\f\"seen": - , hand an .2 t Chapter 2: The Traditional Competitive Model a be quantied ant. (2 it is poesible to add util.ties acrt different iadividuals. That is, everyone has a c mmon quantitative metric, whereby three units of utility (or mile?) for you is eqtiia.ent to the same number of utiles for me Modern economists eschew these assumptions in favor of a milder form ofutilitarian prit 'iples. Mi'J'OCCOHOIHlLS now proceeds under the \"ureto p 17! 1'13. where a policy is considered desirable if it makes someone better off without making anyone worse off. But to go furthersay, to advocate one public program or tax over another as better for soc' there will be winners and losersrequires explicit value judgments. Despite occasional e aims to the contrary, economic theory almost never nplies that one policy 5 better than another, since this would nvolve weighing the be: . ets that accrue to one group against the losses incurred by the other. The most theory can do is demonstrate the advantages and disadvantages ofeach alternative. 'ty as a whole, when Indifference Curves necall that economic theory assumes that people seek to maximize their utilr ity. Utility, the outcome, is on the left side of Equation 2.1, and the de terminants of utility, an example of which is the goods and services people consume, are on the right side. Let: U=f(X,T,Z,.H,.1', where U is a person's utility. There are n goods or services that person conr sumes, three of which are labeled X, T, and Z. The possession of this bundle of goods leads to the person's utility level, U. We further assume that air though there is diminishing marginal utility, consumers do not reach a turn? ration paint, at which an additional unit of X, T, or Z actually reduces their utility. In other words, people are happier when they have more stuffian issue we deal with in chapters 3 and 4. Chapter 4 revisits another important and somewhat hidden assump tion inherent in this theory: People are affected only by the things they pos sess, and are af 'cted neither positively not negatively by what others have, or by how their bundle ofgoods compares to those ofothers. This only becomes apparent if we explicitly denote that we are dealing with only a representative individual, person i. U.=/'(X.,1c.Z,,...,n,) (2.2) Clearly, this person's utility is only affected by what he or she has, not by what others have. We can represent an alternative scenario in which people are affected by both their own possessions and those of others by including another subscript for a representative other individual, j. - vvmm. L. _.. .21\": :9 mm ... a Part I: Introduction :Isecmn - ,. U,:f(X,,X,, \":2 2mm) (2.3) The conventional h :ory 35 ms people see; to maximize their utility, which, ..s we noted, is determined [3) tl : bundle of goods and services they possess. To do so, the ptnchase their ideal bundle based on their desire or VJtZ for the alternative zoods and the prices of these altelnatives, subject, of coulse, to how or ch income they have available to spend. We will use graphs throughout this chapter, as they are helpful in illus- trating these concepts. In doing so, however, we can show at most only two of the many goods and services people wish to haveone on 'h axis. Figure 2.1 shows indifference turner, which represent alternative eomr binations of two goods that result in the same level of utility. Curve U_, conr veys a higher utility than U| because at each point, the person possesses more of both goods. In theory, a consumer has an innite number of indifference curves, each corresponding to different combinations of quantities ofthe two goods. The typi a] indifference curve has three characteristics. First, it tends to have a convethortherorigin shape because ofdiminishl g marginal utility. Once a person has a great deal of one good and little of another, that person has to receive a lot more ofthe former in order to give up even a little bit of the latter. The slope of the indifference curve, which of course varies at each t is not a str. 'ght line, is called the mmyimzl rate qulmimtionl It is equal to the ratio of the marginal utilities of the two goods.Z Second, indifference curves don't bend all the way back around. St: ted more technically, they never exhibit a positive slope. A given quantity on the x or yraxis corresponds to only one point on an indifference curve. This implies that consumers do not reach a satiation pointithey always get more utility from an additional unit ofa good, no matter how much they already have. point i Third, two indifference curves cannot intersect. If they did, then all points on birth curves would confer the same amount of utility. T hat would imply that having more of both goods would not bring higher utility, which violates the denition ofthe curve To make this less abstract, Figure 2,] shows two goods that might appear in a consumer's utility function: visits to phys ans (MDS) and visits to nurse practitioners (Nl's), For expository purposes, it is helpful to assume that all ofa person 5 money is spent on these two services. The quantity of nurse practitioner visits appears on the horizontal axis, and the quantity of physieian visits appears on the vertical axis. The consumer is indii erent to all points on a particular curve since by denition all points bring equal levels of satisfaction. Three NP visits and four MD visits (point A) - e equal in desirr ability to ve NP visits and three MD visits (point B, on curve U]. The person would be even happier to have more (for example, point C on curve U2), but that might involve spending more money than he or she has available. 