the following short-run model.

1. Consider the following short-run model: 01 = @6171 131171 2% = 551:5\"??? Gt _ (EYE32K, EX: any; {Mt _ Eitha where 01 is consumption at time t, I1 is investment G1 is government purchases, EX} and IM1 are exports and imports, 371 is potential output Y1, 1s short- -run output, R1 1s the real interest rate,r is the marginal product of capital, and ac, a\" :19, an, em, 31, and 32 are parameters (a ) (b) Derive the equation for the IS- -curve (that is, the relationship between short-run output and the real interest rate) when 31 6 [0,1) and 32 > 0 Draw the IS diagram (that is, the diagram with the real interest rate on the vertical axis and short- -run output on the horizontal _axis) with two 18- -curves The rst 18- -curve is given by the answer to part _a) when 31: 0 and 32 0 The second 18- -curve is given by the answer to part a) when 0 31 Suppose the real interest rate increases Show graphically what will happen to short run output for both IScurves. Carefully explain why short-run ouftput is more sensitive to changes in the real interest rate in one of the models