Price Discrimination and the Principle of Willingness - Essay Example

Demonstrate how the principle of willingness to pay underlies consumer surplus and the practice of price discrimination. Explain the equilibrium solution to an industry that is able to practice perfect price discrimination. Ans: The conception of the consumer's surplus originated from the Marshallian theory of cardinal utility. Hence to establish the relationship between consumer's surplus and willingness to pay we have to go through the theory of cardinal utility and consumer's equilibrium in single commodity case. The cardinal theory of utility is based on the following assumptions. 1. Utility is cardinally measurable. 2. The utility derived from any commodity is measured by the amount of money that the consumer is willing to sacrifice for that commodity. 3. The marginal utility is represented by the amount of money that the consumer is willing to sacrifice for one additional unit of that commodity. 4. Marginal utility of money is constant. 5. More a commodity is consumed less will be the willingness to pay by the consumer for one additional unit i.e. marginal utility of the commodity is diminishing. (Mukherjee, 2002, pp.172-173) Now we consider the problem of the consumer. The consumer's utility function can be given as While U refers to utility and q refers to quantity If we consider the price of the commodity as P, the total expenditure will be Pq. The total expenditure is some kind of disutility of the consumer. Hence his problem is to maximise subject to q The first order condition requires Or we may write => i.e. the price must be equal to the marginal utility. The second order condition requires In other words we can write that now as P constant Hence we obtain that The marginal productivity curve is diminishing. (Kaish, 1975. p.54) That can be shown by the help of a suitable diagram. Price and Utility (in terms of money) K L N MU E P G H 0 B C A D Quantity In the above diagram the horizontal axis measures quantity in the vertical axis we measure nominal price and utility expressed in terms of money. KD is the marginal utility curve. The price is given by OP. So E is the equilibrium point that obeys the two conditions (both necessary and sufficient). Now we can logically explain why E is the equilibrium point Let us consider that the consumer is consuming 0B amount. For 0Bth unit the consumer is willing to pay BL units of money but he actually needs to pay BG units. His willingness to pay is greater than his actual payment. So he will raise the consumption and consequently there will be a decline in the willingness to pay by the consumer. Finally at point E the willingness to pay matches with the actual payments. The marginal utility curve is the demand curve as it depicts the demand price of the commodity at each corresponding level of consumption. On the other hand at each level of price the equilibrium demand for the commodity by the consumer is determined by the marginal utility curve. In the above diagram the total willingness to pay is measured by summing up the willingness to pay at each level of q. Hence the total willingness to pay is given by the area of 0KEA and actual payment is P.q. 0A*0P= 0PEA. Hence the consumer's surplus is given by the area of KEP. Mathematically we can show C.S as We suppose that is the equilibrium level of consumption which is given by 0A in the figure. As we know that then Hence consumer's surplus can be expressed as The difference between total utility (willingness to pay in terms of money) and the total expenditure on the goods consumed. Graphically the portion below the demand curve and above the price line represents consumer's surplus. (Sen, 2002) First Degree Price Discrimination: The first degree of price discrimination is played by a monopolist while there is no flow of information among the buyers in a single market. In this process the monopolist charges the maximum price for each unit from the buyer that he is willing to pay. In this case monopolist makes individual negotiation with each buyer. This is also known as the price discrimination of the special type namely "take it or leave it". In such a situation the monopolist seller threatens the potential buyers of stopping the supply of that commodity in the market. By this process he can grab the entire surplus and the demand curve in this case plays the role of marginal revenue curve. This can be shown with the help of following diagram. R, C K T V MC E D=MR 0 A B C quantity In the above figure the horizontal and the vertical axes measure quantity and cost, revenue respectively. D is the demand curve for the product. MC is the marginal cost curve faced by the producer. Here the monopolist finds the maximum demand price and charges the price from the consumer. For example for OA th unit of the commodity monopolist would charge the maximum demand price AT. For OB th unit the monopolist would charge BV units of money. Hence we can find that for one additional unit the total revenue changes by the demand price of that unit. That implies the demand curve plays the role of the marginal revenue curve. If the reciprocal demand function is represented by the equation the total revenue function would be represented as. Hence the marginal revenue would be represented as Hence the equilibrium would be achieved where the willingness to pay of the consumer (here marginal revenue) would equal the marginal cost. In this figure E is the equilibrium point and OC is the equilibrium quantity. The total revenue would be represented by the area KEC0. Here the total revenue would be equal to the total willingness to pay. Hence we can say through the first degree price discrimination the entire part of consumer surplus is extracted by the consumer. Let us suppose that the equilibrium quantity is then the total revenue