Marginal Utility Theory of Household BehaviorWhen the theory of consumer behavior was first developed an approach different from the indif-ference curve analysis was utilized. Economists measured thesatisfaction that a person received from a unit of a commodity asthe "utility" (or amount of psychological pleasure) that commodityprovided the consumer. Say you consume 10 units of a commodityper month, the total utility you receive is simply the sum of theutilities (the total psychic pleasure) received for each unit. Say,however, that you've been consuming 10 units of something andyou decide to consume one unit more ... the addition to total utilitybrought about by consuming one more unit, is the marginal utilityof the commodity.DO NOT CONFUSE TOTAL AND MARGINAL UTILITY:<< If you had to choose between giving up totally one of the following, whichwould you choose, water or the movies? >> The movies, naturallysince your total utility from water is infinitely higher than that frommovies.<< However, what if you had the choice of taking one extra bathper month or attending one extra movie per month, which wouldyou choose? >> Probably the movie since the addition to totalutility would likely be larger in the case of an extra movie eventhough the total utility of water is very high. HERE WE'RECOMPARING MARGINAL UTILITIES.TA_Marginal Utility Lecture.lwp Lecture on the Marginal Utility Theory of Demand Page 1Basic hypothesis of utility theory: the utility that any household derives from successive units ofa particular commodity will diminish as its total consumption ofthe commodity increases, the consumption of all other commoditiesbeing held constant.<< How might we picture this? >> Quantity on one axis, total utility on the other. <<The total utility curve is upward sloping, is it straight, or does itbend?>> Bends, downward.Total UtilityMarginal UtilityMU* (slopeof Total UtilityCurve at Q*Q*Q*QoQoMU=0 (slopeof Total UtilityCurve at Qo =0)MU* (= slopeof total utilitycurve above)Additional consumptionbeyond Qo reduces totalutility!<<How might we find marginal utility of an extra unit?>> Pick a point on thegraph and determine how much of an increase in total utility thereis if we increase consumption by one. Can plot another graph withquantity and marginal utility on the axis. Note that when the totalutility curve becomes flat, the marginal utility curve hits zero.TA_Marginal Utility Lecture.lwp Lecture on the Marginal Utility Theory of Demand Page 2Each point on the marginal utility curve represents the slope of acorresponding point on the total utility curve.<<Would you expect that if the hypothesis of diminishing marginalutility holds, that the consumer will pay less for each additionalunit consumed?>> Yes.Now we assume that the household wants to maximize utility (total utility) ... how might they goabout this?1. Consumption of any free good will be pushed to the point at which itsmarginal utility is zero.2. For goods which are not free, the household maximizing its utility will soallocate its expenditure between commodities that the utility of thelast dollar spent on each is equal.In our two commodity world this implies:MUfPf=MUcPc.Or, the household consumes enough of each commodity so that the marginalutility per dollar of the last unit consumed is equal for all goodsconsumed.<<What would happen if the two ratios were not equal?>> Thehousehold could increase its welfare by reallocating consumptionaway from the low ratio to the high ratio.Now, by cross multiplying we can rewrite our equality conditions as:PfPc=MUfMUc.TA_Marginal Utility Lecture.lwp Lecture on the Marginal Utility Theory of Demand Page 3<<Does this look familiar?>> Yes, looks like our equilibriumcondition in indifference curve analysis. So, indifference curvetheory and marginal utility theory propose exactly the same condi-tions for utility maximizationDigression: Baumol and Blinder don’t like the concept of measuring theconsumer’s pleasure in terms of utils or some other measure of psychicbliss, so they convert marginal utility units to money terms by asking thefollowing question: “Suppose Joe is deciding whether or not to buy a piece of pizza; what isthe maximum price he’s willing to pay for that first piece?” Let’s say thathe’s willing to pay $6.00. The value to Joe of this marginal piece of pizzais $6.00. Now, suppose that he’s only willing to pay $5 for the second piece, and $4for the third piece and he’s not willing to pay anything for the 11th piece.Then, we could draw Joe’s marginal utility curve in dollar terms as:Then, Joe’s total utility in dollar terms would simply be the area under hismarginal utility curve. With this way of looking at things Joe will consumepizza until his marginal utility (in dollars) equals zero. That is equivalentto saying as we have done above, that he consumes pizza until MUpizzaPpizza=MUotherGoodPotherGood.Marginal Utility (in $)Q=1Q=11$6$5$0TA_Marginal Utility Lecture.lwp Lecture on the Marginal Utility Theory of Demand Page 41.1. Derivation of the Consumer's Demand Curve:Assume that F is an index of all other goods and we want to determine what the demand curvefor clothing will look like if the price of clothing changes. Assumethat the consumer is in equilibrium and that Pc falls. The equilib-rium condition no longer holds: PfPc>MUfMUc.<<How can we bring the consumer back into equilibrium?>> To restore equilib-rium the consumer must buy more clothing so that (because ofdiminishing MU) MUc falls. If the price of clothing is cut in half,consumption of clothing must rise (and possibly consumption ofother commodities must fall) until the ratio of marginal utilities isagain equated to the price ratio ... this leads to the basic predictionof demand theory:THE LAW OF DEMAND: A rise in the price of one commodity (with income and the prices ofall other commodities constant) will lead to a decrease in the quantity of the commoditydemanded by each household.<<Does the slope of the demand curve depend upon total utility?>> No, itdepends upon the marginal utility over the relevant range ofconsumption ... this we would expect from our indifference curveanalysis where total utilities are never mentioned.1.2. Diamond-Water Paradox:<<Why