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Lecture_08_Intertemporal_Choice

Lecture_08_Intertemporal_Choice - Lecture 8 Intertemporal...

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Lecture 8: Intertemporal Choice c ° 2008 Je/rey A. Miron Outline 1. Introduction 2. Intertemporal Consumption Choice 2. Comparative Statics: Borrowers versus Lenders 3. The Interest Rate and Savings 4. Real versus Nominal Interest Rates 1 Introduction We next want to examine an application of the consumer choice model to a situation where the consumer chooses consumption today versus consumption tomorrow. This application provides a number of useful insights, some of them similar to insights from the labor supply application. The intertemporal choice model is also the foundation for a large fraction of modern macroeconomics and much of modern °nance. We will mention a few of these practical applications here, and you should °nd this material helpful in later courses. In addition, this material provides a good illustration and review of the techniques we have developed so far. Consider a consumer who thinks about how much to consume of some composite good in each of two periods: ( c 1 ; c 2 ) The price of consumption in each period is °xed at 1. The consumer receives an endowment of consumption goods (manna from heaven) in each period: ( ! 1 ; ! 2 ) . 1
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The key issue is specifying how the consumer can transfer endowments across time. Essentially, we want to understand what factors determine how much the consumer chooses to consume this period versus next period. In all the examples below, we assume the consumer has a utility function that depends on the amount of consumption this period and the amount of consumption next period: u ( c 1 ; c 2 ) . This is the most general utility function we could specify for this situation. Often it is useful to choose a more restricted utility function; for example, we might want to make u () additively separable in consumption today versus consumption tomorrow: u ( c 1 ; c 2 ) = v ( c 1 ) + w ( c 2 ) . In many cases, we impose a further restriction and write u ( c 1 ; c 2 ) = v ( c 1 ) + °v ( c 2 ) 0 < ° < 1 . This says that the consumer has the same within period utility function in each period, but that viewed from this period, getting consumption next period is not as good as getting consumption now; the consumer discounts future consumption at the rate ° . Thus, ° is known as the discount factor. 2 Intertemporal Consumption Choice Given this framework, the °rst case to consider is one where the consumption good is non-storable; for example, the good might be food that only lasts one period and then becomes inedible. In addition, we assume that no asset markets exist, so the consumer cannot borrow or lend or buy stocks or own anything that has durable value between periods 1 and 2. In this case, what does the budget set look like?
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