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(BQ) Part 2 book Microeconomic theory - Basic principles and extensions has contents: The partial equilibrium competitive model, general equilibrium and welfare, monopoly, imperfect competition, labor markets, capital and time, asymmetric information, externalities and public goods.
Competitive Markets PART FIVE Chapter 12 The Partial Equilibrium Competitive Model Chapter 13 General Equilibrium and Welfare In Parts and we developed models to explain the demand for goods by utility-maximizing individuals and the supply of goods by profit-maximizing firms In the next two parts we will bring together these strands of analysis to discuss how prices are determined in the marketplace The discussion in this part concerns competitive markets The principal characteristic of such markets is that firms behave as price-takers That is, firms are assumed to respond to market prices, but they believe they have no control over these prices The primary reason for such a belief is that competitive markets are characterized by many suppliers; therefore, the decisions of any one of them indeed has little effect on prices In Part we will relax this assumption by looking at markets with only a few suppliers (perhaps only one) For these cases, the assumption of pricetaking behavior is untenable; thus, the likelihood that firms’ actions can affect prices must be taken into account Chapter 12 develops the familiar partial equilibrium model of price determination in competitive markets The principal result is the Marshallian ‘‘cross’’ diagram of supply and demand that we first discussed in Chapter This model illustrates a ‘‘partial’’ equilibrium view of price determination because it focuses on only a single market In the concluding sections of the chapter we show some of the ways in which such models are applied A specific focus is on illustrating how the competitive model can be used to judge the welfare consequences for market participants of changes in market equilibria Although the partial equilibrium competitive model is useful for studying a single market in detail, it is inappropriate for examining relationships among markets To capture such cross-market effects requires the development of ‘‘general’’ equilibrium models—a topic we take up in Chapter 13 There we show how an entire economy can be viewed as a system of interconnected competitive markets that determine all prices simultaneously We also examine how welfare consequences of various economic questions can be studied in this model 407 This page intentionally left blank CHAPTER TWELVE The Partial Equilibrium Competitive Model In this chapter we describe the familiar model of price determination under perfect competition that was originally developed by Alfred Marshall in the late nineteenth century That is, we provide a fairly complete analysis of the supply–demand mechanism as it applies to a single market This is perhaps the most widely used model for the study of price determination Market Demand In Part we showed how to construct individual demand functions that illustrate changes in the quantity of a good that a utility-maximizing individual chooses as the market price and other factors change With only two goods (x and y) we concluded that an individual’s (Marshallian) demand function can be summarized as quantity of x demanded ¼ x(px , py , I) (12:1) Now we wish to show how these demand functions can be added up to reflect the demand of all individuals in a marketplace Using a subscript i (i ¼ 1, n) to represent each person’s demand function for good x, we can define the total demand in the market as market demand for X ¼ n X i¼1 xi ðpx , py , I i Þ: (12:2) Notice three things about this summation First, we assume that everyone in this marketplace faces the same prices for both goods That is, px and py enter Equation 12.2 without person-specific subscripts On the other hand, each person’s income enters into his or her own specific demand function Market demand depends not only on the total income of all market participants but also on how that income is distributed among consumers Finally, observe that we have used an uppercase X to refer to market demand—a notation we will soon modify The market demand curve Equation 12.2 makes clear that the total quantity of a good demanded depends not only on its own price but also on the prices of other goods and on the income of each person To construct the market demand curve for good X, we allow px to vary while holding py and the income of each person constant Figure 12.1 shows this construction for the case where there are only two consumers in the market For each potential price of x, 409 410 Part 5: Competitive Markets A market demand curve is the ‘‘horizontal sum’’ of each individual’s demand curve At each price the quantity demanded in the market is the sum of the amounts each individual demands For example, at pÃx the demand in the market is x1 ỵ x2 ẳ X FIGURE 12.1 Construction of a Market Demand Curve from Individual Demand Curves px px px p x* x1 x 1* (a) Individual x1 x2 x 2* (b) Individual X X* x2 X (c) Market demand the point on the market demand curve for X is found by adding up the quantities demanded by each person For example, at a price of pÃx , person demands x1Ã and person demands x2Ã The total quantity demanded in this two-person market is the sum of these two amounts (X Ã ¼ x1 ỵ x2 ) Therefore, the point px , X Ã is one point on the market demand curve for X Other points on the curve are derived in a similar way Thus, the market demand curve is a ‘‘horizontal sum’’ of each individual’s demand curve.1 Shifts in the market demand curve The market demand curve summarizes the ceteris paribus relationship between X and px It is important to keep in mind that the curve is in reality a two-dimensional representation of a many-variable function Changes in px result in movements along this curve, but changes in any of the other determinants of the demand for X cause the curve to shift to a new position A general increase in incomes would, for example, cause the demand curve to shift outward (assuming X is a normal good) because each individual would choose to buy more X at every price Similarly, an increase in py would shift the demand curve to X outward if individuals regarded X and Y as substitutes, but it would shift the demand curve for X inward if the goods were regarded as complements Accounting for all such shifts may sometimes require returning to examine the individual demand functions that constitute the market relationship, especially when examining situations in which the distribution of income changes and thereby raises some incomes while reducing others To keep matters straight, economists usually reserve the term change in quantity demanded for a movement along a fixed demand curve in response to a change in px Alternatively, any shift in the position of the demand curve is referred to as a change in demand Compensated market demand curves can be constructed in exactly the same way by summing each individual’s compensated demand Such a compensated market demand curve would hold each person’s utility constant Chapter 12: The Partial Equilibrium Competitive Model 411 EXAMPLE 12.1 Shifts in Market Demand These ideas can be illustrated with a simple set of linear demand functions Suppose individual 1’s demand for oranges (x, measured in dozens per year) is given by2 x1 ¼ 10 À 2px ỵ 0:1I ỵ 0:5py , (12:3) where px ¼ price of oranges (dollars per dozen), I1 ¼ individual 1’s income (in thousands of dollars), py ¼ price of grapefruit (a gross substitute for oranges—dollars per dozen) Individual 2’s demand for oranges is given by x2 ¼ 17 À px ỵ 0:05I ỵ 0:5py : (12:4) Hence the market demand function is Xðpx , py , I , I ị ẳ x1 ỵ x2 ẳ 27 3px ỵ 0:1I ỵ 0:05I ỵ py : (12:5) Here the coefficient for the price of oranges represents the sum of the two individuals’ coefficients, as does the coefficient for grapefruit prices This reflects the assumption that orange and grapefruit markets are characterized by the law of one price Because the individuals have differing coefficients for income, however, the demand function depends on each person’s income To graph Equation 12.5 as a market demand curve, we must assume values for I1, I2, and py (because the demand curve reflects only the two-dimensional relationship between x and px) If I1 ¼ 40, I2 ¼ 20, and py ¼ 4, then the market demand curve is given by X ẳ 27 3px ỵ ỵ ỵ ¼ 36 À 3px , (12:6) which is a simple linear demand curve If the price of grapefruit were to increase to py ¼ 6, then the curve would, assuming incomes remain unchanged, shift outward to X ¼ 27 À 3px ỵ ỵ ỵ ẳ 38 3px , (12:7) whereas an income tax that took 10 (thousand dollars) from individual and transferred it to individual would shift the demand curve inward to X ¼ 27 3px ỵ ỵ 1:5 ỵ ẳ 35:5 À 3px (12:8) because individual has a larger marginal effect of income changes on orange purchases All these changes shift the demand curve in a parallel way because, in this linear case, none of them affects either individual’s coefficient for px In all cases, an increase in px of 0.10 (ten cents) would cause X to decrease by 0.30 (dozen per year) QUERY: For this linear case, when would it be possible to express market demand as a linear function of total income (I1 ỵ I2)? Alternatively, suppose the individuals had differing coefficients for py Would that change the analysis in any fundamental way? Generalizations Although our construction concerns only two goods and two individuals, it is easily generalized Suppose there are n goods (denoted by xi, i ¼ 1, n) with prices pi, i ¼ 1, n Assume also that there are m individuals in society Then the jth individual’s demand for This linear form is used to illustrate some issues in aggregation It is difficult to defend this form theoretically, however For example, it is not homogeneous of