A household's income in the current period is y = 95, and income in the future period is y′ = 115. The household pays lump-sum taxes t = 15 in the current period and t′ = 10 in the future period. The real interest rate r is 0.05, or 5%, per period.
1. Determine the household's lifetime wealth.
2. Suppose that household's preferences are such that it wants to have equal consumption in both periods, meaning c = c′. Determine what the household's optimal current-period and future-period consumptions are, and what optimal saving is. Round up your answers to the second decimal. Is the consumer a lender or a borrower?
3. Now suppose that instead of y = 95, the consumer has y = 140. Again, determine optimal consumption in the current and future periods and optimal saving. Round up your answers to the second decimal. Is the consumer a lender or a borrower? Explain how things change compared to Part (2).
4. ) Go back to y = 95. Now, suppose the real interest rate increased to r = 0.1. Determine the household's lifetime wealth, optimal current-period consumption, optimal future period consumption, and optimal saving using the same assumption that household's preferences are such that it wants to have equal consumption in both periods. Round up your answers to the second decimal. Explain how things changed compared to Part (2).
5. Now let y = 140 and the interest rate is r = 0.1. Determine the household's lifetime wealth, optimal current-period consumption, optimal future-period consumption, and optimal saving using the same assumption that household's preferences are such that it wants to have equal consumption in both periods. Round up your answers to the second decimal.Explain how things changed compared to Part (3)
6. Briefly explain (no more than two sentences) why how c, c′, and s changed after an increase in the real interest rate were different across Part (4) and Part (5).