Indifference Curves and Utility Maximization Chapter 6 Appendix Indifference Curves and Utility Maximization © 2006 Thomson/South-Western

Indifference Curves and Utility Maximization Consumers should be able to rank their preferences for various combinations of goods, for example: Combination A is preferred to combination B Combination B is preferred to combination A Both combinations are equally preferred

Consumer Preferences Indifference curve shows all combinations of goods that provide the consumer with the same utility Thus, the consumer finds all combinations on a curve that are equally preferred Each of the alternative bundles of goods yields the same level of utility, so the consumer is indifferent about which combination is actually consumed

Exhibit 9: An Indifference Curve Moving from point a to b, the consumer is willing to give up four videos to get a second pizza – the marginal utility of the additional pizza per week is just sufficient to compensate for the utility lost from decreasing video purchases by four movies per week Moving from b to c, the person is willing to give up only 1 video for another pizza, etc. Connecting points a, b, c, and d gives the indifference curve I, which represents all possible combinations of pizza and videos that would keep a person at the same level of utility

Marginal Rate of Substitution (MRS) MRS indicates the number of videos the consumer is willing to give up to get one more pizza, while maintaining the same level of total utility Mathematically, the MRS is equal to the absolute value of the slope of the indifference curve

Exhibit 10: An Indifference Map

Exhibit 11: Indifference Curves Do Not Intersect If indifference curves crossed, such as point i, then every point on indifference curve I and every point on curve I' would have to reflect the same level of utility as at point i But point k is a combination with more pizza and more videos than point j and must represent a higher level of utility k Video Rentals per week j i I' I Pizzas per week

Properties of Indifference Curves Each indifference curve reflects a constant level of utility: the consumer is indifferent among all consumption combinations along a given curve Increases in the consumption of one good must be offset by a decrease in the consumption of the other good: indifference curves slope downward Higher indifference curves represent higher levels of utility Law of diminishing marginal rate of substitution: indifference curves are bowed in toward the origin They do not intersect Graphical representation of consumer preferences

Budget 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 entire $40 spent on videos, consumer can purchase 10 videos If spent on pizzas person can afford 5 per week

Exhibit 12: A Budget Line

Summary The 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 Exhibit 13 illustrates this

Exhibit 13: Utility Maximization The utility-maximizing consumer will select a combination along the budget line that lies on the highest attainable indifference curve Given prices and income, this occurs at point e, where I2 just touches or is tangent to the budget line Other attainable combinations along the budget line reflect lower levels of utility

Consumer Equilibrium MRS = Pp / Pv Marginal rate of substitution of pizzas for video rentals can be found from the marginal utilities of pizza and video  MRS = MUp / MUv

Consumer Equilibrium In 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

Effects of a Change in Price What 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 Exhibit 14 illustrates this process

Exhibit 14: Effect of a Drop in Price of Pizza If the price of pizza falls from $8 to $6 per unit, other things constant, the consumer could purchase 6.67 pizzas (40 / 6) if the entire budget was used for pizza Since the rental price of videos has not changed, the maximum number of videos that can be rented remains at 10 As a result of the price change, the lower end of the budget line rotates rightward from 5 to 6.67 After the price change, the new equilibrium is at e”, where pizza purchases increase from 3 to 4 and video rentals remain at 4 The demand curve in panel b shows how price and quantity demanded are related

Exhibit 15: Substitution and Income Effects To derive the substitution effect, assume that you must maintain the same level of utility after the price change as before  consumer’s utility has not changed, but the relative prices faced have changed