If a consumer has preferences U = x1x2 over the steady-state levels of consumption in the two periods of life, show that the utility-maximizing choices satisfy x2/x1 = 1 + r. Use this result to calculate the capital-labor ratio in the steady-state equilibrium given the consumption possibility frontier from exercise 19.4. What is the effect on the capital labor ratio of an increase in n and α? Explain.
Exercise 19.4
Why might the purchase of capital (instead of the rental of capital) affect a firm's profit maximization decision?