Transcript Ch08A-7e[1]
MARGINAL UTILITY AND INDIFFERENCE CURVES 8 APPENDIX Objectives After studying this appendix, you will able to Explain the connection between utility and indifference curves Explain why maximizing utility is the same as choosing the best affordable point Explain why utility exists Two Ways of Describing Preferences The marginal utility model describes preferences by using the concept of utility. The indifference curve model describes preferences by using the concepts of preference and indifference. Figure A8.1 on the next slide illustrates the connection between these two ways of describing preferences. Two Ways of Describing Preferences In part (a), you can see the levels of utility derived from each quantity of movies and soda. Three combinations generate 331 units of utility and two combinations generate 313 units of utility. Indifference curves pass through these points. Maximizing Utility is Choosing the Best Affordable Point Call the marginal utility of movies MUM Call the marginal utility of soda MUS Call the price of movies PM Call the price of soda PS The marginal utility per dollar spent on movies is MUM/PM The marginal utility per dollar spent on soda is MUS/PS. Utility is maximized when MUM/PM = MUS/PS. Maximizing Utility is Choosing the Best Affordable Point Call the marginal rate of substitution of movies for soda MRS. The consumer is at the best affordable point on the budget line when MRS = PM/PS. Maximizing Utility is Choosing the Best Affordable Point To see that maximizing utility is the same as choosing the best affordable point, begin with MUM/PM = MUS/PS and multiply both sides of this equation by PM and divide both sides by MUS to get MUM/MUS = PM/PS. But the best affordable point is when MRS = PM/PS. MUM/MUS = PM/PS. Maximizing Utility is Choosing the Best Affordable Point Because the best affordable point is when MRS = PM/PS, it must be the case that MUM/MUS = MRS. To see that this proposition is true, note first that: U = MUM QM + MUS QS But along an indifference curve, which is where we measure MRS, U = 0, so 0 = MUM QM + MUS QS Maximizing Utility is Choosing the Best Affordable Point Because 0 = MUM QM + MUS QS we know that MUM QM = –MUS QS Now divide both sides of this equation by MUS and by QM to obtain MUM / MUS = –QS /QM Maximizing Utility is Choosing the Best Affordable Point But –QS /QM—rise over run—is the slope of the indifference curve and removing the minus sign, it is the marginal rate of substitution. So MRS = MUM / MUS = –QS /QM The two models of consumer choice give the same answer. One implies the other. Utility Exists! The indifference curve model is powerful because it enables us to derive the downward-sloping demand curve from the assumption of diminishing marginal rate of substitution. The model is also powerful because it implies that utility exists. By observing incomes and prices and the quantities bought at those prices, we can infer a person’s utility schedule and the marginal utilities at each quantity combination. Consumption Possibilities A household’s real income is the income expressed as a quantity of goods the household can afford to buy. Lisa’s real income in terms of soda is the point on her budget line where it meets the y-axis. A relative price is the price of one good divided by the price of another good. It is the magnitude of the slope of the budget line The relative price shows how many sodas must be forgone to see an additional movie. THE END