degree in all prices and income 412 Part 5: Competitive Markets the ith good will depend on all prices and on Ij, the income of this person This can be denoted by xi, j ¼ xi, j ðp1 , , pn , I j ị, (12:9) where i ẳ 1, n and j ¼ 1, m Using these individual demand functions, market demand concepts are provided by the following definition DEFINITION Market demand The market demand function for a particular good (Xi) is the sum of each individual’s demand for that good: Xi ðp1 , , pn , I1 , , Im ị ẳ m X j¼1 xi, j ðp1 , , pn , Ij Þ: (12:10) The market demand curve for Xi is constructed from the demand function by varying pi while holding all other determinants of Xi constant Assuming that each individual’s demand curve is downward sloping, this market demand curve will also be downward sloping Of course, this definition is just a generalization of our previous discussion, but three features warrant repetition First, the functional representation of Equation 12.10 makes clear that the demand for Xi depends not only on pi but also on the prices of all other goods Therefore, a change in one of those other prices would be expected to shift the demand curve to a new position Second, the functional notation indicates that the demand for Xi depends on the entire distribution of individuals’ incomes Although in many economic discussions it is customary to refer to the effect of changes in aggregate total purchasing power on the demand for a good, this approach may be a misleading simplification because the actual effect of such a change on total demand will depend on precisely how the income changes are distributed among individuals Finally, although they are obscured somewhat by the notation we have been using, the role of changes in preferences should be mentioned We have constructed individuals’ demand functions with the assumption that preferences (as represented by indifference curve maps) remain fixed If preferences were to change, so would individual and market demand functions Hence market demand curves can clearly be shifted by changes in preferences In many economic analyses, however, it is assumed that these changes occur so slowly that they may be implicitly held constant without misrepresenting the situation A simplified notation Often in this book we look at only one market To simplify the notation, in these cases we use QD to refer to the quantity of the particular good demanded in this market and P to denote its market price As always, when we draw a demand curve in the Q–P plane, the ceteris paribus assumption is in effect If any of the factors mentioned in the previous section (e.g., other prices, individuals’ incomes, or preferences) should change, the Q–P demand curve will shift, and we should keep that possibility in mind When we turn to consider relationships among two or more goods, however, we will return to the notation we have been using up until now (i.e., denoting goods by x and y or by xi) Chapter 12: The Partial Equilibrium Competitive Model 413 Elasticity of market demand When we use this notation for market demand, we will also use a compact notation for the price elasticity of the market demand function: price elasticity of market demand ¼ eQ, P ¼ @QD ðP, P , IÞ P Á , @P QD (12:11) where the notation is intended as a reminder that the demand for Q depends on many factors other than its own price, such as the prices of other goods (P ) and the incomes of all potential demanders (I) These other factors are held constant when computing the own-price elasticity of market demand As in Chapter 5, this elasticity measures the proportionate response in quantity demanded to a percent change in a good’s price Market demand is also characterized by whether demand is elastic (eQ, P < À 1) or inelastic (0 > eQ, P > À1) Many of the other concepts examined in Chapter 5, such as the crossprice elasticity of demand or the income elasticity of demand, also carry over directly into the market context:3 @QD ðP, P , IÞ P Á , @P QD @QD ðP, P , Iị I income elasticity of market demand ẳ : @I QD cross-price elasticity of market demand ¼ (12:12) Given these conventions about market demand, we now turn to an extended examination of supply and market equilibrium in the perfectly competitive model Timing of the Supply Response In the analysis of competitive pricing, it is important to decide the length of time to be allowed for a supply response to changing demand conditions The establishment of equilibrium prices will be different if we are talking about a short period during which most inputs are fixed than if we are envisioning a long-run process in which it is possible for new firms to enter an industry For this reason, it has been traditional in economics to discuss pricing in three different time periods: (1) very short run, (2) short run, and (3) long run Although it is not possible to give these terms an exact chronological definition, the essential distinction being made concerns the nature of