Chapter3_on_Savings_PV_&_Ricardian_Equivalence

Chapter3_on_Savings_PV_&_Ricardian_Equivalence -...

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1 Chapter 3 Savings, Present Value and Ricardian Equivalence Chapter Overview In the previous chapter we studied the decision of households to supply hours to the labor market. This decision was a static decision, as it was done within the same period. We now turn to another important decision of households for which there is a time element – namely, the household’s saving decision. How much one saves today affects how much one consumes today and in the future. Because ones decision today affects one’s future situation, the decision is intertemporal . This chapter consists of two parts. We begin this chapter by studying the household consumption/savings behavior. As we shall see, the optimization problem and conditions are very similar to those developed in the previous chapter on the household’s labor/leisure decision. In studying this problem, we define the notion of present value, and wealth. The second part of the chapter analyzes the effect of a particular type of tax change on consumer’s savings decision. This is what is known as Ricardian Equivalence. We will postpone the integration of these concepts into a dynamic general equilibrium model until the next chapter. In doing so, we shall examine the US social security system and determine if there is another system that will not go bankrupt and that can make both young and old better off.
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2 I. Microeconomic Foundations Consumer Theory We return to our study of microeconomics and the theory of the consumer. Currently, we are interested in the choice of savings, namely, how much to eat today versus how much to eat tomorrow. For this purpose, we shall begin with an assumption that our consumer lives for only two periods, Periods 1 and 2, and that he/she derives happiness or utility from consumption in Period 1 and consumption in Period 2. For now, we will assume that the household does not derive any utility from leisure. We will relax this assumption in the next chapter. Given these assumptions, the household’ utility function is denoted by ) , ( 2 1 c c U where c 1 is the quantity of the good consumed in the first period and c 2 in the quantity of the good consumed in the second period. Indifference Curves Given that the household’s utility is defined over two goods, we can still represent it via indifference curves and show the optimal saving choice graphically. Figure 1 shows the indifference curves. On the horizontal axis is Period 1 consumption, c 1 , and on the vertical axis is Period 2 consumption, c 2 .
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3 As we saw in our study of the household labor decision, each indifference curve describes all the combinations of consumption in period 1 and consumption in period 2 that gives the household a certain level of utility. The consumer, hence, is indifferent between any of the consumption bundles along a given curve. Again, as long as more consumption of each good is desirable, the indifference curve must be downward sloping. Additionally, as long as people like variety, the indifference curve, is convex, namely,
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This note was uploaded on 05/23/2011 for the course ECON 509 taught by Professor Villamil during the Spring '08 term at University of Illinois, Urbana Champaign.

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Chapter3_on_Savings_PV_&_Ricardian_Equivalence -...

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