The following describes some key relationship for a closed economy: C =7+0.8(Y- T) - 100r 7 =19-150r M = P[15 + 0.5Y-250r] G = T (a) Derive the IS and LM curves for this economy, with the real rate of interest on the left- hand side. Be sure to describe briefly your steps. Use the IS and LM relationship to derive the aggregate demand curve (AD) with Y on the left-hand side. In your results, show G and ?' separately in each of the relationships. (b) You are given the following information: G = 10 and the real money supply is 50. Solve the model for Y and r. If the price level were 1.10, what would be the value of the nominal money supply? As well, calculate the levels of C and / and verify that, along with government spending, they add up to the value of Y that you found. [Hint, you will find the AD curve helpful for the first part.] (c) An authoritative study concludes that potential output in this economy is 88. Based on your answers in part b), is the economy in recession or is it experiencing excess demand? Policymakers do not want the price level or the nominal money supply to change and decide to use fiscal policy to return the economy back to its long-run level of potential output. Calculate by how much G and 7 would have to change to achieve this goal while maintaining a balanced budget. (Note that since the budget is balanced, there are no Ricardian equivalence issues.) (d) In the new equilibrium, calculate what has happened to consumption and investment compared with the initial values you found in part b)? What process is at work? [Hint: you need to find the real interest rate that is consistent with the new equilibrium level of output. ]This economy, which has a exible exchange rate system, can he represented by the following: C\": 23 + t]_?[}" n 5I]r fan2m: if 2 P15 + oer lr] Mir: l_1Ye {a} Derive the IS and LM curves for this economy with the real rate of interest on the left- hand side. {h} Find the levels of l" and e that are consistent with the following: 6:15, T: It], 'ie nominal money sIleqiljpr is til]. the world real rate of interest 6% and the domestic price level {P} is 1.2- If the foreign price level {Pym} is I, what is the level of the nominal exchange rate {em} and N1? {c} Assume that the levels of I", s and em that you found in part b} represent the long-urn equilibrium values. Suppose now that the dmand for money falls and this is represented by a decline in re constant term of the M" equation from 5 to3 while re nominal money supply remains unchanged at tit]. Find the short-mu level of l', at, cm and NI Briey explain what is happening as the economy moves to this short-rim position. {d} From the short-run position that you found in part c}, describe briefly how the economy would get back to its long-run equilibrium position. In long-urn equilibrium. what variables have changed\"? ICalculate re new levels of these variables. This economy, which has a fixed nominal exchange rate, can be represented by the following: = 14+0.8(Y- 7) - 50r / =16-100r M = P(7.5 + 0.5Y- 150r) G-T = 10 NX = 13 -0.1Y- 2e (a) Derive the /S and LM curves for this economy with the real rate of interest on the left- hand side. (b) For a world interest rate of 10%, find the fixed nominal exchange rate (emom) as well the equilibrium levels of Y, P, such that e = 0.75, M = 50 and the foreign price level (Pfar) = 1.50. Based on your answers, does this economy use or contribute to world saving? (c) Suppose that the economy is hit by a recession, which is driven by a fall in investment. In particular, the constant term in the investment equation has declined from 16 to 15. Remembering that the real interest rate is 10%, what is the short-run level of output for this economy? What does the central bank have to do in response to the recession? Calculate the implications for the money supply. (d) To deal with this recession, the government decides to fix the nominal exchange rate at a new, lower level. Assuming that the domestic price level remains unchanged, what would be the new level of the nominal exchange rate that would be consistent with the economy being back at full employment? (Hint: find the real exchange rate first.)