Lecture 1
- 2. Utility Maximization Learning Objective • How do economists model consumer choice? • Define what economists mean by utility. • Distinguish between the concepts of total utility and marginal utility. • State the law of diminishing marginal utility and illustrate it graphically. • State, explain, and illustrate algebraically the utility-maximizing condition.
- 3. Let us consider spending
- 4. Budget or Feasible Set Learning Objective • How does income limit choice?
- 5. Consumer Choice • Suppose that a consumer has a fixed amount of money to spend, M. • There are two goods X and Y, with associated prices pX and pY. • The feasible choices that the consumer can make satisfy pXx+pYy≤M
- 6. Figure 12.1. Budget set • The budget line • The boundary of the budget set, and it consists of the goods that just exhaust the consumer’s budget
- 7. Figure 12.2. Effect of an increase in price on the budget • An increase in the price of one good pivots or rotates the budget line. • Increasing prices and income by the same multiplicative factor leaves the feasible set unchanged.
- 8. 3.1 The Budget Line EQUATION 3.1 PX QX + PY QY ≤ M 7 Unattainable The combination in the 6 combinations region above the budget D 5 line are unattainable, given Ms. Bain’s budget 4 The budget line constraint graphically shows the 3 combinations of two 2 goods a consumer can Budget Ms. Bain’s budget allows her line buy with a given budget 1 to purchase any combination m D on or below the budget line. o p n e a k g y 0 s r t f i E 0 1 2 3 4 5 6 7 Days of horseback riding per semester EQUATION 3.2 M / PS Slope = − M / PH EQUATION 3.3 M PH P Slope = − × =− H PS M PS
- 9. Revealed preference • Can we determine preferences just from the budget and from peoples choices? Or do we have to ask people to state their preferences in order to discover their preferences? • Revealed versus stated preferences
- 10. Revealed preference Suppose you are observed to Choose A, A is then revealed to be preferred to all other points on or below the same budget line M/py A Now if py increases and px falls B so the budget line goes though B, you will Be worse of at B
- 11. Revealed preference Suppose C is chosen then C is revelaed preferred to A M/py A D But if D is chosen over C Then D is reveled preferred to C C B
- 12. Revealed preferences • If some bundles are chosen over others at the same budget and prices then this demonstrates that people prefer that bundle to the alternatives they are offered
- 13. Preferences • Reflexivity • Completeness • Transitivity • Non-satiation
- 14. Utility • Refers not to usefulness but to the flow of pleasure or happiness that a person enjoys —some measure of the satisfaction a person experiences. • Usefulness might contribute to utility, but so does style, fashion, or even whimsy.
- 15. Utility • Suppose there are two goods, X and Y. • Suppose the consumer is both hungry and thirsty, and the goods are pizza and beer. – The consumer would like more of both, reflected in greater pleasure for greater consumption. – Items that one might consume are generally known as “bundles,” as in bundles of goods and services
- 16. Isoquants Learning Objectives • What is an isoquant? • Why does it help to analyze consumer choice?
- 17. Isoquants • Meaning “equal quantity,” are also known as indifference curves and represent sets of points holding utility constant. • They are analogous to production isoquants.
- 18. Figure 12.4. Indifference curves • Each curve represents one level of utility. • Higher utilities occur to the northeast, farther away from the origin. • As with production isoquants, the slope of the indifference curves has the interpretation of the trade-off between the two goods. • The amount of Y that the consumer is willing to give up, in order to obtain an extra bit of X, is the slope of the indifference curve.
- 19. Figure 12.5. Convex preferences • Convex preferences mean that a consumer prefers a mix to any two equally valuable extremes. • Thus, if the consumer likes black coffee and also likes drinking milk, then the consumer prefers some of each—not necessarily mixed—to only drinking coffee or only drinking milk.
