that is, forget the changes described in part (d). Suppose there is no change in imports or exports but government spending increases by $1000 while net taxes increase by $500. Use this information to calculate the equilibrium values of I, Sp, and r.

f. How much investment spending is crowded out by the government deficit in part (e)?

g. Suppose that the information you were given in part (e) is true except that you now know that imports into this economy equal $500 while exports equal $200. Find the new equilibrium interest rate and quantity of loanable funds given this information.

2. 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.

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 195. 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?

3. 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.)

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.

4. 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.