5:54 in: ... \"by\": :9 mm 'm.~bl==.=='1u 1. use-mu: - mm: or. LN Chapter 2: The Traditional Competitive Model - FIGURE 241: Consumer Indifference Curves MD NP Visits The Budget Constraint The choice of how much of each type of visit to purchase depends not onlv on how much the ,'e so. wai-ts ol'each visit type, but also on the p. ice ot'e ch type A .,ional consume. (dened .nd discussed in chapters 4 .nd 5; m uti- mizes utility by spending each 51 essive dollar in a way that )rings aaout the most utility, This me ns that when they have spent their laSt dollar consumers will hav' equaliyed across all the goods in their utility function, the ratio of the marginal utilities (MU) with the ratio ofthe prices (1') ofthe goods, .fwe dene PM as the price ofMl) visits, and PM as the price ofI'V'.' visits, then, for a consumer who has maximized his or her utility, MUM/I'M = MUM/P r (2-4) ",y crossimultiplying and rearranging the terms, we can write it and think of it another way, where the ratios of the marginal utilities are equal to the price ratios ofthc two goods: MUu/MUN I'M/PM. (A5) It is easy to see why a consumer must fulll Equation 2 4 (and there- fore Equation 2 5) to maximize utility Suppose the equality is not met at a particular combination of MD and 41" services purchased (which could be - h\" w u. manna mmsm. 1-2:": to t==;.=,,.....t.==.=m..=.- Part I: Introduction mm. - was\" on 1m - point B in Figure 2.3). In this case, haying more Nl' visits and feuet Ml) visits would benefit the consumer. However, the result will be lower marginal utility of NI' visits (because 0" the diminishing marginal utility of the extra NP visits), and higher marginal utility for MD visits. Lnly when both sides of Equation -4 (or 2.5) are equal will the consumer have nothing left to gain from trading one type ofvisit for another. This must be done within the coir nes of his or her budget, however We can illustrate this concept using another graphical tool, the hmiv get constraint. This is a line that shows how many of each type of visit the consumer can purchase with a given income, and it can be derived through equations 2.6 and 2.7. 1: (PM x M) 1- (.'N x NP) (2.62) and solving for NI' by rearranging the terms, M= I/Ru'l(P,,-p/P,.,) x NP)\" (2.7) where I is income, M is the quantity ofMD services, and NP is the quantity ofnursc practitioner services. Figure 2.2 graphs this, using the assumption that all a person's income during a given period is spent on these two goods. The point at which the budget constraint line intersects each axis shows how many of each good or service the consumer could buy by spending all income on that single service. The rst term of Equation 2.7 shows the intercept on the vertical axis, and the term 'P~1-/PM is the slope. The consumer can afford to purchase any combination of these two services that is either on the line or in the shaded area below and to the left of the line, but cannot afford any combination above and to the right of it It is easy to construct a budget constraint for any level of income since the slope of the line, which is the ratio of the prices of the two goods, does not change. For example, a 50 percent increase in income would shift the budget constraint line outward and to the right by this exact amount. We can also see that the slope of the budget constraint is equal to the price ratio between NP and MD visits.3 The Consumer Optimum How does a consumer decide how many ofeach good or service will maximize utility? He or she chooses the combination of goods that corresponds to the point ot'tangency between the budget constraint and the highest indifference curve, as illu5trated by point A in Figure 2.3 Recall that the consumer has an innite number ofindihence curves: here w ' show ,ust two ofthem. In contrast to point A, at point B the indifterence curve and budget constraint do not have the same slope, This puts the consumer on an indii Ll" \f\"seem". 