9.2          MarginalUtility Theory

Utility

• The benefit or     satisfaction that a person gets from the consumption of a good or service     is called utility.

                                                           

Quantity of movies	Total  utility	Marginal utility
0	0
		24
1	24
		20
2	44
		16
3	60
		12
4	72

• Total utility is the total benefit that     a person gets from the consumption of goods and services. As more of a     good or service is consumed, total utility increases. Marginal utility is the change in total     utility that results from a one-unit increase in the quantity of a good consumed.     Diminishing marginal     utility     is the principle that as more of a good or service is consumed, its     marginal utility decreases.

• The table to the right has the total utility and marginal utility     from an individual’s consumption of movies in a week. As the quantity of     movies increases, total utility increases, but at a decreasing rate – which     reflects diminishing marginal utility. Plotting these points will reveal     the upward sloping but decreasing slope of the total utility curve and the     downward sloping marginal utility curve.

qLandMine: Students often struggle with the concept ofmarginality. A brief and very sloppy use of Bentham’s utility calculus mightsolve the problem while getting the basic concept across. One sweater gives me25 “utils” of bliss, while the second is worth only 23 utils, and so on, untila point come when one more sweater will provoke negative utility as not onlyhave I run out of room in my closet but I’ve just been buried in a wooly avalanche!

Maximizing Total Utility

A consumer’s choicesinfluence the total level of his or her utility by because the choice determinesthe combination of goods that are consumed. Some combinations will generatemore utility than others. The key assumption of marginal utility theory is thatthe household consumes the combination that maximizes its utility.

• The utility-maximizing rule is the rule     that leads to the greatest total utility from all the goods and services     consumed. It has two steps:

·        Allocatethe entire available budget. This part is necessary, because when funds remainin the budget, unallocated, additional total utility can be obtained by purchasingmore.

·        Makethe marginal utility per dollar equal for all goods. The marginalutility per dollar isthe marginal utility from a good relative to the price paid for the good, thatis, the marginal utility from a good divided by its price.

qLand Mine: When you usethe marginal utility per dollar approach to explain utility maximization, youshould be prepared for students’ questioning the reality of the idea that theyactually equate marginal utility per dollar before making a consumptiondecision. Some will say, “I’ve never calculated the marginal utility of anyitem I’ve ever purchased. This material doesn’t make any sense.” You shouldagree with your students that people don’t calculate and compare marginalutilities and prices but point out to them that the goal is to predict choices,not to describe the thought processes that make them. Indeed, one of thechallenges in teaching the marginal utility theory is getting the students toappreciate the fundamental role of a model of choice. Gary Becker had apertinent story you can use: “Josh Beckett [Becker used Orel Hershiser, butHershiser last pitched in 2000] is a top baseball pitcher. He effectively knowsall the laws of motion, of eye and hand coordination, about the speed of thebat and ball, and so on. He’s in fact solving a complicated physics problemwhen he steps up to pitch, but obviously he doesn’t have to know physics to dothat. Likewise, when people solve economic problems rationally they’re reallynot thinking that “well, I have this budget and I read this textbook and I lookat my marginal utility…” They don’t do that, but it doesn’t mean they’re not beingrational any more than Josh Beckett is Albert Einstein.

• Equalize the Marginal     Utility per Dollar: This rule maximizes     utility because any time the marginal utility per dollar spent on one good     exceeds that of another good, the consumer can increase his or her total     utility by spending a dollar less on the good with the lower marginal     utility per dollar spent and spending the dollar on the good with the     higher marginal utility per dollar spent.

Students usually grasp the consumer mustassess the marginal utility lost against the marginal utility gained as onegood is substituted for another. Yet, students usually haven’t thought abouthow much of one good is available from forgoing some quantity of the othergood. Point out that this is not known until the relative prices of the twogoods are known, which is why the marginal utility is weighted by its price.

                                                       

Quantity of movies	Marginal utility	Quantity  of books	Marginal  utility
1	24	1	20
2	20	2	10
3	18	3	8
4	8	4	6
5	4	5	4
6	2	6	2

•  The table to the right has the marginal     utility schedules that are computed from the total utility schedules in     the table above. The price of a movie is $8, the price of a paper back     book is $4, and the consumer has $24 to allocate between movies and books.     To maximize utility, the individual buys 2 movies and 2 books because that     combination of movies and books spends all the available income and sets     the marginal utility per dollar spent of movies equal to that of books.     (Both equal 2.50.).

To show that maximizing total utilityrequires equalizing the marginal utility per dollar spent on each good, workwith the case when they are not equal. Suppose the marginal utility per dollarspent on a movie is 20 and the marginal utility per dollar spent on a soda is10. Ask “If you gained an additional dollar, what would you spend it on and howmuch would your total utility increase?” The students will spend it on moviesand their total utility will rise by 20. Now ask “If you lost a dollar, whatyou cut back on and how much would your total utility decrease?” The studentswill cut back on sodas and their total utility will fall by 10. Now tell themthat they can gain a dollar by cutting back a dollar on sodas. Ask them the netchange in their total utility, which is +10. The point to make is that anytimethe marginal utility per dollar spent on one good differs from that of anothergood, the students can rearrange their consumption by cutting back on the goodwith the low marginal utility per dollar spent and spending the dollar on thegood with the high marginal utility per dollar spent and increase their totalutility.

Finding an IndividualDemand Curve

• If the price of     a good falls and other things remain the same, the marginal utility per dollar     spent on that good rises. As a result, the consumer increases his or her     purchases of that good in order to maximize utility. (As more of the good     is purchased, its marginal utility decreases; as less of other goods are     purchased, their marginal utilities increase. Eventually the consumer     reaches a new equilibrium at which the marginal utility per dollar spent     on all the goods are equal.)

• When the price     of a good falls, the consumer substitutes the now lower priced good for     the other good. So, when the price of a good falls, the consumer increases     the quantity demanded, which is the law of demand.

• When the price     of a good rises, the consumer substitutes away from the now higher priced     good for the other good. So, when the price of a good rises, the consumer     decreases the quantity demanded, which is the law of demand.