earned by the monopolist can be given as ' The total surplus of the monopolist would be given by This surplus would include the entire part of consumer surplus. (Fisher and Waschik, 2002, pp.43-45) Second Degree Price Discrimination: This type of price discrimination is also known as block pricing. This is mainly possible when there are several groups of consumers in the market and there does not exist any flow of information between any two groups. Or in other words some amounts of commodities are sold together and the price for every unit of this amount is charged according to the willingness to pay of the consumer for the last unit of that group. Again for a new lot of commodity some different price would be charged (of course a lower price) the process goes on. In that particular process of price discrimination the monopolist's marginal revenue function looks like a step function. The equilibrium condition is the same. The marginal cost curve intersects the step marginal revenue curve for the attainment of equilibrium. This type of price discrimination helps the monopolist to extract a major part of the consumer's surplus but not the entire surplus is extracted. The extraction of surplus through the process of block pricing (diagram illustrated below) or the second order price discrimination can be shown with the help of the following diagram. The horizontal axis measures quantity and the vertical axis measures revenue and cost. D is the demand curve of the firm. Now we consider the pricing pattern of the firm. For first OM units the monopolist will find what is the willingness to pay for the OM th unit. The willingness to pay for the 0Mth unit is MB. Hence each unit will be sold at MB price per unit. Now we consider next CF units are to be sold. The total sell would be ON. So the willingness to pay for 0Nth unit is NF. Hence CF units would be sold at the rate of NF per unit. Let us consider GE more units. So the total sale becomes 0P and for 0Pth unit willingness to pay is PF. So the GE units are sold at price PE per unit. ABPFGEP becomes the marginal revenue curve (a step function). Here also the monopolist extracts a major part of the entire consumers' surplus. But a smaller amount of the consumer surplus is left in the hand of the consumer. (Gould and Ferguson, 1993, pp.317-319) R, C A B C F G E MC D 0 M N P 2. Show how a profit maximizing monopoly can be allocatively inefficient and yet productively efficient. What are the implications of such a situation when a Government is committed to a rigorous anti-trust policy' To realize the profit maximizing behaviour of a monopolist firm first we have to consider the salient features of monopoly. 1. Monopolist is the single seller in the market. 2. There is no close substitute of the product in the market. 3. The entry of new players is restricted in the market 4. The monopolist owns perfect knowledge about the market. 5. The objective is to maximize profit. All these factors imply that monopolist faces the entire market demand curve and constitutes the entire supply. On the other hand the monopolist has absolute control over price and hence after determining the profit maximizing quantity he would select the price to sell the commodity in the market. So in such a market the producer plays the role of price maker. The profit function of the monopolist can be given as the difference between total revenue and total cost. As price is determined by the monopolist the price can be expressed as a function of quantity and finally the TR is also a function of quantity. The profit function of the monopoly can be written as: The monopolist wants to maximize with respect to q. The first order condition requires: In other words we can say So MR=MC (necessary condition) The second order condition requires Slope of MC must be greater than MR. (Stonier and Hague, 1972, pp.195-197) That can be shown with the help of the following figure. Horizontal axis measures quantity, vertical axis measures revenue and cost. D is the demand curve and MR is the corresponding marginal revenue curve. MC is the marginal cost curve. The equilibrium is attained at point E and OK i the equilibrium level of output. Here MC is equal to KE. But monopolist faces the entire demand and he knows better what the level of consumers' willingness to pay at that level. That's why to clear the market he would charge OB price in the market. Here OB>KE. Hence we can say that monopolist doesn't maintain the marginal cost pricing rule. Hence that would create market distortion and inefficiency. That inefficiency can be revealed by a comparison with a perfectly competitive market having the same cost conditions. R, C MC B E D MR 0 K quantity (McConnell, Brue and Campbell, 2004, p.203) Consumer's Surplus: Perfect Competition and Monopoly Let us compare the perfect market and monopoly in terms of consumer's surplus. We know that under perfect competition numerous sellers sell perfectly homogeneous product. Hence the demand function for the product of any firm is perfectly elastic. On the other hand under monopoly there is a single producer and that implies no close substitute is available. Hence the demand is to some extent inelastic. Hence under perfect competition and under monopoly and e=1 is a special case of monopoly. The revenue function of any firm can be given as: while P= price and q= quantity. The marginal revenue function can be given as Or by a small manipulation of this equation we get 1/(dq/dP)/(P/q)} here -(dq/dP)/(P/q)}=e (price elasticity of demand) Hence we can write (Henderson, and Quandt, 1980, p.176) Under perfect competition so hence Under monopoly so we can say The main objective of a producer in the market is to maximize profit. Profit is the difference between total revenue and total cost. Both revenue and cost are the functions of quantity of output