1. Consider the following shortrun model: C. = 65/. + 31173; 15: = a, B (R, F) Gt angE _ SZY/tfft EXt aemYVt IMf. army/r, where Ct is consumption at time t, It is investment, G: is government purchases, EXt and 11% are exports and imports, Yt is potential output, Y; is short-run output, R; is the real interest rate, 77 is the marginal product of capital, and ea, (1,, (19, (in, am, 61, and 62 are parameters. (a) (b) Derive the equation for the IScurve (that is, the relationship between shortrun output and the real interest rate) when 61 6 [0,1) and 62 2 0. Draw the IS-diagram (that is, the diagram with the real interest rate on the vertical axis and shortrun output on the horizontal axis) with two IScurves. The rst IScurve is given by the answer to part a) when 31 = 0 and 32 = 0. The second IS-curve is given by the answer to part a) when 0 51. Suppose the real interest rate increases. Show graphically what will happen to short-run output for both lSCurves. Carefully explain why shortrun output is more sensitive to Changes in the real interest rate in one of the models