5. Consumption and Interest rates: In this question we consider another cxtension to the basic IS model. In the baseline model, only investment depends on the real interest rate R. Now assume that consumption also depends on the real interest rate. To capture this, we modify our consumption equation as follows: YtCt=ac+mCY~tbc(Rtr) As before, r is the long-run marginal product of capital, which is determined by the long-run model. bc is a positive parameter, and mc is between 0 and 1 . (a) According to the above equation, how does consumption depend on the real interest rate? Provide an intuitive cconomic explanation for this equation. (b) Derive a new IS curve, assuming that the other components of the model are as in the model used to derive our original IS curve in class. (c) Assume the government increases its expenditures. Does this have a larger or smaller effect on short-run output than in our basic IS-curve? (d) Compared to the IS curve we used in class, do changes in the real interest rate have a larger or smaller impact on short-run output? Explain intuitively. (c) Given the behavior of consumption and investment in the data, do you think that consumption is more or less sensitive to interest rates than investment? Depending on your answer, should a realistic model of the cconomy use a value of bC that is larger or smaller than that of b ? 5. Consumption and Interest rates: In this question we consider another cxtension to the basic IS model. In the baseline model, only investment depends on the real interest rate R. Now assume that consumption also depends on the real interest rate. To capture this, we modify our consumption equation as follows: YtCt=ac+mCY~tbc(Rtr) As before, r is the long-run marginal product of capital, which is determined by the long-run model. bc is a positive parameter, and mc is between 0 and 1 . (a) According to the above equation, how does consumption depend on the real interest rate? Provide an intuitive cconomic explanation for this equation. (b) Derive a new IS curve, assuming that the other components of the model are as in the model used to derive our original IS curve in class. (c) Assume the government increases its expenditures. Does this have a larger or smaller effect on short-run output than in our basic IS-curve? (d) Compared to the IS curve we used in class, do changes in the real interest rate have a larger or smaller impact on short-run output? Explain intuitively. (c) Given the behavior of consumption and investment in the data, do you think that consumption is more or less sensitive to interest rates than investment? Depending on your answer, should a realistic model of the cconomy use a value of bC that is larger or smaller than that of b