Assume that initially the IS curve is given by
IS1: Y = 12 – 1.5T – 30i + 2G
and that the price level P is 1, and the LM curve is given by
LM1: M = Y(1 – i )
The home central bank uses the interest rate as its policy instrument. Initially, the home interest rate equals the foreign interest rate of 10% or 0.1. Taxes and government spending both equal 2. Call this case 1.
a. According to the IS1 curve, what is the level of output Y? Assume this is the desired full employment level of output.
b. According to the LM1 curve, at this level of output, what is the level of the home money supply?
c. Plot the IS1 and LM1 curves for case 1 on a chart. Label the axes, and the equilibrium values.
d. Assume that forex market equilibrium is given by i = ([1/E] – 1) + 0.10, where the two foreign return terms on the right are expected depreciation and the foreign interest rate. The expected future exchange rate is 1. What is today’s spot exchange rate?
e. There is now a foreign demand shock, such that the IS curve shifts left by 1.5 units at all levels of the interest rate, and the new IS curve is given by
IS2: Y = 10.5 – 1.5T – 30i + 2G
The government asks the central bank to stabilize the economy at full employment. To stabilize and return output back to the desired level, according to this new IS curve, by how much must the interest rate be lowered from its initial level of 0.1? (Assume taxes and government spending remain at 2.) Call this case 2.
f. At the new lower interest rate and at full employment, on the new LM curve (LM2), what is the new level of the money supply?
g. According to the forex market equilibrium, what is the new level of the spot exchange rate? How large is the depreciation of the home currency?
h. Plot the new IS2 and LM2 curves for case 2 on a chart. Label the axes, and the equilibrium values.
i. Return to (e). Now assume that the central bank refuses to change the interest rate from 10%. In this case, what is the new level of output? What is the money supply? And if the government decides to use fiscal policy instead to stabilize output, then according to the new IS curve, by how much must government spending be increased to achieve this goal? Call this case 3.
j. Plot the new IS3 and LM3 curves for case 3 on a chart. Label the axes and the equilibrium values.