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Lecture 11 Example 4.1 -- Consumption Saving Choice -- Solved

# Lecture 11 Example 4.1 -- Consumption Saving Choice -- Solved

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1/10 ECO 320L INTERMEDIATE MACROECONOMICS Example: Consumption/Saving choice 9/20/2010 Professor Beatrix Paal BRB 3.114 (512) 475-8531 THE OPTIMAL CONSUMPTION/SAVING CHOICE: AN ANALYTICAL EXAMPLE Notation reminder y : pre-tax income during the current period y f : pre-tax income during the future period nt : per capita net tax (tax minus transfer) in the current period nt f : per capita net tax in the future period a : initial assets. y = y nt : after-tax income during the current period (income minus net tax) f y = y f nt f : after-tax income during the future period c : current consumption c f : future consumption ( ) : utility function Example 1: Initial Situation Let the household’s utility function be ( , ) 4ln 6ln f f u c c c c In the initial situation, subscripted with 1, the household’s after -tax incomes and initial assets are given by 1 1 12 60 4 f y y a   And the real interest rate is 1 25% r The household’s PVLR and FVLR can be calculated as

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ECO 320L, Professor Beatrix Paal Example: Consumption/Saving choice updated 9/20/2010 2:18 PM 2/10 PVLR = 60 12 4 56 1 1.25 48 f y y a r FVLR = ( )(1 ) (12 4)1.25 60 70 10 f y a r y , or FVLR = (1 + r ) PVLR = 1.25 56 70 The budget set of the household is illustrated in the figure below: B A C 𝑐 𝑓 56 12 4 = 8 60 70 𝑐
ECO 320L, Professor Beatrix Paal Example: Consumption/Saving choice updated 9/20/2010 2:18 PM 3/10 The household solves the following problem: , max 4ln 6ln . .

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Lecture 11 Example 4.1 -- Consumption Saving Choice -- Solved

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