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Topic 04 - Consumption michael

Topic 04 - Consumption michael - BUAD 350 Topic 04...

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BUAD 350 Topic 04 – Consumption and Saving
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Keywords Intertemporal choice The two-period model Permanent income hypothesis The life-cycle model Rational expectations
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Why are saving rates falling?
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Are Americans saving too little? “It's a bit soon to tell if American consumers made -- and are keeping -- New Year's resolutions to save more money this year. But they should.” Negative personal savings rate: What does it mean?, by Laura Bruce, Bankrate.com
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How de we analyze saving/consumption choices?
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How de we analyze saving/consumption choices?
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U.S. Savings Rate at Highest Point in 15 Years June 26, 2009, New York Times “Tax cuts from the stimulus package and increases in Social Security checks lifted personal incomes sharply in May, the government reported on Friday, but it appeared that many people were putting that money away instead of spending it.”
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Personal Saving Rate, 1947-2010 U.S. Savings & Investment 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 1947-I 1950-I 1953-I 1956-I 1959-I 1962-I 1965-I 1968-I 1971-I 1974-I 1977-I 1980-I 1983-I 1986-I 1989-I 1992-I 1995-I 1998-I 2001-I 2004-I 2007-I 2010-I Percent Pers Sav/GDP Inv/GDP Private Sav/GDP
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Intertemporal Choice Keynes hypothesized that consumption (and therefore saving, since saving = income - consumption) depends on the current level of income alone
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Intertemporal Choice (contd.) In reality, in choosing how much to consume versus save today, the household is making a tradeoff between the present and the future Irving Fisher formalized this tradeoff, and introduced the interest rate as an important determinant of consumption and saving
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The Two Period Model Assume that consumer lives only for two periods: Period 1: Youth Period 2: Old age Notation: Y 1 , Y 2 : Income in periods one and two C 1 , C 2 : Consumption in periods one and two r: (Real) interest rate at which consumer can borrow/lend
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The Two Period Model (contd.) Budget constraints in the two periods: Period 1: C 1 + S = Y 1 Period 2: C 2 = (1 + r)S + Y 2 If S > 0, consumer is saving. If S < 0, consumer is borrowing
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Example 1: Let Y 1 = 150, Y 2 = 220, C 1 = 120 , and r = 10% Question: What would be maximum C 2 for Curtis?
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Example 1: Solution Let Y 1 = 150, Y 2 = 220, C 1 = 120 , r = 10% 1 st period: S = Y 1 – C 1 = 150 – 120 = 30 (Saver) 2 nd period: C 2 = (1 + r)S + Y 2 = 220 + 30*(1 +0.10) = 253 Curtis is a saver, and C 1 = 120, C 2 = 253 is called his “consumption plan”
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Example 2: Let Y 1 = 150, Y 2 = 220, C 1 = 180 , and r = 10% Question: What would be maximum C 2 for Curtis?
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Example 2: Solution Let Y 1 = 150, Y 2 = 220, C 1 = 180 , r = 10% 1 st period: S = Y 1 – C 1 = 150 – 180 = -30 (Borrower) 2 nd period: C 2 = (1 + r)S + Y 2 = 220 – 30*(1 +0.10) = 187 Curtis is a borrower, and C 1 = 180, C 2 = 187 is called his “consumption plan”
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The Two Period Model (contd.) Substitute for S in first equation S = Y 1 C 1 into the second C 2 = (1 + r)S + Y 2 to get C 2 = (1 + r)(Y 1 C 1 ) + Y 2 Divide both sides by (1+r) and rearrange to get a single intertemporal budget constraint : PV (Cons) = PV (Income) r Y Y r C C + + = + + 1 1 2 1 2 1
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Example 1 Revisited Let Y 1 = 150, Y 2 = 220, C 1 = 120, and r = 10% Use the intertemporal budget constraint: C 1 + C 2 / (1 + r) = Y 1 + Y 2 / (1 + r) 120 + C 2 / (1 + 0.1) = 150 + 220 / (1 + 0.1) = 350 C
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