Profit Maximization In a Monopoly

Since a monopoly ischaracterized by asingle seller, themarket demand andthe demand facedby the firm are thesame. The demandwill tend to benegatively Figurerepresentsprofit maximizationby a firm in amonopoly market.

P_x

D

MC

P* Н

AC

Рс К

D

MR AR

0 Q* Qс Q_x

The TR functionincreases up to anoutput level of QBTBthen it declines.Remember that anynegatively slopeddemand function iselastic at high prices(top half of demandwhere priceincreases reduceTR) and inelastic atlow prices (bottomhalf of demandwhere price increases increase TR). The TC increases at a decreasingrate, passes an inflection point and then increases at an increasingrate. Maximum profits is occurs at the output level where TR >TR bythe greatest vertical distance. This occurs at output QBMB. Profits arereflected by the vertical distance, CBMBRBMB, or TRBMB-TCBMB. At point CBMB theslope of the TC (MC) is the same as the slope of the TR at point RBMB(MR). The maximum TR occurs at point MBTB at output level QBTB. If thefirm increases output from QBMB to QBTB profits will decrease because thecosts of the additional units (QBTB-QBMB) is greater than the additionalrevenue produced by those units of output.Unit cost and revenue functions can also be used to show the outputand price decisions of a monopolist. In Figure VIII.2 the demand, AR,MR, MC and AC cost functions are shown.

Figure represents a monopolist. In the long run the monopolistmight adjust the scale of plant, but BTE prevents other firms fromentering and driving profits to normal. Monopoly or market power issuggested by two things. First, the price is greater than the marginalcost (P>MC). Secondly, above normal profits will persist over time.

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An oligopoly is a market that is characterized by the interdependence of firms. The outcomes that follow from the decisions of one firm are dependent on what the other firms do. Augustin Cournot (1801-1877), a French mathematician/economist developed the theory of monopoly and then considered the effects of two interdependent competitors (sellers) in a duopoly. Cournot’s analysis of two sellers of spring water clearly established that the price and output of one seller was a reaction to the price and output of the other seller. If the two collude they can act as a single monopolist and divide monopoly profits. If they compete, Cournot concluded that the output would be times the competitive output. As the number of competitors (N) increases, the result approaches the purely competitive result. Cournot’s recognition of the interdependence of sellers provided the foundation for a variety of approaches to explain the interdependent behavior of oligopolists.

In the 1930’s the “kinked demand” model [published by Paul Sweezy in August 1939 and by R.L. Hall and C.J. Hitch in May 1939] and the “administered price hypothesis” [Gardner C. Means in 1935] were developed as an attempt to explain price rigidities in some markets during the great depression. In 1943 John von

Neumann and Oskar Morgenstern published a path breaking work on game theory. Game theory has been used to try to explain the behavior of independent competitors. There have been a variety of other models that attempted to explain the interdependent behavior in oligopolies. The number of models is evidence that it is a difficult task and there are problems with most approaches. The kinked demand model is used here to emphasize the interdependence of oligopolistic behavior rather than to explain the determination of price.

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