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PERFECT COMPETITION, EFFICIENCY and EXTERNALITIES by Jon D 1 ENVIRONMENTAL AND NATURAL RESOURCE ECONOMICS Part 1: PERFECT COMPETITION, EFFICIENCY AND EXTERNALITIES by Jon D. Harford (Last updated January, 2005) (Note: references to Tietenberg are to his book Environmental and Natural Resource Economics, 7th edition, published by Addison Wesley. Perfect Competition without Externalities (Tietenberg discusses this type of material in Chapter 2 of his book.) Perfect competition is an ideal form of a market economy which represents a simple starting point for analysis of real world economies. In perfect competition large numbers of buyers and sellers exist in each and every market and no one of them believes he has any influence over price. In addition, there is no uncertainty or imperfection in information and all decision makers are rational. Rationality for consumers means maximizing a well- defined utility function subject to an individual budget constraint, while rationality for each producer means each firm maximizes profits by its choice of inputs and output. For consumers, maximizing utility subject to the budget constraint leads to particular choices of consumption goods for each set of price and budget that the consumer faces. By varying the price of one particular good, other things the same, one can derive a relationship between the quantity of one particular good chosen and its price. This relationship is the individual demand curve of a consumer, a relationship which holds prices of other goods and income constant. Assuming that consumption of a unit of a good X by George affects no one except George, the demand curve of George for good X can be interpreted as reflecting the marginal benefit of units of 2 consumption. Referring to the demand curve in Figure 1a, it is seen that at price of $12, George would buy one unit of the good X. Accordingly, the value to George of the first unit of the good must be at least $12. At a price of $11, George would be willing to buy two units of X. From this we can infer that the second unit of X must be worth at least $11. Continuing in this reasoning it is seen that the third unit of X must be worth at least $10, the fourth unit must be worth $9, and the fifth unit must be worth at least $8. Accordingly, we would argue that the total of five units must be worth at least $(12+11+10+9+8)=$50. The total value of five units of the X good we shall call the total benefits of that consumption. Now suppose George faced a price of $8 for the X good and accordingly paid a total ($8)(5)=$40 to acquire five units. The difference between the amount George spent to acquire the five units and the total benefits of those units would be called his consumer surplus. George's consumer surplus is his net benefits of consuming five units of the good. That is, net benefits are the total benefits minus the total costs (his expenditures) of consuming the five units. We know that this net benefit is at least ($50-$40)=$10. The method of refining this estimate is to take ever smaller increments in the amount of the X good and calculate the highest price associated with acquiring that increment. If one takes this process to its ultimate limit, one finds that the total benefits equal the area under the demand curve up to the quantity consumed. Therefore, we can conclude that the value of consumer surplus is the area between the demand curve and the price line over to the quantity consumed. Marginal benefit is the rate of change of total benefits with respect to a change in the good consumed. An estimate of George's marginal benefit a given unit of X is the highest price at which that unit is purchased. Mathematically, 3 George's marginal benefit of consuming an infinitesimal amount of additional good X is the height of his demand curve. Individual demand curves are added horizontally (quantity addition) to obtain the market demand curve for good X. The total benefit, marginal benefit, and consumer surplus associated with the market demand curve for X are calculated in exactly the same fashion as with the individual demand curve. 4 While benefits come from consuming goods, costs come from producing them. Perfectly competitive firms maximize profits under conditions in which they take input and output prices as constants. In the short run this leads to a choice of output in which marginal cost equals price. In the long run equilibrium marginal cost and average cost both equal price. Thus, at the market output that is supplied for any given level of price it can be said that output is being produced at marginal cost. Of course, the supply curve only reflects private costs. That is, costs which the individual firms see as affecting their profits. Referring to Figure 1b, one sees that one unit of output will be produced when the price is $4, thus indicating that the cost to private producers of the first unit of output is no more than $4. At a price of $5, suppliers are willing to provide two units of the good. This indicates that the second unit of the good costs the firms no more than $5. Iterating, it is seen that the third unit 5 costs no more than $6, and the fourth unit costs no more than $7. If uses the same reasoning, but takes ever smaller increments to output, it is seen that the area under the supply curve up to the amount produced is the total private cost of production. Now suppose that suppliers receive $8 per unit for each of five units for a total of $40. Our method of cost accounting would indicate that the total private cost is no more than ($4+$5+$6+$7+$8)=$30. However, in the long run under perfect competition there must be zero economic profit and firms would therefore have revenues equal to opportunity costs. The difference in the two views of costs is that our estimate of $30 takes the view that part of the "costs" of firms are not costs from society's viewpoint, but economic rents. Economic rents are those payments to factors of production above the minimum necessary to keep them in an industry. In other words, economic rents are that part of the payments to factors such as a bricklayer, that is above his opportunity cost as represented, for example, by the level of wage he could receive by working in another industry. The collection of economic rents received by factors of production in an industry is called the producers' surplus. Producers' surplus is represented by the area between the price line, the supply curve, and the vertical axis, up to the quantity produced. The producers' surplus can be considered the net benefits of production to the supply side, just as consumer surplus can be consider the net benefits of consumption to the demand side of the market. It is one of the remarkable things about perfect competition is that it is perfectly efficient given certain conditions. Some of the conditions for its efficiency are merely the conditions for its existence. These include perfect information by all parties about all prices and products, no uncertainty, that economies of scale disappear at output levels small compared to the market 6 demand at a price that reflects average cost, and that goods have attributes that make private ownership possible. An additional condition for the efficiency of perfect competition is that there are no externalities or third-party effects. Since the subject of environmental economics is basically one of applying the notion of externalities to problems such as pollution and congestion, we will have much more to say about this subject. For now, let us turn to Figure 2 to illustrate how perfect competition produces efficiency under the ideal circumstances indicated. By efficiency, it is simply meant that overall benefits minus costs are maximized. In the Figure, it is seen that output Q* clears the market and that area N is consumer surplus, and area M is producer surplus. The total benefits of the production and consumption of Q* is the sum of producers' and consumer surplus. Now suppose that we consider the costs and benefits of expanding output to Q1. One cannot know how the benefits and costs would fall on various parties without 7 describing the policy that would bring about such and increase in output, but we can know what the effect on net benefits would have to be. Specifically, the increase in benefits associated with greater consumption of the good would be represented by area G, while the increase in production cost associated with the increased output would be (G+H). This implies that net benefits would go down by an amount equal to H. One can perform a similar analysis to demonstrate that a reduction in output would also reduce net benefits because consumption benefits would be decreasing faster than the reduction in production costs. Under the circumstances assumed, no form of government intervention can improve efficiency. A POLLUTION EXTERNALITY: THE OUTPUT DIMENSION We now consider a situation in which a perfectly competitive industry produces pollution in direct proportion to the amount of output it produces. In other words, it is assumed that the ratio of pollution (Z) to output (Q) is a constant equal to w=(Z/Q). This pollution creates an external cost to society. For example, it z were an air pollutant, the external cost would be manifested in an increased incidence of respiratory ailments in the general population, reduced visibility, and damage to the surfaces of buildings, cars, and clothing.
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