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lecturenotes2w11 (1)

# lecturenotes2w11 (1) - A Two-Period Economy(Part II Giacomo...

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A Two-Period Economy (Part II) Giacomo Rondina Lecture Notes Prepared for Econ110B Department of Economics University of California, San Diego Winter 2011 These notes build on Part I to show that consumption today C is a positive function of the level of lifetime expected wealth W . In Part I we showed that income and consumption in period t must be related to income and consumption in period t + 1 according to the following relationship ( Y C ) = 1 (1 + r ) ( C 0 Y 0 ) . (1) If we rearrange this equation we get Y + Y 0 (1 + r ) = C + C 0 (1 + r ) . (2) This expression says that whatever is the income of an agent over her lifetime (today and in the future) in terms of apples today, this must be equal to whatever the agent consumes over her lifetime (today and in the future). The left hand side of this equation can be termed the lifetime wealth of agent today and denote it by W = Y + Y 0 (1 + r ) . There are many combinations of current and future income Y and Y 0 that would result in the same level of lifetime wealth W for a given level of the real interest rate r . We can represent this 1

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W 0 ( 1+r ) Apples in the Future W 1 ( 1+r ) Budget Constraint Apples Today W 0 W 1 Figure 1: Total Lifetime Wealth and the Budget Constraint set of points in a diagram and call them the budget constraint for the agent. This is represented by the straight line in Figure 1. Notice the axis of the diagram. The horizontal axis measure the amount of goods (apples) today, while the vertical axis measure the among of goods (apples) in the future. Any point in the diagram corresponds to a combination of apples today and apples in the future. All the points to the right of that line are combinations of apples today and apples in the future that the economic agent cannot a ff ord as her wealth is not enough to buy them. All the points to the left of that line are combinations of apples today and apples in the future that the economic agent can a ff ord and, in addition, some wealth will be not spent by the end of the two periods. All the points on the budget constraint are combinations of apples today and apples in the future that the economic agent can just a ff ord: no wealth will be unspent at the end of the agent’s lifetime.
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lecturenotes2w11 (1) - A Two-Period Economy(Part II Giacomo...

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