Let us assume the following LM curve, where the Fed can set the real interest rate, R, through monetary policy: LM curve: R = F+ c where R is the real interest rate; r is taken to be the marginal product of capital (MPK) and assumed to be fixed at some value. For a given value of r, the Fed can set a value for R by changing the value of c to whatever level it wants at all levels of output; the Fed cannot change the value of the marginal product of capital. The IS curve can be described by the following equation: IS curve: Y = 20 - 0.10*R where Y is actual output (real GDP), measured in trillions of dollars. All of the quantities above, except for Y, are measured in percent. You can assume a value of 2 for r. The economy is in long- run equilibrium when R is equal to r and expected inflation is equal to 2 percent. a) Draw both the IS and the LM curves in the same graph, with R on the vertical axis and Y on the horizontal axis, based on the information given above and assuming that the economy is in long-run equilibrium. Also, make sure that the curves and the axes are all clearly labeled. Show and explain the point of long-run equilibrium in the graph, as well as the equilibrium values (in percent or whatever the case may be) of R and Y on the axes. Explain what equilibrium means for the money market and the goods market at the intersection of the IS and LM curves. (Note: Do NOT give just a graph; you need to explain what is in it and why concerning the equilibrium position.) b) Let us assume that inflation is now rising to 7 percent due to an increase in government spending and other fiscal policy measures that shift the IS curve to the right by an amount equal to 5 percent above the economy's potential output as determined in part a) above. Let us also assume that the Fed reacts to these developments by raising the interest rate according to the following rule: R =F + 0.5*(1 - n*) + 0.5*(GDP gap) where it is the rate of inflation and * is the target rate of inflation, taken to be 2 percent (which is also assumed to be the expected rate of inflation in the long run). The marginal product of capital does not change. Find the value of output for the following two scenarios: 1) output after the change in fiscal policy and before the change in the Fed's interest rate policy; and (2) output after the change in fiscal policy and after the change in the Fed's interest rate policy because of inflation being above 2 percent