Consider an economy with the following output produced by one representative firm: Y = 25N where N is the quantity of labor used. The labor market is competitive, with real wage w determined by market equilibrium. The labor supply is given by: Ns = -20 + 1.2w + 100r + 0.125T
a. The firm maximizes profit by hiring labor such that the marginal product of labor is equal to the market wage. Use this knowledge to form the equation for labor demand, and use this together with the labor supply to solve for the equilibrium in the labor market.
b. Derive the Ys curve by finding the expression for the full-employment output in terms of the real interest rate and taxes. The goods market is described by the following information:
C = 250 + 0.6(Y - T)
I = 250 - 200r
G = T = 400
c. Derive the equation for the Yd curve by using the goods market equilibrium.
d. Find the equilibrium output and interest rate when the economy is in general equilibrium.
e. Households change their behaviors, and consequently the MPC changes to 0.55. Firms also decrease their investments, and as a result, investment changes to I = 240 - 200r. Find the new expression for the Yd curve.
f. Find how much taxes and spending the government needs to implement (while keeping its budget balanced) so that the equilibrium interest rate stays unchanged.