Consider a closed economy. Consumption C is given by the consumption function C = Co + cY where Co denotes autonomous consumption demand and c is the marginal propensity to consume (0 < c < 1). Investment, I, is given by I = 1o - br, where Io is autonomous investment demand and b is the sensitivity of investment to the interest rate, r. Government spending is autonomous so G = Go and there is no tax. Assume initially wages and prices do not adjust. a. ) Derive the IS curve in this case. b. )Assume there is an increase in G (fiscal expansion) at a constant interest rate. Calculate the multiplier if c is 0.75. What is the increase in Y (GDP) if G rises by 100? c. ) Now assume the interest rate can rise when we have fiscal expansion (LM is upward sloping). Using the IS-LM diagram explain clearly why the increase in Y is less than that in part (b)