Question

Consider the following competetive economy

K=150 L=150 Production Function= Y=K^.4L^.6 Consumption Function . C=10+.7Yd I= 40-100R, G=30, T=30 .... MPL= .6K^.4L^-.4 MPK= .4K ^-.6L^.6

Suppose the government increased spending to G = 32 (holding taxes constant T=30).

1. Compute the new value for government saving (Sg) and national savings (S), and use the investment function to calculate the new interest rate (r).
2. Graphically illustrate the impact of increase in government expenditure on the Loanable Funds Market and the Goods Market. (Please be sure to label your graph completely and carefully, and include the initial equilibrium level found in (e.ii) on the same graphs)

Answer 1

Given the values of capital and labor, we see that

Y = (150)*(150)

Real wage rate

Firm hires workers up to a point where the marginal product of labor equals the wage rate. Marginal product of labor MPL = 0.6(K/L)^0.4 = 0.6

Real Rental price

Firm use capital up to a point where the marginal product of capital equals the rental price. Marginal product of capital MPK = 0.4(L/K)^0.6 = 0.6

Equilibrium income

This is solved by substituting K = 150 and L = 150 in Y = K^0.4 L^0.6

Y = K^0.4 L^0.6

Y = (150)^0.4(150)^0.6

Y = 150

Equilibrium income is 150 units

Labor’s share = 0.6*150 = 90 units

Capital’s share = 0.4*150 = 60 units.