4. Assume that G and T are exogenous, and C is determined by the standard. consumption function, but that investment is now endogenous and responds to income: I = b + bY. Assume c + b < 1. (a) Calculate equilibrium output, state the multiplier, and compare it to the simple model with exogenous G, T and I. (b) Using the expression for equilibrium output, derive the marginal effect of a change in the propensity to invest (b), and the propensity to consume (c). (c) Now assume that the propensity to save (i.e. s = 1-c) increases. What happens to equilibrium output, investment, consumption and private, public and national savings? Briefly explain and discuss. int: In (b) you must calculate two partial derivatives:- and For you will need to use the product rule as you'll have c both in the multiplier and in the autonomous spending. If Y = XZ Y'X'ZZ'X or, dy = 0xdX + odz