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Chapter 12 General Equilibrium and Welfare © 2006 Thomson Learning/South-Western An Illustration of General Equilibrium Figure 12-1 shows the market for tomatoes and three of the many other market related to it: 2 The market for tomato pickers. The market for a related product --cucumbers. The market for cucumber pickers. The initial equilibrium is shown by the darker demand and supply curves. FIGURE 12-1: The Market for Tomatoes and Several Related Markets Price S P1 S Wages W1 D D Tomatoes 0 (a) Market for Tomatoes Tomato pickers 0 (b) Market for Tomato Pickers Wages Price S S P2 W2 D 0 3 Cucumbers (c) Market for Cucumbers D 0 Cucumber pickers (d) Market for Cucumber Pickers An Illustration of General Equilibrium The initial set of equilibrium prices are: 4 P1 for tomatoes. W1 for tomato pickers. P2 for cucumbers. W2 for cucumber pickers. Since the markets are in general equilibrium, this will persist unless something happens to change it. Disturbing the Equilibrium Assume the government announces that tomatoes cure the common cold, resulting in an increase in demand. 5 Initially, this would shift the demand curve for tomatoes outward to D’. The increase in tomatoes prices brought about by the increase in demand stimulates the demand for more tomato pickers which shifts outward to D’. Disturbing the Equilibrium 6 The higher wages for tomato pickers increases the costs for tomato growers, shifting the tomato supply curve back to S’. If the demand for cucumbers decreased because of the increase in demand for tomatoes. This decreases the price of cucumbers and leads to less produced. The demand for cucumber pickers falls, and their wages also decrease. FIGURE 12-1: The Market for Tomatoes and Several Related Markets Price S’ S S Wages P1 D’ W1 D’ D D Tomatoes 0 (a) Market for Tomatoes Tomato pickers 0 (b) Market for Tomato Pickers Wages Price S S P2 W2 D D’ 0 7 Cucumbers (c) Market for Cucumbers D D’ 0 Cucumber pickers (d) Market for Cucumber Pickers Reestablishing Equilibrium Eventually we would expect each market to eventually reach a new equilibrium. 8 The new equilibrium in Figure 12-1 is shown by the lighter colored demand and supply curves. There is a rise in tomato prices (to P3), an increase in tomato picker wages (to w3), a fall in cucumber prices (to P4), and a fall in cucumber picker wages (to w4). FIGURE 12-1: The Market for Tomatoes and Several Related Markets Price S’ Wages S S P3 P1 D’ W3 W1 D’ D D Tomatoes 0 (a) Market for Tomatoes Tomato pickers 0 (b) Market for Tomato Pickers Wages Price S S P2 W2 P4 W4 D D’ 0 9 Cucumbers (c) Market for Cucumbers D D’ 0 Cucumber pickers (d) Market for Cucumber Pickers An Efficient Mix of Outputs 10 A technically efficient allocation of resources in which the output combination also reflects people’s preferences is an economically efficient allocation of resources. Figure 12-2 illustrates the requirements for economic efficiency in the mix of outputs. A Simple General Equilibrium Model 11 The best use of resources is achieved at point E. This point is the utility maximizing choice where the person’s indifference curve is tangent to the production possibility frontier. Point E is defined as an economically efficient allocation of resources. FIGURE 12-2: Efficiency of Output Mix Quantity of Y per week P F E U3 G U2 U1 0 12 P’ Quantity of X per week Efficiency in Output Mix 13 Profit maximizing firms will equate the rate at which they can trade X for Y in production to the equilibrium price ratio. Utility maximizing people will equate their MRS to the equilibrium price ratio. Thus, RPT equals MRS, which, when demand equals supply, meets the requirements for economic efficiency. Efficiency of Perfect Competition 14 With an arbitrary initial price ratio, in Figure 12-3, profit maximizing firms will produce the output combination X1, Y1. Societies’ budget constraint, CC, must go through this point since the value of income must equal the value of output. FIGURE 12-3: How Perfectly Competitive Prices Bring about Efficiency Quantity of Y per week C P Initial prices Y1 Y* Y’1 U3 C U2 0 15 X1 X* P’ X’1 Quantity of X per week A Graphic Demonstration 16 On the budget constraint, CC, individuals will demand X’1, Y’1. There is an excess demand for good X1 and an excess supply of good Y1. Firms will produce more X and less Y. FIGURE 12-3: How Perfectly Competitive Prices Bring about Efficiency Quantity of Y per week Efficient prices C* C P Initial prices Y1 Y* E Y’1 U3 C U2 C* 0 17 X1 X* P’ X’1 Quantity of X per week A Graphic Demonstration 18 The market will cause prices to move toward their equilibrium levels P*X and P*Y. People will respond to the changes in prices by substituting Y for X in their consumption choices. These action will eliminate the excess demand for X and the excess supply for Y. Equilibrium is reached at X*, Y* with equilibrium prices P*X and P*Y. A Graphic Demonstration 19 At this price ratio, supply and demand are equilibrated for both goods. Profit maximizing firms will produce X* and Y*. With the income generated, individuals will maximize utility by choosing X* and Y*. Competitive market have generated an efficient allocation of resources. Why Markets Fail to Achieve Economic Efficiency Imperfect competition Externalities Public goods Imperfect information 