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Consumer Theory 7

# Consumer Theory 7 - Economics 21 Intermediate...

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Economics 21 Intermediate Microeconomics Topic 2: Consumer Theory (vii) Application 2: Intertemporal Consumption

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I. Applications Two key areas: (i) Labour Supply; (ii) Intertemporal Choice.
II. Intertemporal Choice Assume individual lives for two periods with a lifetime income endowment of y = ( y 1 , y 2 ) Consumption over time is c = ( c 1 , c 2 ) Now, \$ x saved today (i.e. period 1) will yield \$(1+ r ) x tomorrow (i.e. period 2) The future value of \$ x today is thus \$(1+ r ) x

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II. Intertemporal Choice Conversely, the present value of \$ x received tomorrow (i.e. period 2) is: Intuitively, if we receive \$ x tomorrow, can borrow \$ z today, where: \$ 1 1 + ρ ξ \$ z 1 + ρ ( 29 = 5 ξ ⇒ 5 ζ = 5 1 1+ ρ ξ
II. Intertemporal Choice Thus, given an income endowment of: Then the maximum period 1 income is: And the maximum period 2 income is: ( 29 0 0 0 1 2 , y y y = ( 29 0 0 0 2 2 1 ö 1 y y r y = + + 0 0 0 1 1 2 1 ö 1 y y y r = + +

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y 2 0 y 1 Figure 1: Intertemporal Budget Constraint 0 2 ö y y 1 0 y 2 0 ( 29 0 0 0 1 2 , y y y = 0 1 ö y ( 29 0 0 0 2 2 1 ö 1 y y r y = + + 0 0 0 1 1 2 1 ö 1 y y y r = + +
II. Intertemporal Choice Assume individual consumes in both periods

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Consumer Theory 7 - Economics 21 Intermediate...

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