- 20. 3.2 Indifference Curves The marginal rate of substitution is the maximum amount of one good a consumer would be willing to give up in order to obtain an additional unit of another
- 21. Marginal Rate of Substitution • (MRS) The amount extra of one good needed to make up for a decrease in another good, staying on an indifference curve. is the extra amount of one good needed to make up for a decrease in another good, staying on an indifference curve
- 22. Marginal rate of substitution
- 23. Utility maximization Three possible solution methods: •Tabular solution •Graphical solution •Algebraic solution
- 24. Recalling the budget set • How does income limit choice?
- 26. Budget set
- 27. Discrete goods
- 29. Constrained utility maximisation
- 30. Demand
- 31. Deriving demand
- 32. Demand curve
- 33. Utility maximization • Utility maximization is a matter of selecting a combination of two goods that satisfy two conditions – The point at which utility is maximized must be within the attainable region defined by the budget line. – The point at which utility is maximized must be on the highest indifference curve consistent with condition 1. EQUATION 3.4 P MRS X ,Y = X PY
- 34. 3.3 The Utility-Maximizing Solution PX MRS X ,Y = PY
- 35. 3.4 Utility Maximization and the Marginal Decision Rule
- 36. 3.5 Utility Maximization and Demand
- 37. Algebraic derivation y
- 39. Examples Learning Objective • Are there any convenient functional forms for analyzing consumer choice?
- 41. Example of demand derivation Verify this yourself using WolframAlpha!
- 42. Rearrange to find x Verify this in Wolfram Alpha!
- 43. What about y? But So Once again you can solve this in WolframAlpha. Hint: Break the problem into steps!
- 44. Satiation • The point at which increased consumption does not increase utility.—the point at which increased consumption does not increase utility—would set in at some point. • How many pizzas can you eat per month? How much beer can you drink?
- 45. Figure 12.8. Isoquants for a bliss point • A bliss point, or satiation, is a point at which further increases in consumption reduce utility.
- 46. Substitution Effects Learning Objective • When prices change, how do consumers change their behavior?
- 47. Changes in Consumer Behavior • An increase in the price of a good is really a composition of two effects: an increase in the relative price of the good and a decrease in the purchasing power of money • The substitution effect is the change in consumption resulting from a price change keeping utility constant. The substitution effect always involves a reduction in the good whose price increased. • The amount of money required to keep the consumer’s utility constant from an infinitesimal price increase is precisely the amount required to let him or her buy his or her old bundle at the new prices.
- 48. Figure 12.9. Substitution with an increase in price • An increase in the price of Y causes the budget line to pivot around the intersection on the x-axis • Since the amount of X that can be purchased hasn’t changed. In this case, the quantity y of Y demanded rises.
- 49. Figure 12.10. Substitution effect • The effect on consumption of a change in the relative price, with a sufficient change in income to keep the consumer on the same utility isoquant. • The income effect changes only income.
- 50. Income Effects Learning Objective • How do consumers change their purchases when their income rises or falls?
- 51. Income effect on Consumer Behavior • When an increase in income causes a consumer to buy more of a good, that good is called a normal good for that consumer. • When the consumer buys less, the good is called an inferior good. At a sufficiently high income, most goods become inferior.
- 52. Figure 12.11. Engel curve • The curve that shows the path of consumption as income changes, holding prices constant, is known as an Engel curve
- 53. Figure 12.12. Backward bending— Figure 12.13. Income and substitution inferior good effects
- 54. Price and Income effects • The effect of a price increase decomposes into two effects: a decrease in real income and a substitution effect from the change in the price ratio. For normal goods, a price increase decreases quantity. For inferior goods, a price increase decreases quantity only if the substitution effect is larger than the income effect.
- 55. Mathematical Cleanup Learning Objectives • Are there important details that haven’t been addressed in the presentation of utility maximization? • What happens when consumers buy none of a good?
- 56. • Conditions are available that ensure that the first-order conditions produce a utility maximum. • With convex preferences, zero consumption of one good arises when utility is decreasing in the consumption of one good, spending the rest of income on the other good.