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# textbook_sol8 - Chapter 8 A Two-Period Model The...

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Chapter 8 A Two-Period Model: The Consumption-Savings Decision and Ricardian Equivalence 71 T Textbook Question Solutions Questions for Review 1. Consumers save so that they can smooth their consumption over time. 2. Consumers save by issuing bonds. 3. The consumer chooses how to spread her consumption over time. To make this decision, the consumer needs to know the real interest rate, and the present value of her lifetime wealth. 4. The relative price of future consumption is 1 (1 ) r + , where r is the real interest rate. 5. Current period: s y c t = - - . Future period: ' ' ' (1 ) c y t r s = - + + Substituting for s from the first equation into the second equation shows that the present value of lifetime consumption is equal to the present value of lifetime income minus the present value of lifetime taxes. 6. The slope of the budget line is (1 ) r - + . 7. The horizontal intercept is we . The vertical intercept is (1 ) we r + . 8. To consume the endowment point, the consumer consumes y t - in the first period, and consumes ' ' y t - in the second period. The consumer neither lends nor borrows. 9. More is preferred to less, the consumer likes diversity, and both current and future consumption are normal goods. 10. The preference for a smooth consumption stream implies a declining marginal rate of substitution, and so indifference curves are bowed toward the origin. 11. The consumer wishes to spread an increase in current income over the consumer’s lifetime. First- period consumption, second-period consumption and saving all increase. 12. The excess variability of consumption is explained by credit-market imperfections, and that movements in the equilibrium real interest rate prevent all consumers from simultaneously trying to smooth consumption. Aggregate consumption is constrained by aggregate income, and therefore aggregate consumption must rise during booms and fall during recessions, even though consumers would prefer smoother consumption. 13. An increase in future income increases both current and future consumption. This pattern is achieved by reducing savings. 14. A permanent increase in income produces a larger increase in current consumption, because it is unnecessary to smooth the increase over time.

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72 Williamson • Macroeconomics, Second Edition 15. The market value of stocks is a proxy for the expected present value of lifetime wealth. An increase in stock prices is therefore likely to cause an increase in consumption. In the data, stock prices and aggregate consumption are positively correlated. 16. An increase in the real interest rate includes both a substitution effect and an income effect. In response to an increase in the interest rate, the substitution effect leads to lower first-period consumption, higher second-period consumption, and increased saving. The direction of the income effect depends on whether the consumer is initially a borrower or a lender. For borrowers, the income effect reduces both current and future consumption, and increases saving (less borrowing). For
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textbook_sol8 - Chapter 8 A Two-Period Model The...

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