2019 BUFall EC 202 Dpset 7 PDF

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Fall 2019 - EC202 - Problem Set 7 Question 1 The IS-LM view of the world with more complex financial markets Consider an economy described by Figure 6-6 in the text:

a. What are the units on the vertical axis of Figure 6-6? b. If the nominal policy interest rate is 5% and the expected rate of inflation is 3%, what is the value for the vertical intercept of the LM curve? c. Suppose the nominal policy interest rate is 5%. If expected inflation decreases from 3% to 2%, in order to keep the LM curve from shifting in Figure 6-6, what must the central bank do to the nominal policy rate of interest? d. If the expected rate of inflation were to decrease from 3% to 2%, does the IS curve shift? e. If the expected rate of inflation were to decrease from 3% to 2%, does the LM curve shift? 1

f. If the risk premium on risky bonds increases from 5% to 6%, does the LM curve shift? g. If the risk premium on risky bonds increases from 5% to 6%, does the IS curve shift? h. What are the fiscal policy options that prevent an increase in the risk premium on risky bonds from decreasing the level of output? i. What are the monetary policy options that prevent an increase in the risk premium on risky bonds from decreasing the level of output? Question 2 Consider a bank that has assets of 100, capital of 20 and short-term credit of 80. Among the bank’s assets are securitized assets whose value depends on the price of houses. These assets have a value of 50. a. Set up the bank’s balance sheet. b. Suppose that as a result of a housing price decline, the value of the bank’s securitized assets falls by an uncertain amount, so that these assets are now worth somewhere between 25 and 45. Call the securitized assets ”troubled assets.” The value of the other assets remains at 50. As a result of the uncertainty about the value of the bank’s assets, lenders are reluctant to provide any short-term credit to the bank. Given the uncertainty about the value of the bank’s assets what is the range of the value of the bank’s capital? As a response to this problem the government considers purchasing the troubled assets, with the intention of reselling them again when the markets stabilize. (This is the original version of TARP.). c. If the government pays 25 for the troubled assets, what will be the value of the bank’s capital? How

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much would the government have to pay for the troubled assets to ensure that the bank’s capital does not have a negative value? If the government pays 45 for the for the troubled assets, but the true value turns out to be much lower, who bears the cost of this mistaken valuation? Explain! Suppose instead of buying the troubled assets, the government provides capital to the bank by buying ownership shares, with the intention of reselling the shares again when the markets stabilize. (This is what the TARP ultimately became.) The government exchanges treasury bonds (which become assets for the bank) for ownership shares. d. Suppose the government exchanges 25 of Treasure bonds for ownership shares. Assuming the worstcase scenario (so that the troubled assets are worth only 25), set up the new balance sheet of the bank. (Remember that the firm now has three assets: 50 of untroubled assets, 25 of troubled assets and 25 of Treasury bonds.) What is the total value of the bank’s capital? Will the bank be insolvent? e. Given your answers and the material in the text, why might recapitalization be a better policy than buying the troubled assets? Question 3 Suppose that the markup of goods prices over marginal cost is 5%, and that the wage-setting equation is W = P (1 − u) where u is the unemployment rate. a. What is the real wage, as determined by the price-setting equation? b. What is the natural rate of unemployment? c. Suppose that the markup of prices over costs increases to 10%. What happens to the natural rate of unemployment? Explain the logic behind your answer. Question 4 3

Suppose that the Phillips curve is given by πt = π et + 0.1 − 2ut and expected inflation is given by π + θπt−1 πte = (1 − θ)¯ and suppose that θ is initially equal to 0 and π ¯ is given and does not change. It could be zero or any positive value. Suppose that the rate of unemployment is initially equal to the natural rate. In year t, the authorities decide to bring the unemployment rate down to 3% and hold it there forever. a. Determine the rate of inflation in periods t + 1, t + 2, t + 3, t + 4, t + 5. How does π compare to π ¯? b. Do you believe the answer given in (a)? Why or why not? (Hint: Think about how people are more likely to form expectations of inflation.) Now suppose that in year t + 6, θ increases from 0 to 1. Suppose that the government is still determined to keep u at 3% forever. c. Why might θ increase in this way? d. What will the inflation rate be in years t + 6, t + 7, t + 8? e. What happens to inflation when θ = 1 and unemployment is kept below the natural rate of unemployment? f. What happens to inflation when θ = 1 and unemployment is kept at the natural rate of unemployment? Question 5 The Phillips curve is πt = π et + (m + z) − αut a. 4

Rewrite this relation as a relation between the deviation of the unemployment rate from the natural rate, inflation, and expected inflation. b. We derived the natural rate of unemployment in this chapter and the previous chapter. What condition on the price level and expected price level was imposed in that derivation? How does it relate to the condition imposed in part (a)? c. How does the natural rate of unemployment vary with the markup m? d. How does the natural rate of unemployment vary with the catchall variable z ? e. Identify two important sources of variation in the natural rate of unemployment across countries and across time.

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