1495 words - 6 pages

In an oligopoly, there are a number of firms which are all large enough to have an effect on price. Participants therefore analyse their competitors expected reaction to a change in output or price in order to make a profit maximizing decision. This is unlike for example, a competitive market, where results depend only on a firms own actions. Hence, a firm must know how their competitors will react to changes in price or quantity if they wish to find the optimum levels of output and price.In this essay, I will assume that there are only two firms in the market, this situation is known as a duopoly. I will also assume that both of these firms produce a homogenous product, so that I can ignore the factors of product differentiation and the associated brand loyalty.Having removed the complications of product differentiation and multiple firms, we are left with the factors of output and price as the methods of competition in an oligopoly. This essay will specifically examine the strategic issue of changing the levels of output. There are two different models to study which involve the setting of output: The Stackelberg model, where one firm makes a choice before the other firm and becomes a "quantity leader", and the Cournot model, where there is "simultaneous quantity setting" because when one firm sets it's output it doesn't know what the competitors reaction will be.There is one more form of interaction between firms in an oligopoly, by which firms jointly set price and quantity to maximize their profits. This is known as collusion. I will firstly examine the two models in which firms compete by setting output and then deduce why non-collusion is the inevitable outcome.If firms are simultaneously deciding what quantity to produce, they must guess the quantity their competitor will produce and choose a profit maximizing output accordingly. This is known as the Cournot model.I will look at an example in which each of two firms has the cost function;TC(y) = 20y,the inverse demand function for the firms' output is;p = 80 Q,where Q is the total output. Using these equations each firm can find its optimum level of output.Firm 1's reaction function can be derived as follows (where y1 is firm 1's output):y1(80 y1 y2) 20y1.In the Cournot model we assume that each firm takes the other firm's output as constant in determining its own output.Taking the derivative of this profit with respect to y1 (keeping y2 constant) and setting the derivative equal to zero we obtain:80 2y1 y2 20 = 0,or:y1 = (60 y2)/2.Seen as both firms are facing the same cost function, firm 2's reaction function is also:y2 = (60 y1)/2To find the Cournot equilibrium we solve the pair of equations as a simultaneous equation, obtaining;y1 = (60 ((60 y1)/2))/2,so that y1 = 20; substituting in the equation for y2 we get y2 = 20.We conclude that there is a unique Nash equilibrium, in which the output of each firm is 20. Each firm's profit is(20)(80 20 20) (20)(20) = 400.Each firm is doing the...

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