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American International Journal of Research in Humanities, Arts and Social Sciences Available online at http://www.iasir.net ISSN (Print): 2328-3734, ISSN (Online): 2328-3696, ISSN (CD-ROM): 2328-3688 AIJRHASS is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by International Association of Scientific Innovation and Research (IASIR), USA (An Association Unifying the Sciences, Engineering, and Applied Research) CONSUMER SURPLUS AND PRICES IN PERFECT COMPETITION AND MONOPOLY Suryaprakash Misra Assistant Professor of Economics at NALSAR University of Law, Hyderabad, “Justice City”, Shameerpet, R.R. District - 500078, Andhra Pradesh, INDIA. Abstract: It is well known that existence of monopoly is accompanied by economic inefficiency in the form of dead weight loss and reduced consumer surplus. The consumer surplus that exists in case of perfect competition gets reduced in case of monopoly; as a part of it goes to the monopolist in the form of monopoly profit, a part of it is lost in the form of deadweight loss while the rest remains as consumer surplus in monopoly. This paper shows that under specific conditions there is a definite relationship (in case of monopoly) between monopoly profit, dead weight loss and consumer surplus and between prices in perfect competition and monopoly. JEL Codes: D41, D42 Key Words: Perfect Competition; Monopoly; Consumer Surplus; Dead Weight Loss; Monopoly Profit; Price. I. Introduction: Economic literature is replete with papers that engage in welfare analysis through measuring economic surplus. Welfare is non-decreasing in economic surplus. Magnitude as well as the change in the economic surplus is indicative of welfare. For instance, consumer welfare is measured by the magnitude of consumer surplus. Consumer welfare too is non-decreasing in consumer surplus. Perfect competition is the market form in which consumer surplus is the greatest in magnitude, thus most favorable to the consumers, as it leads to the highest level of consumer welfare. Monopoly is characterized by economic inefficiency, which is in the form of reduced consumer surplus and deadweight loss. The exception to the above said inefficiency is the case of monopoly (usually natural monopoly) where marginal cost pricing is practiced. As, in case of marginal cost pricing, the resulting consumer surplus is the same as that of perfect competition. If we consider perfect competition and the case monopoly (simple monopoly pricing) under linear demand and constant marginal and average cost conditions, then we find that the consumer surplus that existed in case of perfect competition (henceforth CSPC) gets divided into consumer surplus in monopoly (henceforth CSM), monopoly profit (henceforth πM), and deadweight loss (henceforth DWLM). The same can be put forth numerically as follows: CSPC = CSM + πM + DWLM The above stated division of CSPC is shown by the following diagrams: Figure 1. (a) Perfect Competition AIJRHASS 13-134; © 2013, AIJRHASS All Rights Reserved Page 64 S.P. Misra, American International Journal of Research in Humanities, Arts and Social Sciences, 2(1), March-May, 2013, pp. 64-68 Figure 1. (b) Monopoly The above diagram in panel (a) depicts perfect competition, where the demand curve is characterized by the property of linearity and marginal cost by constancy. The diagram shows equilibrium price in perfect competition (henceforth PPC) and equilibrium quantity in perfect competition (henceforth Q PC). Here, CSPC is the area of the triangle PPCDC. The diagram in panel (b), in addition, shows equilibrium price in monopoly (henceforth P M) and equilibrium quantity in monopoly (henceforth QM). As can be seen, CSPC, the area of the triangle PPCDC, gets divided into three main parts, i.e., triangle P MDB (consumer surplus, i.e., CSM), rectangle PPCPMBA (monopoly profit, i.e., πM), and triangle ABC (deadweight loss, i.e., DWLM). CSPC = CSM + πM + DWLM Claim - 1: In case of linear, downward sloping demand curve and constant (and equal) marginal and average costs, the following relationship would be true: CSM = DWLM = πM = CSPC Claim - 2: In case of linear, downward sloping demand curve and constant marginal cost, the following relationship would be true: PPC = {(2)*(PM) – a}; (where ‘a’ is the y-intercept of the demand curve) The above results can be shown (and generalized) with the help of an illustration. Let us consider a linear demand curve, of the form, Q = (i.e., P = a – bQ), (where ‘a’ and ‘b’ are the intercept and slope parameters respectively) and the total cost function to be given by, TC = CQ. Marginal cost in this case would be C (which is a constant). With the help of the above information, cases of both, perfect competition as well as monopoly can be