produced. So the profit function can be given as: the maximization of requires here change in revenue for one additional unit of output=MR change in total cost for one additional unit of output So the equilibrium requires MR-MC=0 that implies MC=MR Under perfect competition MR=P hence equilibrium implies P=MC (Gravelle, and Rees, 2004) Under monopoly P>MR so equilibrium implies P>MC i.e. there is a concept of mark up which is the result of the monopoly power that the monopolist enjoys due to lack of substitutes. Hence the monopolist can extract a part of consumer's surplus. This comparison of consumer's surplus can be shown with the help of the following diagram. Revenue and cost R, C G B C MC P V E F D J MR 0 A K quantity In the above figure the horizontal axis measures quantity and the vertical axis measures revenue and cost. D is the demand curve and MR is the marginal revenue curve for the product of monopolist. MC is the corresponding marginal cost curve of the firm. Under a perfectly competitive market the equilibrium is determined by the equality of price and marginal cost. Hence point E is the point of equilibrium and OP is the equilibrium price, 0K is the equilibrium quantity. The total willingness to pay by the consumer is GEK0. On the other hand the total expenditure of the consumer is 0k*0D=0DEK. The consumers' surplus would be represented by GEK0-0DEK=the area of the triangle GDE. (Hubbard, O'Brien, and Scahill, 2008, p.480) Now we consider monopoly under the same set of conditions. The equilibrium under monopoly is attained by the equality of marginal cost and marginal revenue. Hence F is the equilibrium point. 0A (0P) is the monopoly equilibrium price. We find compared to perfect competition monopoly is subject to higher price and lower equilibrium quantity. Hence there would be a decline in C.S. Under monopoly total willingness to pay for 0A units is represented by the area of GCA0 and the total expenditure of the consumer is 0BCA. Hence C.S is represented by the area of the triangle OBC. Hence ODE-OBC =BDEC represents the loss of consumers' surplus under monopoly. Here we can find that a transformation from perfect competition to monopoly causes a huge decline in the consumers' surplus. This is mainly due to the existence of market power by virtue of which the monopolist can charge mark up over the marginal cost and the marginal cost pricing rule is violated. We find that in this situation the consumer's surplus is hampered and the consumption level is sub optimal. On the other hand from the ground of total supply we find that supply has declined. So we can say that the production level is sub optimal. The optimal utilization of resources secures competitive output level. But under monopoly the output level is lower which implies the existence of excess capacity. That surely implies allocative-inefficiency. Moreover, we find that under perfect competition the amount of producer's surplus is represented by the area of the triangle JED and under monopoly it is JFCB. Out of JFCB the part BCVP is the transfer of surplus from the hand of the consumers to the producers. But there is a loss in producer's surplus that does accrue neither to the producer, nor to the consumer. On the other hand there is a loss of consumer's surplus to the extent GVE which is neither transferred to the producer nor the consumer. These two triangles represent the deadweight loss of monopoly: first one is due to sub optimal level of production and the second one is due to sub optimal level of consumption. Both are the impacts of allocative inefficiency. (Varian, 1999, p.422) The concept of antitrust policy grew in the late 19th century. The antitrust policies by the state were developed over the 20th century to predicate a wide array of policies that would influence the competition. Antitrust policies represent a set of policy instruments to ensure a proper competitive functioning of the market. Such policies are against the regulatory policies that include price and output control, anti dumping laws and access limitations etc. Actually the inefficiencies and the deadweight loss of the society through the monopolistic form of market are the main causes for which the governments of different countries along with the academicians sought to bring an end of market imperfection. The monopoly situations and the adverse effects regarding efficiency made the economists realize the need for a fair competition. The normative economics has always argued in favour of a distortion free market. Monopoly is a distortion of the market. So, the inefficiencies created by the monopolists influenced the state to enforce strict laws for antitrust. (Rubinfeld, n.d.) References 1. Gould, J. P. and E. P. Ferguson, 1993, Microeconomic Theory, 6th Edition, Richard Irwin 2. Henderson, J. M and Quandt, R. E 1980, Micoeconomics: A Mathematical Approach, McGraw-Hill Internationals 3. Fisher, T. C. G. and Waschik, R. G. 2002, Managerial economics: a game theoretic approach, Routledge 4. Gravelle, H. and R. Rees, 2004, Microeconomics, Pearson Education, Chapter: Market 5. Hubbard, G. , O'Brien, A.P. and E. M. Scahill, 2008, Microeconomics, Pearson Prentice Hall 6. Kaish, S. 1975, Microeconomics: logic, tools, and analysis, Harper and Row 7. Mukherjee, S. 2002. Modern Economic Theory, New Age International 8. Rubinfeld, D.L. Antitrust Policy, retrieved on May 9, 2009 from: http://www2.cnr.edu/home/bmcmanus/poetics.html 9. McConnell, C. R. Brue, S. L. and Campbell R. R 2004, Microeconomics: principles, problems, and policies, McGraw-Hill Professional 10. Sen, A. 2000, Microeconomics: Theory and Applications, Oxford University Press 11. Stonier, A.F. and D.C. Hague, 1972, A textbook of economic theory, Wiley 12. Varian, H. R. 1999. Intermediate Microeconomics: A Modern Approach. Fifth edition: W.W. Norton and Company Read More