3. The IS–LM model developed in Chapters 10 and 11 assumes that investment depends only on the interest rate. Yet our theories of investment suggest that investment might also depend on national income: higher income might induce firms to invest more.

a. Explain why investment might depend on national income.

b. Suppose that investment is determined by I = I−+ aY, where a is a constant between zero and one, which measures the influence of national income on investment. With investment set this way, what are the fiscal-policy multipliers in the Keynesian-cross model? Explain.

c. Suppose that investment depends on both income and the interest rate. That is, the investment function is I = I− + aY − br, where a is a constant between zero and one that measures the influence of national income on investment and b is a constant greater than zero that measures the influence of the interest rate on investment. Use the IS–LM model to consider the short-run impact of an increase in government purchases on national income Y, the interest rate r, consumption C, and investment I. How might this investment function alter the conclusions implied by the basic IS–LM model?