Problem Set 3 October 5, 2020 Due Date: Monday, Oct. 12 Blanchard Problems: • Ch. 5: 3, 9 • Ch. 6: 2, 4, 5, 7 Additional Problem: 1. Consider two economies: 1) Y = C(Y − T ) + I(Y, i) + G, with G, T exogenous + +− 2) Y = C(Y − T ) + I(Y, i) + G with G exogenous, but T = T (Y ), and + +− + 0 < TY < 1 (a) For economy one, use the total derivative to derive an expression for di dY . (b) For economy two, use the total derivative to derive an expression for di dY . (c) Is the slope of the IS curve for economy one equal to, steeper than, or atter than the slope for economy two? How do you know? (d) What is the intuition for your result in part iii? (1-2 sentences is ne). 1 3. The response of the economy to fiscal policy a. Use an IS-LM diagram to show the effects on output of a decrease in government spending. Can you tell what hap- pens to investment? Why? Now consider the following IS-LM model: C = Co + C(Y – T) I = bo + bịY - Dzi Z = C +I+G i = i b. Solve for equilibrium output when the interest rate is i. Assume G + b, < 1. (Hint: You may want to rework through Problem 2 if you are having trouble with this step.) c. Solve for equilibrium level of investment. d. Let's go behind the scenes in the money market. Chapter 4 introduced equations that describe equilibrium in the money market. Let's write the equation characterizing the equilib- rium as: M/P = d.Y - dui. Solve for the equilibrium level of the real money supply when i = i. How does the real money supply vary with government spending? 9. The (less paradoxical) paradox of saving A chapter problem at the end of Chapter 3 considered the effect of a drop in consumer confidence on private saving and investment, when investment depended on output but not on the interest rate. Here, we consider the same experiment in the context of the IS-LM framework, in which investment depends on the interest rate and out- put but the central bank moves interest rates to keep output constant. a. Suppose consumer confidence falls, so households save a higher proportion of their income. In an IS-LM diagram where the central bank moves interest rates to keep output constant, show the effect of the fall in consumer confi- dence on the equilibrium in the economy. b. How will the fall in consumer confidence affect consump- tion, investment, and private saving? Will the attempt to save more necessarily lead to more saving? Will this attempt necessarily lead to less saving? 4. Modern bank runs Consider a simple bank that has assets of 100, capital of 20, and checking deposits of 80. Recall from Chapter 4 that checking deposits are liabilities of a bank. a. Set up the bank's balance sheet. b. Now suppose that the perceived value of the bank's assets falls by 10. What is the new value of the bank's capital? What is the bank's leverage ratio? c. Suppose the deposits are insured by the government. Despite the decline in the value of bank capital, is there any immediate reason for depositors to withdraw their funds from the bank? Would your answer change if the perceived value of the bank's assets fell by 15? 20225? Explain. Now consider a different sort of bank, still with assets of 100 and capital of 20, but now with short-term credit of 80 instead of checkable deposits. Short-term credit must be repaid or rolled over (borrowed again) when it comes due. d. Set up this bank's balance sheet. e. Again suppose that the perceived value of the bank's assets falls. If lenders are nervous about the solvency of the bank, will they be willing to continue to provide short-term credit to the bank at low interest rates? f. Assuming that the bank cannot raise additional capital, how can it raise the funds necessary to repay its debt com- ing due? If many banks are in this position at the same time (and if banks hold similar kinds of assets), what will likely happen to the value of their assets? How will this affect the willingness of lenders to provide short-term credit? 5. 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 6-62 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%, with the nominal policy rate unchanged, does the IS curve shift? e. If the expected rate of inflation were to decrease from 3% to 2%, does the LM curve shift? f. If the risk premium on risky bonds increases from 5% to 6%, does the LM curve shift?
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