The production function in an economy is
Y = A(5N- 0.0025N2),
where A is productivity. With this production function, the marginal product of labour is
MPN = 5A- 0.005AN.
Suppose that A = 2. The labour supply curve is
NS = 55 + 10(1 - t)w,
where NS is the amount of labour supplied, w is the real wage, and t is the tax rate, which is 0.5.
Desired consumption and investment are
Cd = 300 + 0.8(Y - T) - 200r;
Id = 258.5 - 250r.
Taxes and government purchases are
T = 20 + 0.5Y;
G = 50.
Money demand is
Md/p- = 0.57- 250(r + πe).
The expected rate of inflation πe is 0.02, and the nominal money supply M is 9150.
a. What are the general equilibrium levels of the real wage, employment, and output?
b. For any level of output Y, find an equation that gives the real interest rate r that clears the goods market; this equation describes the IS curve. (Write the goods market equilibrium condition and solve for r in terms of F and other variables.) What are the general equilibrium values of the real interest rate, consumption, and investment?
c. For any level of output Y, find an equation that gives the real interest rate that clears the asset market; this equation describes the LM curve. (As in part (b), write the appropriate equilibrium condition and solve for r in terms of F and other variables.) What is the general equilibrium value of the price level?
d. Suppose that government purchases increase to G = 72. 5. Now what are the general equilibrium values of the real wage, employment, output, the real interest rate, consumption, investment, and the price level?