A closed economy and is characterized by the following equations: Production function: Y = 3K1/4L3/4 Consumption: C = 12000 + 0.5(Y - T) - 1700r Investment: I = 5000 - 2300r Government spending: G = 4500 Real money demand: L(r, Y) = 0.25Y - 200r Note: Interest rate, r, is expressed in decimal points, i.e., if r = 0.035, then r is 3.5%.

Use the IS-LM model to answer the following questions. Show your calculations and keep your answer to at least 4 decimal places if needed. a) Derive the IS and LM equations in term of their exogenous variables. b) The economy is endowed with 20736 units of capital and 10000 workers. In the initial (long-run) equilibrium, the government runs a budget surplus of 500 and the central bank sets the level of nominal money supply to 35800. Find the full-employment values of real interest rate and price level.

The economy is initially in its long-run equilibrium as shown in part (b). Now, suppose households decide to save more for retirement; and autonomous consumption changes by 2.2%. c) Find the short-run equilibrium values of real output, real interest rate, and investment. Compute the long-run equilibrium values of real interest rate, investment, and price level. d) Suppose the central bank finds the short-run change in real interest rate in part (c) undesirable and wants to keep it at 11% via a change in monetary policy. Find the change in (nominal) money supply that will achieve this goal.