Consider the case of two firms competing in a market. Each firm has a constant marginal cost equal to $10. The demand function is D(p) = 100 − p (p is the price in cents) Firms are competing by choosing prices simultaneously. When prices are equal, each firm gets exactly one half of the total demand. P must be an integer value.
1. Find all the Nash equilibria of this duopoly game.
2. Calculate each firms profit under any equilibria.
3. What is each firms best response?
4. Firm 1 decides to raise the price to 200. If you are firm 2 what price should be set to maximize your profit? What are your profits at the new price?
Consider the case of two firms competing in a market. Each firm has a constant marginal...
Two firms compete in a market with demand given by D(p) = 100 − p, where p is denoted in cents (p=100 is 1 dollar). Firms can only charge prices in whole cents – i.e. p can only take integer values, and not values like 1.5. Marginal costs for each firm are given by MC=10. Firms compete by simultaneously choosing prices. When prices are equal, each firm gets one half of total demand. b. Find all the Nash equilibria of...
1. Suppose there are two firms with constant marginal cost MC = 3 and the market demand is P = 63 − 5Q. (a) Calculate the market price and profits for each firm in each of the following settings: • Cartel • Cournot duopoly • Bertrand duopoly (firms can set any price) (b) Using part a), construct a 3×3 payoff matrix where the firms are choosing prices. The actions available to each of two players are to charge the price...
Consider a Bertrand duopoly in a market where demand is given by Q firm has constant marginal cost equal to 20 100 - P. Each (a) If the two firms formed a cartel, what would they do? How much profit would eaclh firm make? (6 marks) (b) Explain why the outcome in part (a) is not a Nash Equilibrium. Find the set of Nash Equilibria and explain why it/they constitute Nash equilibria. (6 marks) (c) Now suppose that instead of...
Two firms are price-competing as in the standard Bertrand model. Each faces the market demand function D(p)=50-p. Firm 1 has constant marginal cost c1=10 and firm 2 has c2=20. As usual, if one of the firms has the lower price, they capture the entire market, and when they both charge exactly the same price they share the demand equally. 1. Suppose A1=A2={0.00, 0.01, 0.02,...,100.00}. That is, instead of any real number, we force prices to be listed in whole cents....
The players are two firms in a duopoly, and a set of consumers. The two firms produce a homogeneous good. The firms simultaneously choose their prices. Demand adjusts instantaneously according to the equation Q = 6 − p, Each firm has constant costs per unit of output. Firm 1’s cost per unit is 1, and firm 2’s cost per unit is 2. The firms’ payoffs are their profits. If the two firms’ prices are not equal, consumers will buy, according...
Consider two firms competing in a market with a demand function P=150-Q. Both firms have constant marginal cost c>0. There are no fixed costs. They compete by setting prices p₁ and p₂ simultaneously. (Bertrand game.) Which of the following statements is not correct? Select one: a. Both firms charging charging p = c is a Nash equilibrium. b. When firm 1 sets where is the industry monopoly price, firm 2's best response is to set . c. When p₁=c, any price p₂≥c...
Consider a market in which two firms i = 1,2 produce a homogeneousproduct at constant marginal cost c= 4, facing total demand described by the linear inverse demand curve P= 16−Q. First assume that the firms compete by simultaneously choosing prices a la Bertrand. a. Suppose that F1 expects F2 to set some price p2 above the marginal cost c but below the monopoly price pm. What is F1’s best response BR1(p2) to this price p2? b. What is the...
Two firms with differentiated products are competing in price. Firm A and B face the following demand curves: ?? = 70 − 2?? + ?? and ?? = 120 − 2?? + ?? respectively. Assume production is costless. Give equations for and graph each firm’s reaction curve. If both firms set their prices at the same time, what is the Nash equilibrium price, quantity, and profit for each firm? Suppose A sets its price first and then B responds. What...
5. Consider two firms selling differentiated varieties of a product, e.g., Coke and Pepsi. Each firm j chooses a price pj for its own variety. Since these varieties are close substitutes, the demand that each firm faces depends not only on its own price, but also the price of its competitor. Specifically, the demand for j’s variety is given by Dj (pj , p−j ) = max 0, 60 + p−j − 2pj Suppose that both firms can produce any...
Consider two firms (Firm A and Firm B) competing in this market. They simultaneously decide on the price of the product in a typical Bertrand fashion while producing an identical product. Both firms face the same cost function: C(qA) = 12qA and C(qB) = 12qB, where qA is the output of Firm A and qB is the output of Firm B. The demand curve is P = 30 - Q. (i) What will be the Bertrand-Nash equilibrium price (pB) chosen...