Problem
Consider the following variant of the OLG model in which people work in both periods of their lives. They are born and die with zero assets. Assume production is Cobb-Douglas, and people have log utility with a time discount rate of zero. Capital fully depreciates after it is used, so that old people consume only the marginal product of their capital, not the capital itself. Population is constant and normalized to 1.
a. Set-up the consumer problem and and the optimal saving as a function of income and interest rate.
b. Derive the dynamics of capital accumulation and solve the steady-state level of output.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.