The industry demand is P(y) = 14 – 2y. There are two firms with cost functions C1(y1) = 0 and C2(y2) = 0, respectively. a) Find the Cournot equilibrium: quantities, prices, profits, and total surplus.
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The industry demand is P(y) = 14 – 2y. There are two firms with cost functions C1(y1) = 0 and C2(y2) = 0, respectively.
a) Find the Cournot
b) Suppose now that the two firms are owned by the same owner. Find the quantity,
c) Find the maximal surplus possible in this industry. Point out two different sources of inefficiency which makes this total surplus in part (a) smaller.
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- Q. Three firms operate in a market with a Demand function p = 169 - 2Q. All three firms have identical Cost functions: TC = 1200 - 95q + 2q2.i) Given that the firms are able to collude, what is the equilibrium market price and output?ii) If all of the firms cheat and each increases output by two units, what would be the new equilibrium price and the impact on an individual firm’s profits?Two identical firms currently serve a market. Each has a cost function of C(q) = 30q. Market demand is P(Q) = 80 − 0.01Q. The firms compete by setting prices simultaneously as in Bertrand competition. Let PB represent the equilibrium Bertrand duopoly price.The firms have proposed to merge, and they announce that this merger will result in considerable cost savings. The firms’ new cost function will have the form Cm(q) = cq + 100, 000. Note that the merged firm has positive fixed costs while the unmerged firms do not. (a) What is the merged firm’s profit-maximizing price if the merger is approved? Is it possible for the cost savings (via c < PB) to be sufficiently large for the merged firms’ profit-maximizing price to be below the duopoly equilibrium price? (b) Suppose that the Department of Justice permits the merger with the requirement that the new (post-merger) price must be no greater than the pre-merger price. Under what circumstances are the firms willing to go through with…please solve the question completely. Suppose an industry consists of two firms that compete in prices. Each firm produces one product. The demand for each product is as follows: q1 = 25 - 5p1 + 2p2 q2 = 25 - 5p2 + 2p1 The cost functions are C(qi) = 2 + qi for i = 1; 2. (a) Are the products produced by these firms homogenous or differentiated? (b) Find the best response function for each rm. (c) How does the price firm 1 sets change with its belief about the price of its competitor\'s product? (d) What are the Nash equilibrium prices? (e) What is the percentage markup of price over marginal cost here (this is called the Lerner index)? Do the firms have market power? Why does the Bertrand paradox of zero variable duopoly profits apply here? (f) Suppose the firms merged. What is the new price of products 1 and 2? (g) Explain intuitively why the price is higher under monopoly than under Bertrand duopoly? (h) Are total monopoly profits higher or lower than the sum of Bertrand duopoly…
- Suppose the Boston to Philadelphia airline route is serviced by three airlines – US Airways (Firm A) and JetBlue (Firm B) and Continental (Firm C). The demand for airline travel between these two cities is Q = 150 – p. The cost function is C(Q) = 30Q. The cost function is the same for all three airlines. Assume that the three airlines are making investments in airline capacity. In other words, they are simultaneously choosing quantity. (Cournot Competition) Derive US Airways’ residual demand function given JetBlue’s output, qB, and Continental’s output, qC. What is the Marginal Revenue for US Airways? Derive US Airways reaction function Derive the market equilibrium quantity, Q*, price, p*, and Profit.An industry has two firms. The inverse demand function for this industry is p = 74 − 4q. Both firms produce at a constant unit cost of $26 per unit. What is the Cournot equilibrium price for this industry?A homogeneous product duopoly faces a market demand function given by p = 300 - 3Q,where Q = q1 + q2. Both firms have constant marginal cost MC = 100. What is the Bertrand equilibrium price and quantity in this market?
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- Exercise 6.8. Two companies with cost functions C1 (q1 )=5q1 and C2 (q2)= 0.5 q2 ² supply the to the same market. If the inverse market demand function is given by P = 100 - 0,5Q , where Q = q₁ + q₂ , find a) The production level of each firm, the price and the profits if the companies compete according to the Cournot model. (b) The level of production of each undertaking, the price and the profits if the undertakings agree to jointly maximise their profits. Show the results with the help of graphs.. The market for widgets consists of two firms that produce identical products. Competition in the market is such that each of the firms independently produces a quantity of output, and these quantities are then sold in the market at a price that is determined by the total amount produced by the two firms. Firm 2 is known to have a cost advantage over firm 1. A recent study found that the (inverse) market demand curve faced by the two firms is P = 280 – 2(Q1 + Q2), and costs are C1(Q1) = 3Q1 and C2(Q2) = 2Q2. a. Determine the marginal revenue for each firm. b. Determine the reaction function for each firm.Consider a homogeneous good industry (such as an agricultural product) with just two firms and a total market demand Q = 400−P, so the inverse demand is P = 400 − Q. Suppose both firms have a constant marginal cost equal to $100 per unit of output and a fixed cost equal to $10,000. One simple way to depict rivalry in a duopoly (2 firms) is the Cournot model. This model is reasonable in agricultural markets where firms choose production (plantings) in advance and the market price is determined later after the crop is harvested. In the Cournot model we imagine that the two firms simultaneously choose their production or quantity, and that demand (market clearing) determines the price given each firms’ quantity. (a) Suppose (hypothetically) that the second firm produces 0 units, and the first firm anticipates this, so the first firm is the only seller. How much will the first firm produce (in this case the first firm acts like a monopolist and sets output where MR = MC)? Hint: The first…
