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.)