Prove each of the following statements about the steady state with population growth and technological progress.
a. The capital–output ratio is constant.
b. Capital and labour 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 labour 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.