Utopia is a closed economy and is characterized by the following equations:

Consumption: C = 2000 + 0.90(Y - T) - 9000r

Investment: I = 10000 - 8000r

Government spending: G = 13000

Taxes: T = 15000

Real money demand: (M^d/P) = L(Y,i) = 0.55Y - 3000i

Expected inflation: p^e = 0

Production function: Y = 25K^1/3L^2/3

Note:Interest rates, i and r, are expressed in decimal points, i.e., if r = 0.075, then r = 7.5%.

Suppose the IS-LM model can used be to describe Utopia, and answer the following questions.Keep your answers to a minimum of THREE decimal points (for fractions).

a)Derive the IS and LM equations for this economy.(4 points)

b)The supply of capital and labour in this economy are both equal to 4000; and the level of the nominal money supply is 54735.Calculate the long-run or full-employment values of real output, consumption, investment, real interest rate, public saving, private saving, national saving, and the price level.(8 points)

c)Now suppose the government of Utopia has decided that it does not like the present long-run equilibrium level of investment. Hoping to see more physical capital constructed the government decides it wants to raise the short-run level of investment in the economy by 50% by using fiscal policy by changing G. Is it possible to obtain this goal in the short-run? Explain why or why not. If this is possible determine the new short-run equilibrium levels of real output, consumption, investment, real interest rate, public saving, private saving, national saving, and the price level. (8 points)

d) Is it possible for the government of Utopia to double the level of investment (versus the initial short-run equilibrium level) in the long-run by using a change in government spending on goods & services G? Explain why or why not. (5 points)