## Drop in capital with no change in liabilities

ECO 303 Problem Set 2 Deadline: Wednesday, March 27, AT THE BEGINNING OF CLASS

[I will collect all works and then discuss the solutions in class, so you may wish to make a copy of your work before submitting]

1. In June 2008, a bank saw a 10% drop in assets, a 50% drop in capital, but no change in liabilities. (a) How much was the bank’s leverage ratio at the beginning of June 2008? (b) How much was the bank’s leverage ratio at the end of June 2008? (c) In July 2008, the bank’s assets decreased by 10%, while the bank’s li-

abilities remained unchanged. What was the percentage change in the bank’s capital in July 2008?

2. Consider an economy where deposits are 60 billion pesos which constitutes 80% of the money supply. Reserves are 35 billion pesos. (a) Calculate the currency-deposit ratio. (b) Calculate the money multiplier. (c) If the central bank requires each bank to keep 18% of deposits as reserves,

calculate banks’excess reserves. (d) If the central bank buys 2 billion pesos worth of securities, calculate

the percentage change in the monetary base and the percentage change in the money supply assuming that the currency-deposit ratio and the reserve-deposit ratio stay unchanged.

3. If reserves are scarce, how would the money supply change (increase, decrease, or stay the same) and why (due to an increase, decrease, or no change in the monetary base, reserve-deposit ratio, or currency-deposit ratio) if: (a) bank’s deposit insurance is eliminated (b) the central bank decreases the discount rate (c) the central bank increases the rate it pays on bank’s required reserves,

but decreases the rate it pays on excess reserves (d) an article reporting a signi…cant surge in cases involving counterfeit cur-

rency becomes viral

4. The demand for real money balances is given by MP = 4Yp

i 100

, where the

nominal interest rate i is measured in percent. At the beginning of the year, the nominal interest rate is 4%. Over the year, the money supply increases by 2%, the output increase by 1% percent, and the nominal interest rate decreases by 8 BASIS points. (a) If the ex ante real interest rate equals 3%, …nd the expected in‡ation at

the beginning of the year. (b) [In answering this question, you are allowed to use the approximations

regarding percentage changes; see slide 4 of the math review (slide set 2).] Calculate the actual in‡ation rate. (c) Is it true that purchasing power was transferred from lenders to borrow-

ers? Explain.

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5. Jessica bought some shares of stock for a total of $63,000 in 2014 and sold them to Ralph for $60,000 in 2016 who in turn sold them for $63,000 in 2018. The CPI was 205 in 2014, 200 in 2016, 205 in 2018. The tax on capital gains is 15% (It is 0% on capital losses). For simplicity, assume that the tax is paid when the capital gain is realized, i.e., when the stock is sold. (a) How much money did Jessica make in constant 2016 dollars? (b) How much money did Ralph make in constant 2016 dollars?

6. Assume the labor force is 100 million people and there are 2 million discouraged workers who do not have a job but are not looking for one either. On average, it takes 2 months for an unemployed person to …nd a job. A job lasts for 30 months on average. Assume that the unemployment rate is 10 percent at the beginning of March. (a) How much will the unemployment rate be at the beginning of April? (b) Assume that at the beginning of April, the 2 million discouraged work-

ers start looking for a job. How much will the unemployment rate be at the beginning of May? (c) If we wait long enough, the unemployment rate will converge to some

value. Calculate this value.

7. An economy with 6,336 machines and 110 workers has a production func- tion Y = 3K�L1��, where 0 < � < 1. Without any government intervention, CAPITAL income is 1/3 of total income. (a) Find the equilibrium real rental rate. (b) Assume that the government intervenes and sets a minimum real wage

of 8. Find the unemployment rate.

8. A closed economy (NX = 0) without government (G = T = 0) has a production function Y = K1=3L2=3. Capital depreciates at a rate of 2 percent per year. Workers spend 82 percent of their income each year. Investment adds up to the capital stock which is available for production next year. Assume that capital per worker is 8 at the beginning of 2018 and the number of workers stays the same each year. (a) Find output per worker, consumption per worker, investment per worker,

and depreciation per worker in 2018. How much will capital per worker be at the beginning of 2019? (b) Find the steady-state capital per worker, output per worker, consumption

per worker, investment per worker, and depreciation per worker.

9. Answer in one or two sentences: (a) Do you expect money velocity to increase, decrease, or stay the same if

the nominal interest rate decreases. Explain. (b) Currently, a lot of money is used to avoid prosecution for illegal activities.

In this sense, if drugs are legalized, do you expect the OVERALL price level to increase, decrease, or stay the same? Explain. (c) Why is the federal funds rate greater than the overnight reverse repo

rate and smaller than the interest rate on excess reserves? (d) How can unemployment insurance improve workers’productivity?

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