The production function in an economy is

Y=A(5N0.0025N2)

whereAis productivity. With this production function, the marginal product of labor is

MPN= 5A0.005AN

Suppose thatA= 2. The labor supply curve is

NS= 55 + 10(1t)w

whereNSis the amount of labor supplied,wis the real wage, andtis the tax rate on wage income, which is 0.5.

Desired consumption and investment are

C^d= 300+0.8(Y-T) - 200r

I^d= 285.5 - 250r

Taxes and government purchases are

T= 20+0.5Y

G= 50

Money demand is

M^d/P=0.5Y250(r+^e)

The expected rate of inflation,^e, is 0.02, and the nominal money supplyMis 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 theIScurve. (Hint: Write the goods market equilibrium condition and solve forrin terms ofYand 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 theLMcurve. [Hint: As in Part (b), write the appropriate equilib- rium condition and solve forrin terms ofYand other variables.] What is the general equilibrium value of the price level?

d. Suppose that government purchases increase toG= 72.5. Now what are the general equilibrium values of the real wage, employment, output, the real interest rate, consumption, investment, and price level?