100 Economics Key for Problem Set #4
Spring 2007
1. The builder of a new movie theater complex is trying to decide how many screens she wants. The cost of construction is $1,000,000 per screen. The builder is borrowing from the bank at some real interest rate to build the movie theater complex. Listed below are the number of patrons the complex will attract, depending on the number of screens (6 points): Number of Screens 1 2 3 4 5 a. Total Number of Patrons per year 40,000 75,000 105,000 130,000 150,000 Increase in Patrons for each Screen 40,000 35,000 30,000 25,000 20,000 Marginal Revenue of each Screen $80,000 $70,000 $60,000 $50,000 $40,000
Suppose that after paying the movie distributor and all other noninterest expenses the owner expects to net $2.00 per ticket sold. The increase in patrons for each screen is the change in the total number of patrons per year. The marginal revenue for each screen is the increase in patrons for each screen (number of tickets) times $2.00 per ticket.
b.
If the bank is charging a real interest rate (R) of 0.045, then the marginal cost of borrowing to pay for each screen is $45,000. Using the profit-maximizing rule that a firm invests so long as the marginal revenue marginal cost, the builder will build 4 screens.
c.
If the bank is charging a real interest rate (R) of 0.055, then the marginal cost of borrowing to pay for each screen is $55,000. Using the profit-maximizing rule that a firm invests so long as the marginal revenue marginal cost, the builder will build 3 screens.
d.
If the bank is charging a real interest rate (R) of 0.075, then the marginal cost of borrowing to pay for each screen is $75,000. Using the profit-maximizing rule that a firm invests so long as the marginal revenue marginal cost, the builder will build 1 screen.
e.
If the bank is charging a real interest rate (R) of 0.095, then the marginal cost of borrowing to pay for each screen is $95,000. Using the profit-maximizing rule that a firm invests so long as the marginal revenue marginal cost, the builder will build 0 screens.
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2. Consider the following investment and private saving schedules for the U.S. (6 points). Real Interest Rate (R)
Percentage
Investment (I)
Private Saving ( S private )
Public Saving ( S public )
National Saving (S )
Trillions of dollars Trillions of dollars Trillions of dollars Trillions of dollars
0 1 2 3 4 5 6 7 8 9 10
2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2
-0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
a. The U.S. government (federal, state and local) ran a combined a budget deficit in 2006 of 200 billion or 0.2 trillion. A budget surplus or public saving (Spublic) is defined as T G, while a budget deficit is defined as G T. A budget deficit of 0.2 trillion therefore implies that public saving (Spublic) must be -0.2 trillion. National saving (S) is the sum of private saving (Sprivate) and public saving (Spublic). b. With a budget deficit of 0.2 trillion, the equilibrium real interest rate (R) is 5% and the equilibrium level of investment (I) is 1.5 trillion dollars. c. Suppose that the U.S. balanced government the budget (no deficit or surplus) in 2006. As a result, public savings (Spublic) would be 0.0 and national savings (S) would equal private saving (Sprivate). The new equilibrium real interest rate (R) would be 4% and the new equilibrium level of investment (I) would be 1.6 trillion dollars.
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d. The elimination of the budget deficit increases national savings (S). Remember that it is households and the government who save and firms who invest in new plant and equipment. In other words, it is different groups that save and then that invest. So, when savings increases, investment does not automatically increase. What causes investment to increase in part c is that the real interest rate (R) falls from 5% to 4%. As a result of lower cost of investment, more investment projects become profitable like in question 1. 3. Consider the following balance sheets for the Bahamas. The desired reserve-deposit ratio in the commercial banks of Bahamas is 0.10 or 10 percent (5 points).
Central Bank of Bahamas Assets Gov't bonds 100 m Liabilities Currency Reserves 90 m 10 m Reserves Loans Gov't bonds Commercial Banks of Bahamas Assets 10 m 90 m 200 m Liabilities Deposits 300 m
Total assets
100 m
Total liabilities 100 m (Monetary Base)
Total assets
300 m
Total liabilities
300 m
a. Using your knowledge of balance sheets, fill in the missing entries in the above tables. Note that the reserves of the central bank has to match the reserves of the commercial banks. However, the government bonds for central bank do not have to match the government bonds of the commercial banks. b. Suppose that the Central Bank of Bahamas conducts an open market purchase of 1 m. The Central Bank of Bahamas would purchase 1m worth of government bonds from the commercial banks and sell 1m worth of reserves in exchange.
The Money Multiplier Formula:
change in money supply = change in deposits + change in currency held by public change in deposits = change in reserves / desired reserve-deposit ratio
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c. Suppose that the public decides to hold 1.0 m in deposits and 0.0 m in currency. change in the money supply = change in deposits + change in currency held by public = 1.0 m / 0.10 + 0.0 m = 10 m + 0.0 m = 10 million. d. Suppose that the public decides to hold 0.5 m in deposits and 0.5 m in currency. change in the money supply = change in deposits + change in currency held by public = 0.5 m / 0.10 + 0.5 m = 5.0 m + 0.5 m = 5.5 million. 4. This question has you examine the quantity equation of money (3 points). a. The quantity equation of money is M V = P Y where M = quantity of money V = velocity of money P = price level Y = real GDP b. In 2006, the quantity of money (M) was 7.0 trillion, velocity (V) was 2 and the price level (P) was 1.5 in value. Using the quantity theory, one can solve for the level of real GDP (Y) in 2006 as Y =
M V 72 14 = = = 9.33 trillion. P 1.5 1.5
c. Suppose that the Federal Reserve doubles the quantity of M2 to 14.0 trillion in 2007. In the long run, the level of velocity (V) and the level of real GDP (Y) would stay the same: V = 2 and Y = 9.33 trillion. Therefore, the price level (P) would double from 1.5 to 3.0.
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