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A Two Period Model: Consumption-Savings Decision Ricardian Equivalence

2012/7/21. ECO 2021 Intermediate Macroeconomic Theory Professor C. K. Yip. 2. Two-Period Model of the Economy. Focus on the consumer's and government's behavior.A consumer's consumption-savings decision (intertemporal choice) involves a trade-off between current and future consumption.By saving, a

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A Two Period Model: Consumption-Savings Decision Ricardian Equivalence

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    1. 2012/7/23 ECO 2021 Intermediate Macroeconomic Theory Professor C. K. Yip 1 A Two Period Model: Consumption-Savings Decision & Ricardian Equivalence Chapter 8

    2. 2012/7/23 ECO 2021 Intermediate Macroeconomic Theory Professor C. K. Yip 2 Two-Period Model of the Economy Focus on the consumers and governments behavior. A consumers consumption-savings decision (intertemporal choice) involves a trade-off between current and future consumption. By saving, a consumer gives up consumption in exchange for assets in the present, in order to consume more in the future. The governments decision concerning the financing of government expenditure, involves a trade-off between current and future taxes. Policy Implication: Ricardian equivalence theorem

    3. 2012/7/23 ECO 2021 Intermediate Macroeconomic Theory Professor C. K. Yip 3 Consumers Assumptions: N consumers, where N is a large number Each consumer lives for two periods, current and future period. Each consumer receives exogenous income in both periods. Put aside the work-leisure decision. Income can differ across consumers. Zero wealth endowment (no assets) in the current period. Each consumer pays lump-sum taxes in both periods.

    4. 2012/7/23 ECO 2021 Intermediate Macroeconomic Theory Professor C. K. Yip 4 Consumers Assumptions: Only bond is traded in financial market. Consumers can lend and borrow at the same real interest rate, r (Perfect credit market). No risk for holding bonds. Define bonds: A bond issued (by the government) in the current period is a promise to pay a certain amount, say 1 + r units, of consumption good in the future period. ? 1 unit of c can be exchanged for 1 + r units of c' in the credit market. r is the real interest rate on each bond.

    5. 2012/7/23 ECO 2021 Intermediate Macroeconomic Theory Professor C. K. Yip 5 Consumers Notations: y and t denote real income and tax in first period. y' and t' denote real income and tax in second period. Current period budget constraint: c + s = y t (1) Consumers after-tax income can either be saved (s) or consumed (c). Saving > 0 (< 0) ? Buys (sells) a bond with part of his income. ? The consumer is a lender (borrower).

    6. 2012/7/23 ECO 2021 Intermediate Macroeconomic Theory Professor C. K. Yip 6 Consumers Future period budget constraint: c' = y' t' + (1 + r)s (2) Apart from the after-tax income, the consumer receives the interest and principal on savings. For only two periods, no incentive to save in the second period. ? Consumer will consume everything he has in the second period. Next, to combine the two constraints into one lifetime budget constraint: From (2), we have

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