7. Two firms produce identical goods, with a production cost of c> 0 per unit. Each firm sets a nonnegative price (p₁ and 2). All consumers buy from the firm with the lower price, if p1 # P2. Half of the consumers buy from each firm if p₁ = P2. D is the total demand. Profit of firm i is: 0 if pi > p; (no one buys from firm i); Pi-c DPC if p₁ = p; (Half of customers buy from firm i); 2 D(pic) if pi < p; (All customers buy from firm 2) Find the pure strategy Nash equilibrium: a) Both firms set p = 0. b) Firm 1 sets p = 0, and firm 2 sets p = c. c) Both firms set p = c. d) No pure strategy Nash equilibrium exists.
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- 2.- Each of two firms, firms 1 and 2, has a cost function C(q) = 1 2 q; the demand function for the firms' output is Q = 1.5-p, where Q is the total output. Firms compete in prices. That is, firms choose simultaneously what price they charge. Consumers will buy from the firm offering the lowest price. In case of tying, firms split equally the demand at the (common) price. The firm that charges the higher price sells nothing. (Bertrand model.) (a) Formally argue that there could be no equilibrium in prices other than p1 = p2 = 1 2. (b) Solve the same problem, but this time assuming that firms compete in quantities.Now, suppose that firm 1 has a capacity constraint of 1/3. That is, no matter what demand it gets, it can serve at most 1/3 units. Suppose that these units are served to the consumers who are willing to pay the most. Thus, even if it sets a price above that of firm 1, firm 2 may be able to sell some output. (c) Obtain the (residual) demand of firm 2 (as a function of its own…5 The market demand for curve for Xn good is: P = 100 - (q1 + q2) The market quantity is: Q = q1 + q2 and TC = 40Q Where q1 represents the quantity for firm 1 and q2 represent the quantity for firm 2. TC represents the total cost for both firms. a. Determine the best response function for firm 1 and firm 2. b. Determine the equilibrium q1 and q2.2.- Each of two firms, firms 1 and 2, has a cost function C(q) = 0.5q; the demand function for the firms' output is Q = 1.5 - p, where Q is the total output. Firms compete in prices. That is, firms choose simultaneously what price they charge. Consumers will buy from the firm offering the lowest price. In case of tying, firms split equally the demand at the (common) price. The firm that charges the higher price sells nothing. (Bertrand model.) (a) Formally argue that there could be no equilibrium in prices other than p1 = p2 = 0.5 (b) Solve the same problem, but this time assuming that firms compete in quantities.Now, suppose that firm 1 has a capacity constraint of 1/3. That is, no matter what demand it gets, it can serve at most 1/3 units. Suppose that these units are served to the consumers who are willing to pay the most. Thus, even if it sets a price above that of firm 1, firm 2 may be able to sell some output. (c) Obtain the (residual) demand of firm 2 (as a function of its own…
- PROBLEM (5) (In a market with demand Q = 780 - p, there are 3 identical firms, A, B and C; each with a total cost function TC(Q) = 3(Q)^2. Calculating the market price under each of the 2 scenarios below, rank/order the Consumer Surplus in each scenario (don’t calculate each CS; just rank them); (i) B and C jointly form the fringe supply and A is the dominant firm in the dominant firm model. (ii) They act as perfectly competitive firms -as if trying to maximize total surplus and minimize DWL- that is, their joint MC serves as the “market supply” for the competitive market. Please answer all the parts!Two profit-maximising firms-firm 1 and firm 2-produce an identical good at no cost and simultaneously choose their prices, which must be between 0 and 1. That is, firm 1 chooses P1 contained in [0, 1] and firm 2 chooses p2 contained in [0, 1] (i.e., 0 ≤ p1, p2 < 1). If p1< p2, the cheaper firm gets a demand of 1 and the more expensive firm gets a demand of 0. If P1 = P2, each firm gets a demand of 0.5. Firm 1 has a capacity constraint x contained in [ 0,1 ]but firm 2 has no capacity constraint. Therefore, the demands are (Q1,Q2) =( (х, 1 -х) (min{x, 0.5}, max{1 - x, 0.5}) ( (0,1) if p1 <p2 if P1 = p2 if p1 > P2. For any capacity constraint x contained in (0,1) (i.e., 0 < x < 1), find all Nash equilibria of that game. Suppose now that each firm can only choose among three possible prices: 0, 0.5, and 1; that is p1, p2 € {0,0.5, 1}. For any capacity constraint x € (0, 1) (i.e., 0 < x < 1), find all Nash equilibria