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

Find competetive EQM by leaving out goods market in your initial computations.
a) Calculate disposable income (Yd), C, Private Savings then use this information to determine the Gov Savings and National Savings

b) Use national savings (S) and the investment function (I) to determine the real interest rate (r). Draw the graph of the Loanable Funds Market showing the supply of loanable funds, demand for loanable funds, and the equilibrium price and quantity. (Labor Graph carefully)

c) Verify Warlas Law holds. (Hint: We know from Walras’ Law that because we have an economy with 4 markets and have solved for 3 of them, the 4th market (the goods market) clears. You can verify it by solving for the interest rate (r) in the goods market.) Draw the graph for the Goods Market showing AD, AS and the long-run equilibrium.

Please and thank you!

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.