analyzed. Diagrammatic illustration of both the market forms will depict the stated quantities in the claim. Following diagrams depict perfect competition and monopoly. Figure 2. (a) Perfect Competition AIJRHASS 13-134; © 2013, AIJRHASS All Rights Reserved Page 65 S.P. Misra, American International Journal of Research in Humanities, Arts and Social Sciences, 2(1), March-May, 2013, pp. 64-68 Figure 2. (a) Monopoly The diagram in panel (a) shows perfect competition. The diagram shows P PC = C and QPC = . Here, CSPC is the area of the triangle PPCaD. Numerically QPC, PPC and CSPC would be as follows: QPC = ; PPC = a – b = CSPC = ; and . The diagram in panel (b) shows monopoly. As can be seen, CS PC is divided into three parts, namely, consumer surplus (CSM), the area of the triangle PMaE; monopoly profit (πM), the area of the rectangle PPCPMEF; and dead weight loss (DWLM), the area of the triangle FED. The diagram also shows PM = and QM = . Numerical magnitudes of QM, PM, CSM, πM and DWLM would be as follows: QM = ; M P = ; πM = ; CSM = DWLM = ; and . The above quantities are coherent with the claims, that, (1). CSM = DWLM = πM = CSPC and (2). PPC = {(2)*(PM) – a}; (where ‘a’ is the y-intercept of the demand curve) Explanations of the Claims: Claim - 1: In case of linear, downward sloping demand curve and constant (and equal) marginal and average costs, the following relationship would be true: CSM = DWLM = πM = CSPC Expalnation: Consider a demand curve, of the form, Q = (i.e., P = a – bQ) and total cost, of the form, TC = CQ. The notations are defined as follows: ‘a’ and ‘b’ are the intercept and slope parameters of the demand curve; ‘P’ and AIJRHASS 13-134; © 2013, AIJRHASS All Rights Reserved Page 66 S.P. Misra, American International Journal of Research in Humanities, Arts and Social Sciences, 2(1), March-May, 2013, pp. 64-68 ‘Q’ are the price and quantity respectively. ‘C’ in the total cost is a constant. Following diagrams illustrate the cases of perfect competition (panel (a)) and monopoly (panel (b)). Figure 3. (a) Perfect Competition Quantities in perfect competition would be as follows: Equilibrium output (QPC): P = MC (the profit maximizing condition) P = a – bQ = C Q= QPC = Substituting the value of the QPC in the demand function would give the value of equilibrium price (PPC): P = a – bQ P = a – bQPC P = a – P = C PPC = C Consumer Surplus: Consumer surplus is the area of the triangle CaD CSPC = CSPC = = Figure 3. (b) Monopoly Quantities in monopoly would be as follows: Equilibrium output (QM): TR = P*Q ⇒ (a – bQ)*Q ⇒ TR = aQ – bQ2 AIJRHASS 13-134; © 2013, AIJRHASS All Rights Reserved Page 67 S.P. Misra, American International Journal of Research in Humanities, Arts and Social Sciences, 2(1), March-May, 2013, pp. 64-68 ⇒ MR = a – 2bQ MR = MC (the profit maximizing condition) ⇒ a – 2bQ = C ⇒ Q = ⇒ QM = Equilibrium price (PM): Substituting the value of the QM in the demand function would give the value of equilibrium price (PM): P = a – bQ P = a – bQM P = a – P = C PM = Monopoly profit (πM): Profit = TR – TC = {(PM*QM) – (C*QM)} = area of the rectangle PPCPMEF. ⇒ = πM = Consumer surplus (CSM): Consumer surplus is the area of the triangle P MaE, CSM = = Dead Weight Loss (DWLM): Dead Weight Loss is the area of the triangle FED, DWLM = It can be seen that, (a). CSPC = CSM + πM + DWLM and (b). CSM = DWLM = πM = CSPC Claim - 2: In case of linear, downward sloping demand curve and constant marginal cost, the following relationship would be true: PPC = {(2)*(PM) – a}; (where ‘a’ is the y-intercept of the demand curve) Proof: P = a – bQ; TC = CQ TR = aQ – bQ2 MR = a – 2bQ MR = MC (the profit maximizing condition) a – 2bQ = C Q = QM = Substituting the value of the QM in the demand function would give the value of equilibrium price (P M): PM = a – bQ ⇒ P = a – b = Since C = MC = PPC, substituting PPC for C and solving further yields the following result: PPC = {(2)*(PM) – (a)} Hence, the claim is proved. References: [3] [4] A. Cournot (1838): “Recherches sur les Principes Mathematiques de la Theoriedes Richesses,” English Edition, Researches into the Mathematical Principles of the Theory of Wealth, N.Bacon (ed.), New York: Macmillan. Alfred William Stonier and Douglas Chalmers Hague (1958), “A Textbook of Economic Theory”, 2nd edition, New York: Longmans : Green & Co. Joan Robinson (1933): “The Economics of Imperfect Competition”, London: Macmillan. E.H. Chamberlin (1933): “The Theory of Monopolistic Competition”, Cambridge: Harvard University Press. [5] F.Y. Edgeworth (1925): “The Pure Theory of Monopoly,” Papers Relating to Political Economy, 1, 111-142. [6] Paul A. Samuelson and William Nordhaus (2011), “Economics” 19th edition: Mc Graw Hill Education. [1] [2] AIJRHASS 13-134; © 2013, AIJRHASS All Rights Reserved Page 68