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Topic 2 - utility & indifference curve utility & indifferen..
Topic 2 - utility & indifference curve utility & indifference curve.

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University of Toronto St. George
Loren Brandt

Topic 2 – Utility & Indifference Curve (Lecture 2 Sept 21st)  Utility Function: CU = u(x , x , x , … , x ) 1 2 3 n Math representation of preference ordering: a. X>Y  U(x)>U(y) b. X~Y  U(x)=U(y) * numbers in the utility function are “ordinal” not “cardinal”* From the utility function, we only know the order of the preference (whether X is before Y), not the strength of the preference (whether the utility of X is 3 times greater than Y) * These utility functions are only unique to a “positive monotonic transformation”. e.g. V[U(x) = [U(X)]2 = 3 + 2U(X) = 5 + lnU(X) All these are examples of “positive monotonic transformation” of the Utility function; The preference order is the same;  Indifference Set/curve 1. Set of commodity bundles that satisfies U(x , x1) 2 U (some level of utility) x2 -- Indifference curve pass to the right indicate higher utility (assume “more is better”) --Slope of the indifference curve: x1 o 2. Total Differentiate “U(x 1 x2) = U ” MU of x1 MU of x2 *MU of x : the utility one gets from consuming one more unit of x1, holding x2 constant. 1 Implication: Measure the rate at which the consumer would be willing to substitute one good for another e.g. 0.5 0.5 Suppose U(x ,1x 2 = x1 * x2 MRS (x for x ) = U1/U2 = x2/x1 2 1 Assume U=100. X1 X2 MRS 100 100 1 225 44.44 0.1975 400 25 0.0625 Implication: MRS d
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