Consider a closed economy in steady-state, with an inflation rate of 5% and shortrun output equal to zero. Assume people have adaptive expectations. Suppose there is a positive productivity shock (for example, a shock that suddenly lowers firms' prices).

a) Using the IS/MP and Phillips curve diagrams, show what the effect of this shock is on output and inflation, both in the short-run and long-run (assuming that the central bank keeps the real interest rate constant).

b) Suppose now that the positive productivity shock coincides with a temporary increase in the marginal product of capital. How does this affect your analysis in (a)?

c) Are your answers in (a) and (b) different if the central bank keeps the nominal interest rate constant instead of the real interest rate?

d) Suppose that consumption, in addition to investment, depends on the real interest rate. This is captured by the following equation describing consumption:

Ct/(Yt)=ab(Rtr)

where Rt is the domestic real interest rate, r the exogenous marginal product of capital, and b is a parameter. Briefly explain the intuition behind this consumption function. How does the response of this economy to the increase in the marginal product of capital differ from the response of the original economy from parts a)-c) to that same shock?