4. Suppose that consumption is also affected by the real interest rate: If Rt is higher than the long-run marginal product of capital, r, which also equals the long-run interest rate, then consumers save more and consume less. To incorporate the effect of real interest rates on consumption, write the consumption equation as follows: Ct=Yt[acbc(Rtr)+mcY~t]. (a) Derive the IS-curve, assuming that It,Gt,EXt, and IMt are as in the basic IS curve presented in lectures. 12 (b) Assume that the economy is initially in its long-run equilibrium. Suppose the Federal reserve raises the nominal interest rate. Use the IS-MP model to explain how this policy affects output and the real interest rate in the shortrun. (c) How does the change in monetary policy affect consumption and investment? (d) How would the change in monetary policy affect consumption and investment if consumption did not depend on the interest rate? 4. Suppose that consumption is also affected by the real interest rate: If Rt is higher than the long-run marginal product of capital, r, which also equals the long-run interest rate, then consumers save more and consume less. To incorporate the effect of real interest rates on consumption, write the consumption equation as follows: Ct=Yt[acbc(Rtr)+mcY~t]. (a) Derive the IS-curve, assuming that It,Gt,EXt, and IMt are as in the basic IS curve presented in lectures. 12 (b) Assume that the economy is initially in its long-run equilibrium. Suppose the Federal reserve raises the nominal interest rate. Use the IS-MP model to explain how this policy affects output and the real interest rate in the shortrun. (c) How does the change in monetary policy affect consumption and investment? (d) How would the change in monetary policy affect consumption and investment if consumption did not depend on the interest rate