of that game. Repeat parts (a) and (b) for the…You make delicious cupcakes that you mail to customers across the country. Your cupcakes are so unique and special that you have a great deal of pricing power. Your customers have identical demand curves for your cupcakes, and a representative customer’s demand curve is shown below. (It’s not needed, but the demand curve equation is P=5-0.2Q or Q=25-5P.) Suppose your MC=$1/cupcake, whether you produce lots or just a few cupcakes. To keep things simple, suppose there are no fixed costs, so FC=0. a) Acting as a monopolist, show the standard pricing analysis on the graph below that identifies your profit-mamximing price and quantity for your representative customer. Shade areas representing your profit and CS. (PS and profit are the same here since FC=0). b) Suppose you offer a quantity discount: first 10 cupcakes at $3 each and any cupcakes over 10 are offered at a discounted price. What discount price will maximize your profit? Show this quantity discount arrangement on your graph…
- Brand X is one of many firms in a competitive industry where each firm has a constant marginal cost of 2 dollars per unit of output. If marginal cost for Brand X rises to 4 dollars per unit and marginal costs of all other firms in the industry stay constant, by how much does the price in the industry increase? a. 2 dollars b. 1 dollar c. 0 dollar d. 2/n, where n is the number of firms in the industry e. None of the above.Two different boutique wineries supply two towns: town A and town B. Winery 1 supplies town A and Winery 2 supplies town B. Both wineries have a constant marginal cost c = 20. Assume that consumers are indifferent between the wines from different wineries and that they purchase wine only in the town they live. Demand for wine in town A is given by pA=40−12qA; the demand for wine in town B is given by pB=70−qB. a) Find the price p1, quantity sold q1, and profit π1 of Winery 1 in town A. b) Find the price p2, quantity sold q2, and profit π2 of Winery 2 in town B. c) Assume that the two wineries decide to merge (i.e. to unite) and become Winery Co. The Winery Co sells wine in both towns at the same price (i.e. the price of wine in town A is the same as the price of wine in town B). The marginal cost is still equal to 20. What is the total demand for wine from the residents of both towns? Find the price pM, quantity sold in each town (qA and qB) and the total profit πM of Winery Co. d)…Suppose two firms face market demand of P=150-Q, where . Both firms have the same unit cost of C, cost C=27. Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. What is the follower’s total revenue function? Determine the equilibrium output level for both the leader and the follower. Determine the equilibrium market price. Determine the profits of the leader and the follower.
- Solve only c and d 2. There are 2 groups with different demand in a market, as follows: ?!=40−?1 and ?"=100−2?2 a. Give the inverse demand curves and marginal revenue in each of these groups. b. If marginal cost is flat at $10, calculate the profit-maximizing quantities and prices associated with this market place. Are the prices for each group different? Comment on the outcomes. c. Calculate the producer surplus associated with the outcomes generated in part b. d. Now calculate the equilibrium price and quantity if the firm charges one price across all consumers. What is the producer surplus associated with this outcome and how does it differ to that calculated in part c?Suppose two firms face market demand of P=150-Q, where . Both firms have the same unit cost of C, which consist of your student number a plus 20 (i.e. if your student number a=3, then cost C=20+3=23). Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. 1.What is the follower’s total revenue function? 2.Determine the equilibrium output level for both the leader and the follower. 3.Determine the equilibrium market price. 4.Determine the profits of the leader and the follower.Two firms produce goods that are imperfect substitutes. If firm 1 charges price p1 and firm 2 charges price p2, then their respective demands are q1 = 12 - 2p1 + p2 and q2 = 12 + p1 - 2p2 So this is like Bertrand competition, except that when p1 > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, p1 = BR1(p2) is the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. (b) Notice that for any given price p1, firm 1’s demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the best reply to p2 = 0 (c) What prices for firm 1 are…