ECON 305 Lecture Notes - Lecture 2: Bertrand Competition, Profit Maximization, Demand Curve

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ultramarinebeetle695

11 Dec 2014

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Very different demand curves: bertrand is kinked, cournot is smooth. Cournot"s solution is intuitive while bertrand"s is not. Edgeworth"s model, limited capacity: if a firm has limited capacity to produce there is no single point equilibrium. If firm 1 has limited capacity, then firm 2 has a monopoly power over these consumers firm 1 cannot serve. That means firm 2 has an incentive to charge a higher price because it can make profit on all of the unsatisfied consumers that firm 1 cannot deliver output to. Given that both firms have limited capacity, what works for firm 2 works for firm 1 as well. >firms have extremely limited capacity at some relatively low level of output. Figure 2 bertrand model with limited capacity. Chamberlin: recognized interdependence with joint profit maximization. Firms recognize interdependence and would attempt to jointly maximize profits assuming similar cost and demand curves (of course to be discarded in the real world).

Related Questions

Consider the following Bertrand competition model. Two firms choose their prices simultaneously and the market demand is Q(p). A firm with the lowest price serves the entire market. They split the demand equally if prices are equal. Each firm i = 1, 2 has constant unit of production (i.e., marginal cost) ci > 0 where c1 > c2,and so the firms marginal costs are different. a) Show that p1 = p2 = c1 is not a Nash equilibrium. b) Show that there is no Nash equilibrium where the firms pick the same price (i.e., p1 = p2). c) Is there a Nash equilibrium of this game? d) Suppose now that the prices are discrete and so firm is price must be a multiple of a cent: That is, pi - {0.01, 0.02, 0.03, ..., 0.01n, ...} where n is some positive integer. What is the Nash equilibrium now?

tanhound189

1. A firm that is a pure competitor has P > ATC and P > MC on the output (Q) it is presently producing and selling. Is this firm maximizing its profits? If not, which direction should it change its output if it wants to maximize its total profit?

2. Is a pure competitor in short-run or long-run equilibrium if it has P=MC=ATC? Explain.

3. There is free entry in the model of pure competition. Assuming that P > ATC for a vast number of firms producing a standardized product for a given market, what will happen to market supply as the consequence? What will happen to the market price (P) of the product these firms are producing?

4. Firms in the pure competition have horizontal demand functions. (The market determines product price, so firms in this competitive market are price takers.) Do firms in this model have to lower prices if they want to sell more output? Why or why not?

copperporcupine291

Consider a variant of the 𝑛-firm version of Cournot’s model in which each firm’s average cost function is U-shaped, rather than being constant. Suppose that there are infinitely many firms, all of which have the same cost function 𝐶. Assume that 𝐶(0) = 0, and that for 𝑞 > 0 the function 𝐶(𝑞)/𝑞 (the average cost function) has a unique minimizer q; denote the minimum of 𝐶(𝑞)/𝑞 by p. (See Figure 1.) Assume that the inverse demand function 𝑃 is decreasing.

Show that in any Nash equilibrium of the game the firms’ total output 𝑄^∗ satisfies

𝑃(𝑄^∗ + 𝑞) ≤ 𝑝 ≤ 𝑃(𝑄^∗). (1)

(That is, the price is at least the minimal value p of the average cost, but is close enough to this minimum that increasing the total output of the firms by q would reduce the price to at most p.)

To establish these inequalities, show that if 𝑃(𝑄^∗) < 𝑝 or 𝑃(𝑄^∗ + 𝑞) > 𝑝, then 𝑄^∗ is not the total output of the firms in a Nash equilibrium, because in each case at least one firm can deviate and increase its profit. (You need to identify the firm that can profitably deviate and the deviation it can profitably make.)

Figure 1: The Average Cost Function of Each Firm

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ECON 305 Lecture Notes - Lecture 2: Bertrand Competition, Profit Maximization, Demand Curve

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