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Econ 154a Problem Set 3

# Econ 154a Problem Set 3 - I Problem 1 Two-Period Model of...

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I. Problem 1: Two-Period Model of Savings and Investment 1. Analysis of a decrease in current income, X (X 0 and X f are set to 100; X 1 is set to 50; r is set to 0.05 and the consumer’s utility function is maximized when C = C f ): Two-Period Model of Savings and Investment 0 50 100 150 200 250 0 50 100 150 200 250 Present Consumption (C) Future Consumption (Cf) Original Lifetime Budget Constraint Original Utility Indifference Curve Shifted Lifetime Budget Constraint Shifted Utility Indifference Curve Current consumption, C, decreases (from 100 to 74.39 in this case); future consumption, C f , decreases (from 100 to 74.39 in this case); saving, S, decreases (from 0 to -25.61 in this case). Since, C = X – S, Δ C = Δ X – Δ S. As stated above, Δ S is negative, so – Δ S is positive and Δ C > Δ X. However, because Δ C and Δ X are both negative, | Δ C| < | Δ X|. 2. Analysis of a decrease in the real interest rate, r (X and X f are set to 100; r 0 is set to 0.50; r 1 is set to 0.05 and the consumer’s utility function is maximized when C = 2C f ):

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Two-Period Model of Savings and Investment 0 50 100 150 200 250 0 20 40 60 80 100 120 140 160 180 200 Present Consumption (C) Future Consumption (Cf) Original Lifetime Budget Constraint Original Utility Indifference Curve Shifted Lifetime Budget Constraint Shifted Utility Indifference Curve Intermediate Budget Line When the real interest rate drops for a borrower, the price of present consumption decreases relative to the price of future consumption. Thus, the borrower will substitute present consumption for future consumption (lowering saving and future consumption while increasing present consumption). Additionally, when the interest rate drops, the borrower will pay less in interest than he had originally projected, this is equivalent to a rise in the total income available for consumption; acting to smooth consumption, the consumer will split the additional income between present and future consumption. Also, the increase in present consumption implies a decrease in saving. Taken together, these effects predict a decrease in saving and an increase in present consumption; the effect on future consumption is indeterminate.
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