Prove each of the following statements about the steady state of the Solow model with population growth and technological progress.

a. The capital– output ratio is constant.

b. Capital and labor each earn a constant share of an economy’s income. [Hint: Recall the definition MPK= f( k + 1) - f(k).]

c. Total capital income and total labor income both grow at the rate of population growth plus the rate of technological progress, n + g.

d. The real rental price of capital is constant, and the real wage grows at the rate of technological progress g. ( Hint: The real rental price of capital equals total capital income divided by the capital stock, and the real wage equals total labor income divided by the labor force.)