the supply response that is assumed to be possible In the very short run, there is no supply response: The quantity supplied is fixed and does not respond to changes in demand In the short run, existing firms may change the quantity they are supplying, but no new firms can enter the industry In the long run, new firms may enter an industry, thereby producing a flexible supply response In this chapter we will discuss each of these possibilities Pricing in the Very Short Run In the very short run, or the market period, there is no supply response The goods are already ‘‘in’’ the marketplace and must be sold for whatever the market will bear In this situation, price acts only as a device for rationing demand Price will adjust to clear the market of the quantity that must be sold during the period Although the market price In many applications, market demand is modeled in per capita terms and treated as referring to the ‘‘typical person.’’ In such applications it is also common to use many of the relationships among elasticities discussed in Chapter Whether such aggregation across individuals is appropriate is discussed briefly in the Extensions to this chapter 414 Part 5: Competitive Markets FIGURE 12.2 Pricing in the Very Short Run When quantity is fixed in the very short run, price acts only as a device to ration demand With quantity fixed at QÃ, price P1 will prevail in the marketplace if D is the market demand curve; at this price, individuals are willing to consume exactly that quantity available If demand should shift upward to D , the equilibrium market price would increase to P2 Price D′ S D P2 P1 D′ D S Q* Quantity per period may act as a signal to producers in future periods, it does not perform such a function in the current period because current-period output is fixed Figure 12.2 depicts this situation Market demand is represented by the curve D Supply is fixed at QÃ, and the price that clears the market is P1 At P1, individuals are willing to take all that is offered in the market Sellers want to dispose of QÃ without regard to price (suppose that the good in question is perishable and will be worthless if it is not sold in the very short run) Hence P1, QÃ is an equilibrium price–quantity combination If demand should shift to D , then the equilibrium price would increase to P2 but QÃ would stay fixed because no supply response is possible The supply curve in this situation is a vertical straight line at output QÃ The analysis of the very short run is not particularly useful for many markets Such a theory may adequately represent some situations in which goods are perishable or must be sold on a given day, as is the case in auctions Indeed, the study of auctions provides a number of insights about the informational problems involved in arriving at equilibrium prices, which we take up in Chapter 18 But auctions are unusual in that supply is fixed The far more usual case involves some degree of supply response to changing demand It is presumed that an increase in price will bring additional quantity into the market In the remainder of this chapter, we will examine this process Before beginning our analysis, we should note that increases in quantity supplied need not come only from increased production In a world in which some goods are durable (i.e., last longer than a single period), current owners of these goods may supply them in increasing amounts to the market as price increases For example, even though the supply of Rembrandts is fixed, we would not want to draw the market supply curve for these paintings as a vertical line, such as that shown in Figure 12.2 As the price of Rembrandts increases, individuals and museums will become increasingly willing to part with them From a market point of view, therefore, the supply curve for Rembrandts will have an upward slope, even though no new production takes place A similar analysis would Chapter 12: The Partial Equilibrium Competitive Model 415 follow for many types of durable goods, such as antiques, used cars, vintage baseball cards, or corporate shares, all of which are in nominally ‘‘fixed’’ supply Because we are more interested in examining how demand and production are related, we will not be especially concerned with such cases here Short-Run Price Determination In short-run analysis, the number of firms in an industry is fixed These firms are able to adjust the quantity they produce in response to changing conditions They will this by altering levels of usage for those inputs that can be varied in the short run, and we shall investigate this supply decision here Before beginning the analysis, we should perhaps state explicitly the assumptions of this perfectly competitive model DEFINITION Perfect competition A perfectly competitive market is one that obeys the following assumptions There are a large number of firms, each producing the same homogeneous product Each firm attempts to maximize profits Each firm is a price-taker: It