economics problem set

ECO 301 Problem Set 2 Deadline: Tuesday, October 27, at the beginning of class

1. Imagine that you deposit in a bank $5,000. The bank keeps 9 percent in reserves and lends the rest. Did the bank create money? How much? Now, imagine that the borrower who received the loan deposits the money in another bank which keeps 9 percent of the deposit in reserves and lends the rest. Did this other bank create money? How much? If the process repeats in�nitely (i.e., each borrower deposits his/her loan in a bank which lends 91 percent of it), what would be the amount of money in the economy?

2. Are credit cards money? Explain why or why not.

3. A bank has a leverage ratio of 20. Find the percentage change in bank�s assets that would decrease bank�s capital to 0 (assuming bank�s liabilities are unchanged).

4. Consider an economy where 90 percent of the money is held as demand deposits and the rest as currency. Banks hold 5 percent of deposits as reserves. The monetary base is 400 billion pesos. (a) Calculate the money supply. (b) How would the peso money supply change (increase, decrease, or stay the

same) and why (because of an increase, decrease, or no change in the monetary base, reserve-deposit ratio, and/or currency-deposit ratio) if:

(i) a tax on checks written on demand deposit accounts is introduced (ii) the Central bank increases the repo rate (iii) bank deposit insurance is eliminated (iv) the Central bank decreases the rate it pays on excess reserves? (v) the number of �rms paying their employees in bitcoin and the num-

ber of merchants accepting it increases? (vi) a strong recession worsens the quality of banks�asset portfolios? (vii) the Central bank purchases peso-denominated government bonds?

5. Consider the following money demand function:� M P

�d = Y

3i2 ,

where the nominal interest rate i is measured in decimals. (a) Find the velocity of money. (b) If the money supply decreases by 1 percent while the output decreases

by 2 percent, what is the real interest rate given a (constant) nominal interest rate of 1.7 percent? (c) If the money supply increases by 0.5 percent, the output decreases by

1 percent, and the nominal interest rate increases by 1.5 percent, what is the in�ation rate?

6. Give an example of a shoe-leather cost of in�ation.

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7. If the Fed surprisingly announces that it will increase the discount rate in �ve months, would the price level change now? If yes, explain how (increase or decrease) and why. If no, explain why. Would your answer change if the Fed�s announcement was already expected by the market? Explain.

8. In 2014, you purchased 50 shares of stock for $100 each. In 2015, you sold them for $105 each and paid a 15 percent tax on your capital gain. The stock in question did not pay any dividends in 2014-2015. (a) How much did you make after you paid the tax? (b) How much did you make after you paid the tax in constant 2015 dollars

if CPI was 220 in 2014 and 224.4 in 2015? (c) Recalculate (a) and (b) if in 2015 you sold the shares for $107 each and

the CPI was 220 in 2014 and 228.8 in 2015.

9. Assume the labor force is 150 million people. It takes 1.5 months for an unemployed person to �nd a job. A job lasts for two years. (a) Assume that the unemployment rate is 10% this month. How much

would it be next month? How much would it be in two months? (b) Do you expect the unemployment rate to converge to some value in the

long run? If yes, calculate this value.

10. An economy with 1,000 machines and 125 workers has a production function Y = 3K1=3L2=3. (a) What would be the unemployment rate if the government determines a

minimum real wage of: (i) 2 units of output? (ii) 4.5 units of output?

[Hint: You may start by determining the equilibrium real wage without the minimum wage constraint. Then, you should check whether the constraint is binding, i.e., whether the equilibrium real wage is less than the legal minimum. If that is the case, there will be unemployment equal to the supply of labor less the demand of labor at the minimum real wage.]

11. An economy has a production function Y = K1=3L2=3. The economy is closed (i.e., there is no trade) and there is no government. Consumption is 70 percent of total income. Capital used in production loses 1/30 of its value for one year. Investment adds up to the capital stock which is available for production next year. Labor supply is constant in time and equals 125. (a) Find consumption per worker this year, next year, and the year after the

next if aggregate capital K is 1,375 this year. (b) Would the consumption per worker converge to some value in the long

run? If yes, calculate this value.

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