# Econ: Utility and Straight-line Indifference Curves Essay

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Indifference curves cannot cross each other. (This rule follows from the transitivity and nonsatiation assumptions.)

Indifference curves cannot slope upward. (This rule follows from the nonsatiation assumption.)
Indifference curves farther from the origin contain higher levels of utility. (This rule follows from the nonsatiation assumption and the fact that indifference curves do not cross.) Indifference curves are bowed in toward the origin. (This rule follows from the convexity assumption and the fact that indifference curves farther from the origin contain higher levels of utility.) Points on the same indifference curve represent bundles yielding the same amount of utility. A curve or locus of bundles in the consumption set for a consumer among which the consumer is indifferent.

Properties

Defination

indifference curve

Chapter 3

The good measured on the horizontal axis is yielding no utility for the consumer The same amount of good 2 is always needed to compensate the consumer for the loss of one unit of good 1

Flat indifference curves

Straight-line indifference curves: perfect substitutes Right-angle indifference curves: perfect complements Bowed-Out Indifference C urves: Nonconvex Preferences a bundle for which the marginal rate of substitution equals the ratio of the prices of the goods in the bundle

different curves

Adding any amount of only one good to bundleayields no additional utility

optimal consumption bundle revealed preference theory

A set of indifference curves for a consumer

indifference map

The best bundle to choose from a set of available bundles would then be the one that was assigned the biggest utility number by the agent’s utility function or, more precisely, the one that maximized the utility function over the feasible set of consumption bundles.

A representation of an agent’s preferences that tells the agent how good a bundle is by assigning it a (possibly ordinal) utility number.

Utility Function

Note that with additive utility functions, the enjoyment that a person receives from one type of good (say good x) is independent of the enjoyment or utility he receives from another type of good (say goody). The goods enter such utility functions in an additiveandseparable manner. With these functions, a person need not consume both goods to get positive levels of utility. The same is not true of multiplicative utility functions.

additive utility function simply adds the number of units of goodsxandythat are consumed and uses the total of the units to define the total utility of a bundle. U=x+y

Note that such a person will receive no utility unlessbothgoods are simultaneously purchased. In this case, the goods do not enter the utility function in a separate fashion.

the amount of enjoyment the agent receives from goody(raspberries) directly depends on how many units of goodx(apples) he consumes.

multiplicative utility function U=xy Utility Function

if the utility numbers we assign to objects have no meaning other than to represent the rankingof these goods in terms of a person’s preferences if not only the utility numbers assigned to bundles but also their differences are meaningful people are interested only in their own utility or satisfaction and make their choices with just that in mind more of anything is always better if a consumer is indifferent between a goods bundlexand a goods bundley, then he would prefer (or be indifferent to) a weighted combination of these bundles to either of the original bundlesxory

ordinal utility

cardinal utility

selfishness nonsatiation

Chapter 2