assumes that its actions have no effect on market price Prices are assumed to be known by all market participants—information is perfect Transactions are costless: Buyers and sellers incur no costs in making exchanges (for more on this and the previous assumption, see Chapter 18) Throughout our discussion we continue to assume that the market is characterized by a large number of demanders, each of whom operates as a price-taker in his or her consumption decisions Short-run market supply curve In Chapter 11 we showed how to construct the short-run supply curve for a single profitmaximizing firm To construct a market supply curve, we start by recognizing that the quantity of output supplied to the entire market in the short run is the sum of the quantities supplied by each firm Because each firm uses the same market price to determine how much to produce, the total amount supplied to the market by all firms will obviously depend on price This relationship between price and quantity supplied is called a shortrun market supply curve Figure 12.3 illustrates the construction of the curve For simplicity assume there are only two firms, A and B The short-run supply (i.e., marginal cost) curves for firms A and B are shown in Figures 12.3a and 12.3b The market supply curve shown in Figure 12.3c is the horizontal sum of these two curves For example, at a price of P1, firm A is willing to supply qA1 and firm B is willing to supply qB1 Therefore, at this price the total supply in the market is given by Q1, which is equal to qA1 ỵ qB1 The other points on the curve are constructed in an identical way Because each firm’s supply curve has a positive slope, the market supply curve will also have a positive slope The positive slope reflects the fact that short-run marginal costs increase as firms attempt to increase their outputs Short-run market supply More generally, if we let qi(P, v, w) represent the short-run supply function for each of the n firms in the industry, we can define the short-run market supply function as follows 416 Part 5: Competitive Markets The supply (marginal cost) curves of two firms are shown in (a) and (b) The market supply curve (c) is the horizontal sum of these curves For example, at P1 firm A supplies qA1 , firm B supplies qB1 , and total market supply is given by Q1 ẳ qA1 ỵ qB1 FIGURE 12.3 Short-Run Market Supply Curve P P P SB SA S P1 q A1 (a) Firm A DEFINITION q B1 qA Q1 qB (b) Firm B (c) The market Total output per period Short-run market supply function The short-run market supply function shows total quantity supplied by each firm to a market: QS P, v, wị ẳ n X iẳ1 qi ðP, v, wÞ: (12:13) Notice that the firms in the industry are assumed to face the same market price and the same prices for inputs.4 The short-run market supply curve shows the two-dimensional relationship between Q and P, holding v and w (and each firm’s underlying technology) constant The notation makes clear that if v, w, or technology were to change, the supply curve would shift to a new location Short-run supply elasticity One way of summarizing the responsiveness of the output of firms in an industry to higher prices is by the short-run supply elasticity This measure shows how proportional changes in market price are met by changes in total output Consistent with the elasticity concepts developed in Chapter 5, this is defined as follows DEFINITION Short-run elasticity of supply (es , P) e S, P ¼ percentage change in Q supplied @QS P Á : ¼ @P QS percentage change in P (12:14) Several assumptions that are implicit in writing Equation 12.13 should be highlighted First, the only one output price (P) enters the supply function—implicitly firms are assumed to produce only a single output The supply function for multiproduct firms would also depend on the prices of the other goods these firms might produce Second, the notation implies that input prices (v and w) can be held constant in examining firms’ reactions to changes in the price of their output That is, firms are assumed to be price-takers for inputs—their hiring decisions not affect these input prices Finally, the notation implicitly assumes the absence of externalities—the production activities of any one firm not affect the production possibilities for other firms Models that relax these assumptions will be examined at many places later in this book ... Equation 12. 5 as a market demand curve, we must assume values for I1, I2, and py (because the demand curve reflects only the two-dimensional relationship between x and px) If I1 ¼ 40, I2 ¼ 20 , and. .. AC and MC curves Chapter 12: The Partial Equilibrium Competitive Model 435 Now MC ẳ 3q2 16q ỵ 100 and 4,950 : AC ẳ q2 8q ỵ 100 ỵ q Setting MC ¼ AC yields 2q2 À 8q ¼ 4,950 , q ( 12: 56) ( 12: 57)... requires QD ¼ 0:1PÀ1 :2 I ẳ 1011 ịP1 :2 ( 12: 34) ẳ Qs ¼ 6,400PwÀ0:5 ¼ 1 ,28 0P or or P2 :2 ¼ ð8 1011 ị=1 ,28 0 ẳ 6 :25 108 P ẳ 9,957, Q ¼ 1 ;28 0 Á PÃ ¼ 12, 745,000: ( 12: 35) Hence the initial equilibrium in