1. Consider the following model of short-run output: I": =C'I+l't+(lF:+JEIJr'I-JIMi C:=(ac+cl':)}_: ' I:=[af_b(R:_F}]Ir: ' Gx=aGE5 EXI=EEY ' Mr=acri where 1: is potential output, I": =(Il'I If )f E is the percentage deviation of actual output Yf from potential (the short-run output gap), F is the long-run return to capital (marginal product of capital net of depreciation). We take I7; and Fas given (determined by the long-run model). (a) Combine the equations and solve to obtain the IS relation, showing if: as a function of RI . (b) Now invert the equation, showing R; as a function of ii, i.e. the equation of the IS curve (with ftt on the vertical axis). Draw it (marking the point where I\": = {l and R! = F ). What determines the intercept (how high the curve is)? What determines the slope? Does the multiplier effect (coming 'om c 3* 0) make the IS curve atter or steeper (compared to a case where c = 0)? (c) Show that in the absence of shocks (when the short-run variables coincide with the long-run values) the coefficients must satisfy ac + a], + at? +11\" am -1 = . ((1) Assume now ac=.6, af=.2, (19:11.2, a=.l, am=.1, b=1f2, c=1f3, F=4% . Suppose that initially if: = U and RE = F , and then a recession in the rest of the world reduce the foreign demand for our country's domestic products: i.e. the coefcient a\" drops from 0.10 to 0.09. At the initial real interest rate, what would happen to our country's short-rim output? What would be the percentage deviationi': '2' (e) We have argued that the central bank can effectively control the real interest rate in the short run by setting the nominal interest rate (given that ination does not change immediately). That's represented by the horizontal MP line in the ISsMP diagram. Faced with the aggregate demand shock described in the previous point (d), what would the central bank do to bring output back to potential? Compute the value that the real interest rate should take to offset the shock. Show the effect of the shock and of the monetary policy change in the [Sum diagram