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### Consumer Preferences

A consumer’s choice of what bundle to consume determines her product-level demand at the given prices.

Choice reflects preferences under constraints. We need a way to represent preferences, and then combine this information with other information about the constraints.
Analysis of these two sides of the problem allows us to derive consumer demand.

A preference relation that is complete, reflexive, and transitive can be represented by a continuous utility function. Continuity means that small changes to a consumption bundle cause only small changes to the preference level.

An indifference curve contains equally preferred bundles. Equal preference ⇒ same utility level. Therefore, all bundles in an indifference curve have the same utility level. So the bundles (4,1) and (2,2) are in the indifference curve with utility level U ≡ 4

### Utility Maximization The most preferred affordable bundle is called the consumer’s ORDINARY DEMAND at the given prices and budget. Ordinary demands will be denoted by x1*(p1,p2,m) and x2*(p1,p2,m). When x1* > 0 and x2* > 0 the demanded bundle is INTERIOR. the slope of the budget constraint, -p1/p2, and the slope of the indifference curve containing (x1*,x2*) are equal at (x1*,x2*).

The study of how ordinary demands x1*(p1,p2,m) and x2*(p1,p2,m) change as prices p1, p2, and income, m, change.

The curve containing all the utility-maximizing bundles traced out as p1 changes, with p2 and m constant, is the p1- price offer curve.

The plot of the x1-coordinate of the p1- price offer curve against p1 is the ordinary demand curve for commodity 1.

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