Discuss the Salient Features of Both the Cournot and Duopoly Models of Competition
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DISCUSS THE SALIENT FEATURES OF BOTH THE COURNOT AND DUOPOLY MODELS OF COMPETITION. [25]
A duopoly is an economic or political condition in which power is concentrated in two persons or groups.
Cournot competition is an economic model used to describe an industry structure in which companies compete on the amount of output they will produce, which they decide on independently of each other and at the same time. In the Cournot model, the strategic variable is the output quantity. The Main Assumptions of the Cournot duopoly are two firms produce the same goods, firms independently and simultaneously choose how much quantity to produce and each firm is myopic; it expects the competitor to keep the same quantity even after it sets its own quantity. (search.mit.edu). It has the following features: There is more than one firm and all firms produce a homogeneous product; firms do not cooperate; firms have market power, i.e. each firms output decision affects the goods price; the number of firms is fixed; firms compete in quantities, and choose quantities simultaneously; the firms are economically rational and act strategically, usually seeking to maximize profit given their competitors decisions and there is also a barrier to entry. An essential assumption of this model is the “not conjecture” that each firm aims to maximize profits, based on the expectation that its own output decision will not have an effect on the decisions of its rivals. Price is a commonly known decreasing function of total output. Each firm has a cost function. The cost functions may be the same or different among firms. The market price is set at a level such that demand equals the total quantity produced by all firms.
GRAPHICAL REPRESENTATION OF COURNOT DUOPOLY MODEL
Analysis of model with 2 firms and constant marginal cost
p1 = firm 1 price, p2 = firm 2 price
q1 = firm 1 quantity, q2 = firm 2 quantity
c = marginal cost, identical for both firms
Equilibrium prices will be:
p1 = p2 = P(q1 + q2)
This implies that firm 1s profit is given by Π1 = q1(P(q1 + q2) − c)
Calculate firm 1s residual demand: Suppose firm 1 believes firm 2 is producing quantity q2. What is firm 1s optimal quantity? Consider the diagram 1. If firm 1 decides not to produce anything, then price is given by P(0 + q2) = P(q2). If firm 1 produces q1 then price is given by P(q1 + q2). More generally, for each quantity that firm 1 might decide to set, price is given by the curve d1(q2). The curve d1(q2) is called firm 1s residual demand; it gives all possible combinations of firm 1s quantity and price for a given value of q2.
Determine firm 1s optimum output: To do this we must find where marginal revenue equals marginal cost. Marginal cost (c) is assumed to be constant. Marginal revenue is a curve – r1(q2) – with twice the slope of d1(q2) and with the same vertical intercept. The point at which the two curves (c and r1(q2)) intersect corresponds to quantity q1(q2). Firm 1s optimum q1(q2), depends on what it believes firm 2 is doing. To find an equilibrium, we derive firm 1s optimum for other possible values of q2. Diagram 2 considers two possible values of q2. If q2 = 0, then the first firms residual demand is effectively the market demand, d1(0) = D. The optimal solution is for firm 1 to choose the monopoly quantity; q1(0) = qm (qm is monopoly quantity). If firm 2 were to choose the quantity corresponding to perfect competition, q2 = qc such that P(qc) = c, then firm 1s optimum would be to produce nil: q1(qc) = 0. This is the point at which marginal cost intercepts the marginal revenue corresponding to d1(q
Bertrand competition describes interactions among firms (sellers) that set prices and their customers (buyers) that choose quantities at that price. In the Bertrand model, rather than choosing how much to produce, each firm chooses the price at which to sell its good. The main assumptions of Bertrand Competition are a fixed number of firms produce a homogeneous product, firms simultaneously choose what price they want to charge, since consumers