20 Imperfect Competition 21 Imperfect competition is a market situation in which buyers or sellers have some influence on the prices of goods or services. In this case, the firm is not a price taker so marginal revenue does not equal price. Relative prices do not reflect relative marginal costs, and inefficiency can result (for example, monopoly dead-weight loss). Externalities 22 Externalities represent additional costs-those that arise from the external damage. The firm, however, only responds to private input costs, it disregards the social costs of pollution. This results in a gap between market price and social marginal cost, which leads to a misallocation of resources. Public Goods 23 Price cannot equal marginal cost (which is zero), since the fixed cost of providing the good would not be covered. The incentive is for people to refuse to pay for the good hoping others will purchase, and thus provide the good. This causes society to not allocate enough resources to public goods. Imperfect Information 24 It has been assumed that economic actors are fully informed, especially about equilibrium market prices. Without this information, the “invisible hand” results do not hold. Without perfect information, a consumer would have problems (costs) finding quality and the prices charged by different firms. Efficiency and Equity 25 Equity is the fairness of the distribution of goods or utility. A primary problem with this concept is developing an accepted definition of “fair” or “unfair” allocations of resources. Opinions vary from, an allocation is fair if no laws are broken in obtaining it to a fair allocation requires all people share equally. The Edgeworth Box Diagram The Edgeworth box diagram is a graphic device for illustrating all of the possible allocations of two goods (or two inputs) that are in fixed supply. 26 It can be used to show how the production possibility frontier is constructed. It can also be adapted to illustrate voluntary exchange between two individuals. FIGURE 12-4: Edgeworth Box Diagram OJ Total Y OS Total X 27 The Edgeworth Box Diagram for Exchange 28 For consumer Smith, quantities of X are measured along the horizontal axis rightward from her axis OS, and quantities of Y are shown along the vertical axis above OS. Consumption for the other consumer, Jones, is shown starting from the origin OJ. At point E, for example, Smith gets XES, YES and Jones gets XEJ, YEJ. FIGURE 12-4: Edgeworth Box Diagram E XJ E Total Y YJ E E YS OS E XS Total X 29 OJ Mutually Beneficial Trades 30 All possible allocations of the goods between Smith and Jones are shown within the box. To identify those which provide mutually beneficial trades, indifference curves representing the preferences of Smith and Jones are shown in Figure 12-5. Mutually Beneficial Trades Smith’s indifference curve map is drawn with origin OS. Jones’s indifference curve map is drawn with origin OJ. 31 Movements in the northeasterly direction represent higher levels of utility for Smith. Movements in a southwesterly direction represent higher levels of utility for Jones. FIGURE 12-5: Edgeworth Box diagram of Pareto Efficiency in Exchange Jones’s X OJ U1J Jones’s Y U2J M4 US4 3 Total Y UJ M3 4 UJ 3 M2 F US 2 US M1 1 E Smith’s Y OS Total X Smith’s X 32 US Mutually Beneficial Trades 33 Any point for which the MRS for Smith is unequal to that for Jones represents an allocation where mutually beneficial trades can take place. Such a point, E, is shown where the indifference curves intersect. Any point inside the oval-shaped area represent mutually beneficial trades. Efficiency in Exchange When the marginal rates of substitution are equal, such as points M1 through M4, mutually beneficial trades are no longer possible. 34 Movements away from these tangency positions result in at least one person being made worse off. The movement from M2 to E, for example, makes Smith worse off and Jones no better off. Contract Curve The contract curve is the set of efficient allocations of the existing goods in an exchange situation. Points off that curve are necessarily inefficient, since individuals can be made unambiguously better-off by moving to the curve. 35 In Figure 12-5, this curve is the set of points, such as M2, on the line connecting OS to OJ. Contract Curve 36 A movement to the curve from off the curve represents mutually beneficial trades, but a movement along the curve does not since one of the parties is always worse off. If the contract curve is interior to the Edgeworth box, the individuals’ MRS will be equal along the curve. Efficiency and Equity Suppose, for example, that everyone agreed that the only fair allocation is one of equal utilities. 37 Point E in Figure 12-6 might be such a point. Assume point A is the initial endowments; the initial holdings of good from which trading begins. FIGURE 12-6: Voluntary Transactions May Not Result in Equitable Allocations Jones’s X OJ Jones’s Y 1 UJ M4 Total Y U2J U3J U4S M3 4 E UJ U3S M2 A M1 Smith’s Y OS Smith’s X 38 1 US Total X U2S Efficiency and Equity 39 Point E lies outside of the region on the contract curve, between M2 and M3, which is mutually preferable to point A. Smith would not voluntarily agree to point E since she would be made worse off. With unbalanced initial endowment, a equal allocation is not possible through mutually beneficial trade.