Indifference curve

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Indifference Curves and Utility Maximization

CHAPTER

6 Appendix

© 2003 South-Western/Thomson Learning

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Marginal utility analysis requires some numerical measure of utility in order to determine the optimal consumption combinations

Economists have developed another, more general, approach to utility and consumer behavior

This approach does not require that numbers be attached to specific levels of utility

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All this new approach requires is that consumers be able to rank their preferences for various combinations of goods

Specifically, the consumer should be able to say whether

Combination A is preferred to combination BCombination B is preferred to combination A. orBoth combinations are equally preferred

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Consumer PreferencesIndifference curve shows all combinations of goods that provide the consumer with the same satisfaction, or the same utility

Thus, the consumer finds all combinations on a curve equally preferred

Since each of the alternative bundles of goods yields the same level of utility, the consumer is indifferent about which combination is actually consumed

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Indifference CurvesFor a person to remain indifferent among consumption combinations, the increase in utility from eating more pizza must just offset the decrease in utility from watching fewer videos

Thus, along an indifference curve, there is an inverse relationship between the quantity of one good consumed and the quantity of another consumed indifference curves slope down

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Indifference CurvesIndifference curves are also convex to the origin they are bowed inward toward the origin

The curve gets flatter as you move down it

The marginal rate of substitution, or MRS, between pizza and videos indicates the number of videos that the consumer is willing to give up to get one more pizza, while maintaining the same level of total utility

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Marginal Rate of Substitution

The MRS measures the consumers willingness to trade videos for pizza depends on the amount of each good the consumer is consuming at the time

Mathematically, the MRS is equal to the absolute value of the slope of the indifference curve

For example, in moving from combination a to combination b, the consumer is willing to give up 4 videos to get 1 more pizza slope between these two points equals –4 MRS = 4; from b to c, MRS = 1

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Marginal Rate of SubstitutionThe law of diminishing marginal rate of substitution says that as a persons consumption of pizza increases, the number of videos that they are willing to give up to get another pizza declines

This implies that the indifference curve has a diminishing slope as we move down the indifference curve, the consumption of pizza increases and the marginal utility of additional pizza declines

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Indifference Map

We can use the same approach to generate a series of indifference curves, called an indifference map graphical representation of a consumer’s tastes

Each curve in the map reflects a different level of utility

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Properties of Indifference Curves

A particular indifference curve reflects a constant level of utility the consumer is indifferent among all consumption combinations along a given curveIf total utility is to remain constant, an increase in the consumption of one good must be offset by a decrease in the consumption of the other good indifference curves slope downwardHigher indifference curves represent higher levels of utility

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Because of the law of diminishing marginal rate of substitution, indifference curves are bowed in toward the origin

Indifference curves do not intersect

Indifference curves are a graphical representation of a consumer’s tastes for the two goods

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Once we have the consumer’s indifference may, we turn to the issue of how much of each good will be consumed?

To answer this question, we must consider the relative prices of the two goods and the consumer’s income

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Budget LineBudget line depicts all possible combinations of movies and pizzas, given prices and your budget

Suppose movies rent for $4, pizza sells for $8, and the budget is $40 per week if you spend the entire $40 on videos, consumer can purchase 10 videos, and if on pizzas person can afford 5 per week

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SummaryThe indifference curve indicates what the consumer is willing to buy

The budget line shows what the consumer is able to buy

When the indifference curve and the budget line are combined, we find the quantities of each good the consumer is both willing and able to buy

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Consumer Equilibrium

Consumer equilibrium occurs where the slope of the indifference curve is equal to the slope of the budget line

Recall that the absolute value of the slope of the indifference curve is the marginal rate of substitution, and the absolute value of the slope of the budget line equals the price ratio

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Consumer Equilibrium

Thus,

MRS = Pp / Pv

Further, the marginal rate of substitution of pizzas for video rentals can be found from the marginal utilities of pizza and video MRS = MUp / MUv

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Consumer EquilibriumIn fact, the absolute value of the slope of the indifference curve equals MUp/MUv and the slope of the budget line equals pp / pv the equilibrium condition for the indifference curve approach can be written as

V

V

P

P

PMU

PMU

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Effects of a Change in PriceWhat happens to the consumer’s equilibrium consumption when there is a change in price?

The answer can be found by using indifference curve approach to derive the demand curve

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Income and Substitution Effects

The law of demand was initially explained in terms of an income effect and a substitution effect

With indifference curve analysis we have the analytical tools to examine these two effects more precisely

Technology

Indifference curve