03. Utility and Choice

# 03. Utility and Choice - Utility and Choice Professor John...

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Utility and Choice Professor John Diamond ECON 370: Microeconomic Theory Lecture 3

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2 Preferences, ICs, and Utility Functions If consumer preferences are Complete Reflexive Transitive Continuous (no jumps) Then, preferences can be represented by a continuous utility function . Continuity: small bundle changes cause only small changes to the preference level
3 Utility Functions A utility function U(x) represents a preference relation if and only if: x‟ > x” U(x‟) > U(x”) x‟ < x” U(x‟) < U(x”) x‟ x” U(x‟) = U(x”). The utility function must preserve the preference ordering

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4 Utility Functions Utility is an ordinal (ordering) concept Example If U(x) = 6 and U(y) = 2, then x > y But x not preferred three times as much as y Indifference curve (note that this is a set): all equally preferred bundles Equal preference same utility level Therefore, all bundles on an indifference curve have same utility level
5 Utility Functions and Indifference Curves Example: Suppose bundles (4,1) and (2,2) are on the indifference curve with utility level U Bundle (2,3) is on the indifference curve with utility level U 6. Implies indifference curves:

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6 Utility Functions and Indifference Curves U 6 U 4 (2,3) (2,2) (4,1) x 1 x 2 p
7 Utility Functions and Indifference Curves Or could visualize in three dimensions: Plot consumption bundles in horizontal plane Plot the utility level on a vertical axis Start with several points Add indifference curves through points Add more indifference curves to represent all preferences over all consumption bundles

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8 U(2,3) = 6 U(2,2) = 4 U(4,1) = 4 Utility Functions and Indifference Curves 3-D plot of consumption, utility levels for 3 bundles x 1 x 2 Utility
9 Utility Functions and Indifference Curves U U Higher indifference curves contain more preferred bundles. Utility x 2 x 1

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