Question

Q5 (7 Marks) [CLO 4 In oligopoly market every company wants to apply price competition. Use the Bertrand model to discuss how can a firm 2 to set the price (P2) of its product case by using diagram if you have some information: Demand Q a-b.P, a firm 1 sets price (P1) for its product (q1). (q2). Illustrate the

Answer 1

Bertrand competition is a model of competition used in economics, named after Joseph Louis Francois Bertrand. It describes interactions among firms (sellers ) that set prices and their customers (buyers) that choose quantities at that prices set. The model rests on very specific assumptions. There are at least two firms producing a homogenous (undifferentiated ) product and cannot cooperate in any way. Firms compete by setting prices simultaneously and consumers want to buy everything from a firm with a lower price (since a product is homogeneous and there are no consumer search costs ).

If two firms charge the same price, consumers demand is split evenly between them. It is simplest to concentrate on the case of duopoly where there are just two firms, although the results hold for any number of firms greater than 1. A crucial assumption about the technology is that both firms have the same constant unit cost of production, so that marginal and average costs are the same and equal to the competitive price. This means that as long as the price it sets is above unit cost, the firm is willing to supply any amount that is demanded (it earns a profit on each unit sold ). If the price is equal to unit cost, then it is indifferent to how much it sells, since it earns no profit.

According to the Cournot Bertrand Model, two firms 1 and 2, compete in a static Cournot Bertrand game where firm 1 is the Cournot -type firm that competes in output and firm 2 is the Bertrand -type firm that competes in price. Firm I's output level is q and its price is p, The goal of each firm is to maximize its profit. Products are substitutes and products may vary over a variety of characteristics Product differentiation of this sort can be incorporated into a linear demand system. The inverse demand function for firm i is p_i =a-q_i - d q _j, where j is firm I's rival, a is a positive constant and d is an index of product differentiation. Products 1 and 2 are perfectly homogeneous when d=1 and each firm is monopolist when d=0.

Thus, product differentiation diminishes as d$\small \rightarrow$1. In the Cournot Bertrand Model, this system must be solved so that demand is a function of the strategic variables q1 and p2. Firms face the same linear cost function. In the case of perfectly homogenous goods, the equilibrium price equals marginal cost, only firm 1 survives (firm 2 produces no output ), and firm 1 produces the perfectly competitive level of output.

So, firm 2 can set its price (P2) of its product equal to (q2) using the Bertrand Model as discussed above.