L2Preferences - Introduction to Microeconomics Lecture 2...

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Introduction to Microeconomics Lecture 2 Preferences, Utility and Choice Simon Cowan
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Outline Preferences Utility functions Indifference curves Examples of common utility functions Using utility theory to model household choices: utility maximization and the budget constraint
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Preferences: what do households care about? We think of households or consumers as having given preferences over bundles of goods Goods/services are interpreted broadly: current goods, e.g. films and meals out saving v. spending now: good 1 is spending now, good 2 is spending in the future Time spent at leisure, and consumption of goods and services Examples of bundles: x = {3 apples, 2 bananas}, y = {2 apples, 4 bananas}
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The basic preference relations x is strictly preferred to y : xPy y is strictly preferred to x : yPx Indifference: x and y are “indifferent”: xIy x is preferred to y means either strict preference or indifference: xRy . In fact strict preference and indifference can be defined in terms of the preference relation, R, and “not”. xPy if and only if xRy and not xIy xIy if and only if xRy and yRx
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Three assumptions about preferences 1. Completeness: all possible bundles can be compared 2. Reflexivity: xRx . All bundles are at least as good as themselves (not a very exciting property) 3. Transitivity: if xRy and yRz then xRz . Those of you doing Logic will later learn about the logic of relations. Preference, R , is a relation which is analogous to the “greater than or equals” relation for numbers, which is always reflexive, transitive and complete. Indifference, I , is a relation which is reflexive, symmetric and transitive. Analogous to “equals”. Strict preference, P , is a relation which is irreflexive, asymmetric and transitive. Analogous to “greater than”.
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Representation by a utility function Preferences satisfying the three assumptions can be represented by a utility function The utility function is denoted by u (.) and its domain is the set of bundles
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L2Preferences - Introduction to Microeconomics Lecture 2...

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