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Two producers, A and B produce identical products at identical costs. Their unit costs are constant over any range of output and the total demand in the market they share is linear.
It is assumed that both the producers know exactly what the total demand is—both can see every point on the demand curve. Both producers want to maximise the profits.
Each one sees what the other is doing and then acts accordingly. They adjust their outputs, not their prices.
We know that if demand is linear and unit costs are constant, the profit maximising monopoly output is exactly half the competitive output. The competitive output where price equals MC can be called the opportunity output of a monopolist.
The monopolist never wants to produce more than the opportunity output because if he does, unit cost would exceed price. His optimum output is half the opportunity output.
Assume producer A is the first to take action. He looks over the market and produces and sells half the opportunity amount because by doing so, he maximises his profits.
Next, B appears on the scene and sees what A’s output is; B simply takes it for granted that A will continue to produce and sell the same volume of output.
The other half of the opportunity therefore belongs to B. To maximise his profits, he produces and sells an amount equal to half of the half (i.e., one-fourth) of the opportunity output.
Then A sees that B is now selling a quarter of the opportunity output. Because B’s action has brought down- the price, A has to recalculate his position. He assumes that B’s output will stay at a quarter. Hence his chance is the other three quarters of the opportunity output.
Half of this is 3/8th. So A cuts his output back. Then B expands his output and so it goes on. At the end, each one is producing exactly one-third of the opportunity (or competitive) output.
Cournot’s sellers produce two-thirds of the competitive output. It can be shown that three produce three quarters and then n would produce of the competitive output. The greater the number of sellers, the larger will be the fraction.
Therefore, as the number of seller’s increases, their combined output and price will come closer and closer to the competitive level.
Therefore the total output of both the mineral springs is OM+MB=OB. When the total output OB is offered for sale in the market, the price will be zero (cost of production is assumed to be zero).
Suppose one of the producers starts his business first. He is the monopolist because he is the only producer. He will produce OM output which is his maximum daily output, for his profits will be maximum at OM and will be equal to OMPQ.
Since the costs have been assumed zero, the entire revenue OMPQ will represent profits. The producer will fix the PM Price. Now suppose another producer enters into the business and he sees that the first producer is producing OM amount of output.
The second producer thinks that the first producer will continue to produce MO which is 1/2 of OB, without paying any heed to what output he himself decides to produce.
Under such circumstances, the second producer will regard segment PB as the demand curve confronting him and he will produce MN amount of output which is 1/2 of MB.
Now the total output would be OM+MN=ON and the price will fall to NR per unit. The total profits made by the two firms would be ONRS which are less than OMPQ. Of the total profits ONRS, the first firm will earn OMTS and the second firm will earn MNRT.
Since the profits of the first seller are reduced due to the second seller producing MN, he will again think over the situation but assume that the second producer will continue to produce the same output MN.
Under the circumstances the best that the first producer could do is to produce 1/2 (OB— MN) =OC. Therefore, he reduces his output from OM to OC.
The total output will be OC+MN=OD and the price of the product will be DE and the total profits of the two producers will be ODEF.