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Chapter 4 Utility Functions

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Utility Ordinal Utility: The only property of a utility assignment is “how it orders the bundles of goods.” The size of the utility difference between two bundles does not matter. Cardinal Utility: It attaches a significance to the magnitude of utility. The size of the utility difference between two bundles has some sort of significance.

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Panel A: A monotonic transformation Panel B: non-monotonic transformation since it sometime decreases.

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The utility function can be represented by a general function: u=f(x1, x2)

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Quasi-linear Utility Function: U=x1+v(x2)=x1+ln(x2)

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The Cobb-Douglas Utility Function U=(x1)^c (x2)^d where ^ represents the superscript Note: goods are imperfect substitutes

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Other Utility Functions: Leontief Function: u=min[a*x1, b*x2] (perfect complements) Linear Function: u=a*x1+b*x2 (perfect substitutes) Lexicographic Preference: A is preferred to B if (I) x1(A) > x1(B) or (ii) x1(A)=x1(B) but x2(A)>x2(B).

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Leontief Function x1 x2 Examples: (1) Left and right shoes (2) coffee and sugar

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Linear Function x1 x2 Example: yellow and red pencils (assuming that colors are not your concern)

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Lexicographic Function x1 x2.. B A A is inferior to B Example: x1 (health) x2 (money) for a terminally ill patient

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Marginal Utility Definition: Effect on utility with a little more of good 1 Formally, MU1=dU/dx1=[u(x1+dx1, x2)- u(x1, x2)]/dx1

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MRS The rate at which a consumer is just willing to substitute a small amount of good 2 for good 1. Formally, MRS=MU1/MU2=[dU/dx1]/[dU/dx2], i.e., marginal utility ratio. This is nothing but the slope of the indifference curve Given strict convexity assumption, MRS diminishes as we move down along a indifference curve

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This concludes the Norton Media Library Slide Set for Chapter 4 Intermediate Microeconomics 6 th Edition by Hal R. Varian W. W. Norton & Company Independent and Employee-Owned

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