Question

Mankiw) Explain why each of the following statements is true. Discuss the impact of monetary and fiscal policy in each of these special cases. a.If investment does not depend on the interest rate, the IS curve is vertical. b.If money demand does not depend on the interest rate, the LM curve is vertical. c.If money demand is extremely sensitive to the interestrate, the LM curve is horizontal

Answer 1

Solution:

All four statements are true.

a. If investment does not depend on the interest rate, the IS curve is vertical.

Solution: For a generic IS curve, Y = a ? b ? r, Y = a when b = 0, i.e., when investment does not depend on the interest rate (assuming that the real interest rate does not enter the consumption function). When the IS curve is vertical, monetary expansions (contractions) shifting in the LM curve will have no short-run impact on real output, but the real interest rate will fall (rise). Fiscal expansion (contraction) shifting the IS curve will still increase (decrease) short run real output, and there is no longer any countervailing investment crowd-out (crowd-in). So monetary policy loses efficacy and fiscal policy gains traction. Answers for ‘False’ also accepted if you argue that the real interest rate will still enter the IS curve through consumption.

b. If money demand does not depend on the interest rate, the LM curve is vertical.

Solution: For a generic LM curve, Y = a/P + b ? r, Y = a/P when b = 0, i.e., a vertical line for a fixed short-run price level when money demand does not depend on the interest rate. When the LM curve is vertical, fiscal expansions (contractions) will have no short-run impact on real output, but the real interest rate will rise (fall). Monetary policy can still increase or decrease short run real output; the response of the interest will be particularly strong. So monetary policy gains efficacy and fiscal policy loses all traction.

c. If money demand does not depend on income, the LM curve is horizontal.

Solution: True. Ms P = L(r) when Y doesn’t enter the money demand function, yielding a single market clearing real interest rate for a given money supply. When the LM curve is horizontal, monetary expansions or contractions (vertical shifts of the LM curve) will affect both output and the real interest rate. Fiscal policy can still increase or decrease short run real output; there will be no impact on the real interest rate, so fiscal expansion doesn’t produce any countervailing investment crowd-out