An economy is described by the following equations: Cd=100+0.5(YT)500rId=700500rMd/P=10+0.5Y200(r+e) where Y is real output, P is the price level, r is the real interest rate, e is inflation expectation, T is a lump-sum tax, Cd is desired consumption, Id is desired investment, and M is the nominal supply of money which is set by the central bank. i. Derive an algebraic expression for the IS and LM curves with the real interest rate on the left hand side. ii Derive two algebraic expressions for the AD curve. One with real output (Y) on the left hand side and one with the price level (P). iii. Assume expected inflation, e, is 2%, full employment output, Y, is 750 , nominal money supply, M, is 1024, government spending, G, is 400 and the government budget is balanced. Use your results from parts i. and ii., to find the price level, P, and the real interest rate, r. iv. Draw this economy using the IS-LM-FE framework. Make sure to label your axes and curves. v. Now assume there is a temporary negative productivity shock and the new full employment level of output, Y, is now 740 . Find the price level, P, as well as the real interest rate, r, in the long run. Describe the transition between the old and the new long run equilibria. Assuming prices are sticky, in response to this temporary negative shock, the authorities could intervene to bring back the economy faster to the new long run equilibrium and to keep the price level constant. a) The government could use its fiscal policy ( G and T). Calculate the change required in G and in T (two different cases). [Hint: Use the AD curve to find the required change.] b) Instead, the central bank could use its monetary policy (M). Calculate the change required in M c) Explain why the authorities might want to intervene. viii. Now suppose the shock is permanent instead of temporary. Re-draw the economy using the IS-LM-FE framework. Make sure to label your axes and curves. Explain your reasoning. [Note: No calculations or numbers are required.] An economy is described by the following equations: Cd=100+0.5(YT)500rId=700500rMd/P=10+0.5Y200(r+e) where Y is real output, P is the price level, r is the real interest rate, e is inflation expectation, T is a lump-sum tax, Cd is desired consumption, Id is desired investment, and M is the nominal supply of money which is set by the central bank. i. Derive an algebraic expression for the IS and LM curves with the real interest rate on the left hand side. ii Derive two algebraic expressions for the AD curve. One with real output (Y) on the left hand side and one with the price level (P). iii. Assume expected inflation, e, is 2%, full employment output, Y, is 750 , nominal money supply, M, is 1024, government spending, G, is 400 and the government budget is balanced. Use your results from parts i. and ii., to find the price level, P, and the real interest rate, r. iv. Draw this economy using the IS-LM-FE framework. Make sure to label your axes and curves. v. Now assume there is a temporary negative productivity shock and the new full employment level of output, Y, is now 740 . Find the price level, P, as well as the real interest rate, r, in the long run. Describe the transition between the old and the new long run equilibria. Assuming prices are sticky, in response to this temporary negative shock, the authorities could intervene to bring back the economy faster to the new long run equilibrium and to keep the price level constant. a) The government could use its fiscal policy ( G and T). Calculate the change required in G and in T (two different cases). [Hint: Use the AD curve to find the required change.] b) Instead, the central bank could use its monetary policy (M). Calculate the change required in M c) Explain why the authorities might want to intervene. viii. Now suppose the shock is permanent instead of temporary. Re-draw the economy using the IS-LM-FE framework. Make sure to label your axes and curves. Explain your reasoning. [Note: No calculations or numbers are required.]
