Theory of Markets
(Stigler, Simon, Oliver Williamson and Elinor Ostrom, Jean Tirol)
In the 1930’s, the dominant Perfect Competition market structure did not fit the fact of reality. Joan Robinson and Chamberline have developed a new theory of market structure. Joan Robinson explained her theory in The Economics of imperfect Competition and Chamberline discussed his views in Monopolistic Competition. While Joan Robinson discusses the imperfection in the market structure, Chamberline tries to blend both Monopoly and Competition and develop a theory of Monopolistic Competition. According to Chamberline Firms do not start in most cases with Monopoly but they strive to create monopoly by differentiating their products.
Let us give a brief account of the main features of each type of Market structure and explain how prices are determined under each category. In a Monopoly, there is only one seller and the product is unique and he has a large degree of control in setting either the price or quantity sold. The Duopolist refers to two sellers and Oligopoly refers to more than two but few sellers, whose products are either differentiated or homogeneous. Monopolistic Competition is a market where there are many sellers (both large Groups and Small Groups) whose products are differentiated but only slightly and who have some degree of control over price or quantity sold. The conventional model of Perfect Competition refers to a large number of sellers selling identical products and no single seller has any control over price and his Demand Curve is horizontal.
Under Perfect competition there is a free entry and exit of Firms and there is no scope for excess profits by any single Firm in the long run. Since P is given, it’s P = M.R and it maximizes profit where P = M.R. =L.M.C =A.R=L.A.C. At the given price, the firm’s M.R = A.R. is horizontal. The A.R. curve is tangent to long-run A.C. curve from below at the minimal point of A.C and M.C. curve cuts the A.C. curve from below at the minimal point of A.C. As there is free entry and exit of Firms, long-run equilibrium of the Firm under Perfect Competition is at point of minimum average cost. In the long-run, the equilibrium of the firm is given by P=M.R.=L.M.C.=L.A.C. There are no excess profits
A monopolist is a single seller and he is the Industry. The demand curve for his product is downward sloping and as such M.R is also downward sloping. The MC slopes upwards. The point of intersection of the downward sloping MR and upward sloping MC determines the equilibrium output. The demand determines his price. As compared to perfect competition, a Monopolist output is less and price is more. Under Monopolistic, competition, the demand curve for the product of a firm may be expected to have a negative slope, for customers will have different degrees of loyalty to the firms whose products are differentiated. In the short run, firms may earn excess profits. But in the long run Firms will enter and compete away the profits. Firms earn only normal profits.
Duopoly refers to a situation where there are only two sellers and oligopoly to more than two sellers (but few). Augustine Cournot, in his book titled Mathematical Principles of the Theory of Wealth., proposed a Duopoly model, which is named after him. The model assumes: Two produces A and B produce identical products and have identical costs. For simplicity, Cost of Production is assumed to be zero and the total demand in the market they share is linear. Both Firms know exactly what the total demand is. Further both accept the market price and neither sets it and each Duopolist, in making his own plan of output assumes that his rival’s reaction will be to maintain the same level of his output and each attempt to maximize profit the Duopolists act independently and do not collude.
We shall follow the explanation given by Stigler in discussing Cournot’s model.
Suppose two Firms each own a mineral spring whose water is much valued by customers. There are no costs of Production. Cournot proceeds to analyse the problem, subject to the assumptions mentioned above. Let the demand curve be P=I00-Q, and retain the condition of no Cost. In the case of Monopoly he maximises the total revenue, PQ (cost are zero)
TR = PQ = I00.Q – Q2
MR = I00 - 2Q (derivative of TR, wrt to Q)
Setting MR = MC, I00 - 2Q = O (MC = O),
2Q = I00, Q = 50 and P = I00 – 50 = 50
If there is only one producer, a Monopolist, his profit maximizing output is 50 and price is 50.
Using the same example, let us consider the case of Duopoly.
P=I00 - (QA+QB)
Step I. Let A set any output say, 40 which fetches a price of 60 (P = 100 – Q)
2). Then B will take A’s output as given, and seek the output that maximizes his (B’s) profits. The market for B will be the remaining part of the demand curve. In the case of a linear demand curve, the MR curve bisects the horizontal line drawn from the Price axis to the demand curve. Suppose a total demand curve (of both duopolists) is drawn and mark the A’s out put on the X axis and draw a vertical line to cut the demand curve. From that point of intersection, if we draw, MR curve (of B) it will cut the remaining part of the horizontal axis in to half. As Mc = 0, it is equal to horizontal axis. The profit maximizing output for B will be exactly half of the Competitive output. Hence the output of B will be ½ (100 - 40) = 30. The price in the Market is
100-(40 + 30) = 30
3). Then A sets his output to maximize his profits, on the assumption that B’s output will be 30. Then A will produce ½ (100-30)=35
4). It is now B’s turn. It will produce ½ (100-35)=32.5
5). Then A will produce 33.75; then B will produce 33.125 and so on
This is an infinite series. The final solution will be for each Duopolist to produce is 331/3 units, with a market price of 33 1/3. Output supplied by the two Duopolists is 2/3 of the total of I00.
Paul Sweezy developed the Kinked demand curve model to explain the price rigidity under Oligopoly. The market situation contemplated by Sweezy is one in which rivals will quickly match Prices reductions, but only hesitantly and incompletely if at all follow price increases. This pattern of expected behavior produces a ‘kink’ at the existing Price.
There is no incentive for the Firm under Oligopoly to either raise the prevailing Price or decrease it. That is why Prices under Oligopoly remain stable. If the marginal Cost curve passes over the range of discontinuity of the marginal revenue curve. Output and Prices remain unchanged at the existing levels.
Stigler:
After a thorough analysis of empirical evidence, Stigler concludes that “evidence reveals neither Price experiences nor the pattern of changes of Price quotations that the theory leads us to expect”.
Other Models:
There are other models Duopoly & Oligopoly. In the Collusion model the two duopolists act in concert to maximize their joint profits. In this model maximization proceeds in the same manner as in multi-plant monopolists. A German Economist Stackel Berg developed a leadership-followership model of duopoly named after him. According to the Stackelberg model, a firm which is a follower behaves exactly as the Cournot firm. A leader takes advantage of the assumptions that the other firm is behaving as a follower. The Market shares model of duopoly assumes that one firm always wishes to maintain a fixed share of the market and the other firm is willing to let it so. In the Dominant firm model of Oligopoly the dominant firm sets the price for the product and other small firms who cannot have any influence on price will take the price set by the dominant firm as given and act as perfect competitors in determining their outputs.
In a real world situations, we come across other complex situations and pricing practices. There are multiple products, and Joint products. There are peak-load pricing of products, Full cost pricing and pricing of bundled goods. There is price discrimination for differentiated products under imperfect markets and there are different degrees of price discrimination.