7 puma m an . Chapter 2: The Traditional Competitive Model FIGURE 2.4: Derivation of Demand Curve, Step 1 M I) Vlslts 6 8 10 N P Visits nor the person's income changes. It is further assumed that a pe.s..n s ttstes ire unu'teretl. Thus, in dC.l\\'II]5 the curve oni; one thin price ofnutse practitioner services. Demand curves have a further interpretation: They show the marginal utility a consutner derives from the purchase of the good or services We as sume individuals purchase those products whose marginal utility exceeds their prices Note that the down ward slope of a demand curve follows the decrease in marginal utility as the quantity ofa good consumed rises. This topic will be explored further in Chapter 4, when revealed prelerence and the concept of consumer surplus are discussed, Although one needs actual data on consulner behavior to draw an ac curate demand curve, in general it will slope downward to the right, indicat ing that people will demand more when the price is lower. In functional form: a. ies Anerc, the mm: P., I. T) (2.8) where 1 'is demand for a particular good or service, P is its price, I" is the price of alternatives, I is income, and T is tastes. flagrant: dzmandihow much is demanded by all indiuduals Combinediis simply the sum of the individuals\" demands. Alternative goods, the subscript u, can be categorized two ways: as mmplsmmt: or as must tum. Complements are goods that are used in 9 s. m. .t. serum usimnszn in; m mam e: mum/m .m. magmas\": a Part I: Introduction Listens): . "mu an 1: i/ FIGURE 2.5: Derivation of Demand Curve, Step 2 Price of NPVlsits 6 10 Quantity of NP Visits Demanded conjunction with the good being studied, and substitut.s ate those that are used instead. We ran therefore rene Equation 2.6 as folio\" s: D=f(P~P'PI'T) (2.9) where I), is the pr-ee OfSlleDrutL'S and Pr is the price ofcomplements. What is perhaps mOSt noteworthy about these equations is the unob- trusive role of T, taStes, '1 his one variable represents much ofwhat it is to bc a human being,. t'sycholoLy and sociology have studied how indiVidual tastes are formed and the wa,s in which the, are manifested, But economic theory takes the taste variable as predetermined and unaffected by the person's en- vironment. In the health services area, perhaps the major component of '1 relates to health status. If people are sick, they are obviously more likely to use medi cal care than ifthey are well. In that sense, they have a "taste" for healtlL This would not be a good way to classify your desire for medical services if, say, you were hit by a truck, but there is no other place for it in Equation 2.8. As a result, the demand for health is sometimes expressed as: Duran 11.2.1, HM; (2.1\") where H5 is the patient's health status. In Equation 2.10, tastes no longer capture health status, only the nonihealth related determinants of demand. m. m u. xcrszn mums-uni m H. mm H m,\" ,,___ am (Hamish): Chapter 2: The Traditional Competitive Model Ill As we saw, a smgL demand curve car. Illustrate any relatzonshlp me tv ecu t .e .,uantiiy and pric- of a particular good. We assume, however, that the other determinants ofclemand --the prices of alternative goods, inco-re, health status, and tastesremain unchanged. If they do change, the demand curve mast also shift For example, when a person gets sick, his or her de mand curve is likely to shift outward and to the rightas shown by the de mand curve labeled D1 in Figure 2.3indicating that he or she will demand more medical care at all price levels. Nevertheless, the amount demanded is still expected to depend, in part, on the price of medical care. The relationships between demand and income and between demand and the price ofother goods are more complicated. In general, we would ex pect the demand curve to shift outward and to the right if income rises. This is true ot'normaload . But there are goods and services with the opposite re- lationship: When income rises, demand Falls. and when income Falls. demand rises. These are known as infkrim'goodxialthough the term does not imply tuiything pejorative. In the health services area, :u1 example might be visits to emergency rooms (HRS). Those with higher incomes are more likely to have a usual provider ofcare, and therefore to seek care from an ER less frequently. Thus, ifincome rises we would expect a person's demand curve for ER visits to shift downward and to the left; at any price, the quantity of ER services demanded will be lower. The relationship between demand for one good and the price ofother goods is even more complicated, and we will explore it further when we discuss elasticities of demand. Two goods are considered substitutes if an increase in the price ofone leads to an increase in the demand for the other, and complements if the opposite is true. (A more technical denition, involv- ing crossprice elasticities of demand, is provided later in this chapter.) Most goods and services are substitutes. A classic example is beef and chicken. If the price of beef rises, demand for chicken will increase as people substitute the latter for the former. A classic example of complementary goods is auto mobiles and tires. If the price ot'cars rises, demand for cars will decrease, and therefore so will the demand for tires. A health services example ofcomple ments is the relationship between inpatient hospital care and outpatient phyi sician services. Although these would seem to be substitutes, there is some evidence to indicate that they are complements: As the price ofphysician out- patient services rises, the demand fbr inpatient hospital care falls. (The reason will be explained in Chapter 4.) In summary, if the price ofa substitute rises, the demand for the good shifts outward and to the right and the opposite occurs for complements