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Chapter 9


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ECON 325
Sadik Arouba

A Two Period Model: The Consumption­ Savings Decision and Credit Markets This chapter focuses on intertemporal decisions--that is, decisions that involve economic trade offs across periods of time. This chapter also examines the implications of intertemporal decision making for how government deficits affect macroeconomic activity. This model consists of many consumers, and a government that need not balance its budget and can issue debt to finance a government deficit. The Ricardian equivalence theorem is an important of implication of this model. The theorem states that there are conditions under which the size of a government’s deficit is irrelevant to, in that it does not affect any macroeconomic variables of importance or the economic welfare of any individual. The consumption-savings decision is an intertemporal decision in the sense that it involves trade off between current and future consumption. Similarly, the government’s decision to finance its expenditures is an intertemporal decision in the sense that it involves trade off between future and current taxes. For instance, if the government chooses to lower taxes in the present, it must borrow from the private sector to do so, which implies that taxes will rise in the future in order for the government to pay off its debt. Essentially, the government’s financing decision is one about the quality of saving, or the size of the government deficit, making it related to the consumption-savings decisions of private consumers. The first period is the current period, and the second period is the future period. A key variable of interest in this model is real interest rate--that is, the interest rate at which consumers and the government can borrow and lend. The real interest rate determines the relative price of future consumption in terms of present consumption. An important point of interest with regards to consumer choice is how present and future savings and consumption are affected by changes in the real market interest rate and in the consumer’s present and future income. Another important point of interest is consumption smoothing--that is, the tendency for consumers to seek a consumption path over time that is smoother than income. Consumption-smoothing behavior is implied by certain properties of indifference curves. Consumption-smoothing behavior also has important implications for how consumers respond in the aggregate to changes in government policies or other features of their external environment that affect their income streams. The Ricardian Equivalence Theorem establishes conditions under which the timing of taxation does not matter for economic activity. This theorem attaches importance to the size of the government budget deficit. A key implication of this theorem is that a tax cut is not a free lunch. Interesting issues arise due to frictions in the credit market that cause departures from the Ricardian Equivalence Theorem. A Two Period Model of the Economy: A consumer’s consumption-saving decision (a dynamic decision, that is one that has implications over more than one period in time) fundamentally consists of a trade off between current and future consumption. Through saving, a consumer gives up consumption in exchange for assets in the present to consume more in the future. Also, a consumer can dissave by borrowing in order to increase current consumption, and thus sacrifice future consumption when the loan is repaid. (Borrowing/Dissaving/Negative Savings). Consumers: N is the number of consumers. Each consumer lives for two periods. Each consumer receives exogenous income. (Lowercase letters represent variables at individual level, and uppercase letters represent variables at aggregate levels) y is the consumer’s real income in the current period y is the consumer’s real income in the future period t is the lump-sum tax that each consumer pays in the current period t is the lump-sum tax that each consumer pays in the future period Suppose incomes can be different for different consumers, but all consumers pay the same taxes. s is the consumer’s savings in the current period Then the consumer’s budget constraint in the current period is: c+s=y-t………………………(1) c is the current consumption Eqn (1) states that consumption plus savings is equal to disposable income. We assume that the consumer starts the current period with no assets. If s>0, then the consumer is a lender on the credit market, and if s<0, then the consumer is a borrower. We assume that the financial asset being traded in the credit market is a bond. In this model, bonds can be issued by both consumers and the government. If a consumer lends, then he or she buys bonds, and is he or she borrows, then there is a sale of bonds. Two important assumptions: I. bonds are indistinguishable because a consumer cannot default on his or her debt, that is there is no risk associated with holding a bond. II. Bonds are traded directly into the credit market. In this model, the issue of a bond in the current period is a promise to pay 1+r units of
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