Suppose there are two firms in an industry and the inverse demand function for the industry is: P= 45 - 20 Assume that the MC functions for the two firms are: MC1 = 15 MC2 = 12 What is the price under Courbet model? O 15 O 24 O 30 O 36 O 21
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- Assume that annual inverse demand for a particular product is P=150-Q. The product is offered by a pair of Bertrand competitors, each with marginal costs of $75. The discount factor is 0.9. What is the current equilibrium price and total surplus? Now, assume though that if R&D is conducted at rate x, it incurs one-off costs of r(x)=10x^2 and reduces the marginal costs to (75-x). Suppose that one firm decides to conduct R&D at rate x=10. This research will be protected by a patent of T years. a) What profit(ignoring the one-off costs of R&D) does the innovating firm make each year during the period of patent protection? b) What is the new equilibrium price and total surplus once patent protection expires? c) Use your answer above to write the total surplus from the innovationWhile there is a degree of differentiation between major grocery chains like Albertsons and Kroger, theregular offering of sale prices by both firms for many of their products provides evidence that these firmsengage in price competition. For markets where Albertsons and Kroger are the dominant grocers, thissuggests that these two stores simultaneously announce one of two prices for a given product: a regularprice or a sale price. Suppose that when one firm announces the sale price and the other announces theregular price for a particular product, the firm announcing the sale price attracts 1000 extra customers toearn a profit of $5000, compared to the $3000 earned by the firm announcing the regular price. Whenboth firms announced the sale price, the two firms split the market equally (each getting an extra 500customers) to earn profits of $2000 each. When both firms announced the regular price, each companyattracts only its 1500 loyal customers and the firms each earned $4500 in…. (Requires calculus). In the model of a dominant firm, assume that the fringe supply curve is given by Q = -1 + 0.2P, where P is market price and Q is output. Demand is given by Q = 11 – P.What will price and output be if there is no dominant firm? Now assume that there is a dominant firm, whose marginal cost is constant at $6. Derive the residual demand curve that it faces and calculate its profit-maximizing output and price. highest bidder, but both the winning and losing bidders must pay her their bids. So if Jones bids $1 they pay a total of $3, but Jones gets the money, leaving him with a net gain of $98 and Smith with -$1. If both bid the same amount, the $100 is split evenly between them. Assume that each of them has only two $1 bills on hand, leaving three possible bids: $0, $1 or $2. Write out the payoff matrix for this game, and then find its Nash equilibrium.
- Consider a market for energy drinks consisting of only one firm. The firm has a linear cost function: C(q)=4q, where q represents quantity produced by the firm. The market inverse demand function is given byr P(Q)=24-2Q, where Q represents total industry output. Based on the given information answer the following. a. Now suppose a second firm enters the market. The second firm has an identical cost function. What will be the Cournot equilibrium output for each firm? b. Whay is the Stackelberg equilibrium output for each firm of firm 2 enters second? How much profit will each firm make in yhe Cournot game? How much in Stackelberg? c. Which type of market do consumers prefer: monopoly, Cournot duopoly or Stackelberg duopoly?consider a market with inverse demand P(Q) = 10 − Q and two firms with cost curves C1(q1) = 2q1 and C2(q2) = 2q2 (that is, they have the same marginal costs and no fixed costs). They compete by choosing quantities. Suppose that Firm 1 chooses quantity first and is able to credibly commit to this choice. Then firm 2 choose its quantity after observing firm 1’s quantity. In the SPNE of this game, what is the price faced by consumers?- p = 3- p = 4- p = 5- p = 6- p = 7The inverse market demand for fax paper is given by P=100-Q. There are two firms who produce fax paper. Firm 1 has a cost of production of C1= 15*Q1 and firm 2 has a cost of production of C2=20*Q2 a) Suppose firm 1 and firm 2 compute simultaneously in quantities. What are the Cournot quantities and prices?What are the profits of firm 1 and 2?b) Suppose firm 1 and firm 2 compete simultaneously in prices. What are the Bertrand quantities and prices?What are the profits of firm 1 and 2?
- 2. Consider a two-firms Cournot model with constant returns to scale. Assume also that the inverse demand function is P = 100 – 2Q, with marginal cost equal to 20for both firms, where Q = q1 + q2 . a) Derive the Nash equilibrium of this model and compare it with Monopoly and Perfect competition.Suppose two Bertrand competitors, F1 and F2, make identical products for a market with inverse demand P = 600 – 0.5Q. Both firms have the same costs Ci = 20qi, and each firm has sufficient capacity to supply the entire market. a. What prices will the firms choose? How much might each produce and what profit would they make? Is the result a Nash equilibrium? Explain. b. Suppose F1 improves its efficiency, reducing its cost to C1 = 16q1. What will happen in this market? Explain. c. Assume now that the firms have their original identical costs, but that F1 has only 100 units of capacity and F2 has only 200 units of capacity. What prices will the firms choose now? Explain why neither firm will want to decrease its price at the equilibrium you identify. Why would neither firm want to increase its price? Prove this for F1.Please no written by hand 1. Suppose the automobile manufacturing industry has two firms, General Motors and Ford. Assume that the market demand function is Q = 1,000 − p, and each firm’s marginal cost and average cost are $40. a. What is the marginal revenue for General Motors? Assume, ??? represent residual demand for General Motors and ?? represents residual demand for Ford. b. What is the best response function for General Motors and Ford? c. What is the Nash-Cournot equilibrium in this market? d. Graph the best response curves for both General Motors and Ford, placing the quantity produced by General Motors (???) in the x-axis. Label intercepts and Nash-Cournot equilibrium.
- Suppose you are the economic adviser ofa company producing three brands of mobile pnones;Nokia 10, Samsung X and iPhone 7. Suppose further that, your company currently sells 120units of iPhone Z at e800 per unit, 150 units of Samsung X at e800 per unit and 200 units ofNokia 10 at e100 per unit, but in a bid to maximize profit, the company's managing directorproposes an increase in price of Samsung X from e800 to e1000 per unit for which quantitydemanded is anticipated to fall from 150 to 100 units; iPhone Z from e800 to e 1200 per unitfor which quantity demanded is anticipated to fall from 120 to 100 units; and Nokia 10 from100 to 200 per unit for which quantity demanded is expected to fall from 200 to 100 unitsUsing the mid-polint formula. compute the price elasticity of demand for each brand.From your answer in i, what is the type and economic interpretatiom of each brand'sii.value of elasticity.Consider a market of 6 firms that compete through production. Demand is given as P = 220 – 2Q. Each firm has a marginal cost of $20. a. What will be the equilibrium firm quantities, market price, and firm profits? b. Suppose two firms merge in this market to become a leader. What will be the new equilibrium firm quantities, market price, and firm profits? Was it profitable for the firms to merge into a leader? Note that n = 5 after the merger. c. Suppose another two firms merge to form a second leader in the market. What will be the new equilibrium firm quantities, market price, and firm profits? Was it profitable for the followers to merge into a co-leader? Note that n = 4 and L = 2 after the merger:Consider a duopoly market with 2 firms. Aggregate demand in this market is given by Q = 500 – P, where P is the price on the market. Q is total market output, i.e., Q = QA + QB, where QA is the output by Firm A and QB is the output by Firm B. For both firms, marginal cost is given by MCi = 20, i=A,B. Assume the firms compete a la Cournot. 1. What are the equilibrium quantities? 2. What is the total quantity supplied on this market? 3. What is the equilibrium price in this market?