090906_Intertemporal consumption choice

090906_Intertemporal consumption choice - Inter-temporal...

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Inter-temporal Consumption Choice Lecture 1 05 September 2009
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The Basic Economic Concepts of Consumer Choice z We assume a unique happiness function for every individual (utility function). We call such function the individual’s subjective preference. z Every individual is going to maximize his happiness subject to some constraints. z E.g., max [ U(x, y) ] subject to P x X+P y Y W
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The Basic Economic Concepts of Consumer Choice z We can represent individual’s preference, U(x, y) , by indifference curves on the x-y diagram. x y U 0 U 1 U 2 Represent higher levels of utility U 0 < U 1 < U 2
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The Basic Economic Concepts of Consumer Choice z The constraint of P x X+P y Y W can be shown as the budget line. x y Budget line ( Slope = P x /P y ) W/P y W/P x Feasible Consumption Set
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The Basic Economic Concepts of Consumer Choice z Maximizing utility means picking the best feasible consumption point ( C* ). The equilibrium condition is: (slope of indifference curve) MRS = P x /P y (Slope of budget line) Where MRS = MU x /MU y x y U 0 U 1 U 2 W/P y W/P x C* (with consumption of x* and y*) x* y*
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Intertemporal Resources Allocation z For inter-temporal consumption choice, we employ the same rationale. Now, x becomes current consumption ( C 0 ) and y becomes future consumption ( C 1 ). That means, our happiness depends on two things: current and future consumption. C 0 C 1 U 0 U 1 U 2
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Intertemporal Resource Allocation z In order to have the indifference curves as described with nice convex- to-the-origin shape, we assume: More is better than less. Diminishing marginal utility of consumption for a single period. U(C 0 ,C 1 ) C 0 U = U(C 0 ,C 1 =constant) MU > 0 Ù ( U / C 0 ) > 0 MU is diminishing i.e., ( 2 U / C 2 ) < 0
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Intertemporal Resource Allocation z With the assumptions, we have the following diagram. The slope of the indifference curve represents the individual s subjective rate of time preference. C 0 C 1 U 0 z We call the slope the marginal rate of substitution between current consumption and future consumption. The math expression is: MRS = MU(C 0 )/MU(C 1 )= ( U / C 0 ) / ( U / C 1 )
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The Constraint z Constraints depend on the options available for the individual to
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This note was uploaded on 10/12/2010 for the course BANKING AN 001 taught by Professor Bogdukevich during the Fall '10 term at London Business School.

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090906_Intertemporal consumption choice - Inter-temporal...

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