1. Suppose there are 2 firms {A,B} producing the same homogeneous good with constant marginal costs cB = cA. What is the Bertrand equilibrium? Suppose cB
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- 32.- 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…1 Consider two identical firms with a unit cost of production of $10 and a market demand of p= 60-y. (a) What is firm 1’s optimal output level as a function of firm 2’s output? (b) What is firm 2’s optimal output level as a function of firm 1’s output? (c) What is the Cournot equilibrium output level for these firms? (d) What is the Cournot equilibrium price level? Show your work step by step.
- 21. In the industry, only two firms (Firm 1 and Firm 2) operate and they produce a homogenous good. They collude: they maximize their joint profit and split it equally between them. Firm I has the total cost of producing q; units of output given by the function TC(q)-8q1. The total cost of producing q: units of output for Firm 2 is TC(q)-q. Only integer quantities are allowed (no fractions). The market demand for the good is Q(P)-72-P, where Q is the quantity demanded and P is the unit price of the good. How many units of the good do cach firm produce in the equilibrium? A. Each firm produces 14 units. B. Firm I produces 32 units, and Firm 2 produces 2 units. C. Firm 1 produces 28 units, and Firm 2 produces 4 units. D. Each firm produces 16 units. E. None of the aboveConsider the Bertrand competition setup with 2 firms producing identical goods. The market demandis given by Q = 100 − P. T C1 = 30q1 and T C2 = 70q2. Derive the Bertrand equilibrium (prices andquantities of both firms) here.Homework (Ch 14) 1. There must be many buyers and sellers-a few players can't dominate the market. 2. Firms must produce an identical product-buyers must regard all sellers' products as equivalent. 3. Firms and resources must be fully mobile, allowing free entry into and exit from the industry. The first two conditions imply that all consumers and firms are price takers. While the third is not necessary for price-taking behavior, assume for th problem that a market cannot maintain competition in the long run without free entry. Identify whether or not each of the following scenarios describes a competitive market, along with the correct explanation of why or why not. Scenario Competitive? In a small town, there are two providers of broadband Internet access: a cable company and the phone company. The Internet access offered by both providers is of the same speed. Several stores in the mall sell hooded sweatshirts. Each store's sweatshirts reflect the style of that particular store.…
- 3 In a Cournot market with two firms, the inverse market demand curve is P=50-2Q, where Q=q1+q2(Firm 1’s output is ; Firm 2’s output is ). Both firms have a constant marginal cost of 14. If Firm 2 produces 12 units of output, how much should Firm 1 produce? Group of answer choices 3 6 0 12Question 3 Suppose that the cost function of a firm is C(q)=4q. Suppose that this is the only firm in the market, and demand is Q(p)=10-p. What is the amount of the good produced in a competitive equilibrium in this economy? 7 4 6 3 51. marginal costs e, = c, = c, = 20. The inverse demand function is given by P = 100 - Q. where Q = q, + 4: + 93- Consider a market with three firms (i - 1, 2, 3). which have identical a) Identify the reaction functions for each firm and compute the Cournot equilibrium, i.e., the market price and quantity. b) What happens to the market price if all three firms merge compared to part (a)?
- PROBLEM (5) In a dominant firm market with demand Q = 30 − p, the dominant firm has MC(Q) = 2Q (that is, with TC(Q) = Q^2) and the fringe is composed of 5 identical firms, each with MC(Q) = 10Q (that is, with TC(Q) = 5Q^2). (a) Calculate the market price in the dominant firm model. Calculate the quantity produced by the fringe. (b) Now assume that the 5 fringe firms form a “union”, and act as 5 “plants” of the union firm and this union firm competes as one single firm against the dominant firm in quantities, as in Cournot competition. What is the Cournot-Nash equilibrium price and quantity in this market organization? (c) Now, the dominant firm convinces the “union” not to compete with it but instead collude (to maximize the sum of profits) to form a cartel. What is the market price and quantity? (d) Back to the problem description. If all the firms (the dominant firm and the 5 fringe firms) acted as price takers, as in the perfect competition, what would be the market equilibrium…24