(I) Duopoly with homogeneous product: quantity and price competitionConsider a market with two firms (firms 1 and 2). The (inverse) demand curve is:p = 30 - 2q where q= q1 + q2Suppose Firm 1 has a marginal cost (c1) of 6 and Firm 2 has a marginal cost (c2) of 12.Assume neither firm has a fixed cost.(1) Suppose firms choose quantities sequentially: Firm 1 chooses q and after that decision is knownFirm 2 chooses q2. Calculate the SPNE.(2) Suppose firms choose prices sequentially: Firm 2 chooses its price first and after that decision isknown Firm 1 chooses its price. What is the SPNE? Justify.

A duopoly model with homogeneous products is a model where firms choose output or prices,…

Answered: I) Duopoly with homogeneous product:…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Consider the differentiated goods Bertrand price competition model where firms A and B produce similar goods and sell them at pA and pB. The demand for each firm’s product is given byqA =60−2pA +pB andqB =60–2pB +pA ,and there are NO costs of producing either good (all costs are 0). (a)Calculate the (Bertrand) equilibrium prices and the net profits of each firm (b) Now suppose that -instead of competing to maximize their own individual profits- the firms decide to “collude” and set prices pA and pB to maximize their joint profits (sum of their profits). What would be each firm’s optimal price and net profits? Compare these prices and profits with what you found in (a) (greater/smaller/the same?).
onsider a homogenous good industry with four firms. Total demand is given by D(p)=200-p.The variable (=marginal) cost of each of the firms is c1=10, c2=20, c3=30 and c4=35. Firms compete in prices. Suppose firms 1 and 2 merge into one entity and produce with a marginal cost of 15. Which of the following statements is correct? After the merger, total welfare increases by $500. After the merger, total welfare decreases by $500. After the merger, total welfare increases by $1000. After the merger, total welfare decreases by $1000. None of the above.
Two firms sell substitutable products; the market price is: P = 90-Q, where Q Q₁ + Q2 is the total market quantity, which consists of Q1₁ (the quantity produced by Firm 1) and Q2 (the quantity produced by Firm 2). The firms choose their quantities simultaneously. Firm 1's costs are C₁ 6Q₁ + Q². Firm 2's costs are C₂ = Q². = O Which is the payoff function for Firm 2? O π₂ = 90Q₂ - 2 Which is the best response function for Firm 1? O π₂ = 90Q₂ - Q²². πT2 π₂ = 45 - Q² Q₁ Q₂₁ 2 O π₂ = 45 - 1²/20₁². Q₁ Q₁ 3 = 16. ²/Q²-Q₁2. = 32- 2- 1/1/202₂. 3 Q₁ = 45. Q1 = 40 + ²/Q₂₁ 2.2. = 10- -
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a)Consider a homogeneous goods industry where two firms operate and the linear demand is given by p(y1 + y2 ) = a - b(y1 + y2 ), where p is the market price, and y1 (y2) is the output produced by firm 1 (2). There are no costs for firm 1 or firm 2. Derive the best responses (reaction curve) for firm 1 and firm 2. Explain the term best response (reaction curve). Illustrate the best responses in a diagram. b) For the case in (a) determine the Cournot equilibrium (Nash equilibrium in quantities) when firm 1 and firm 2 compete simultaneously in quantities. How large are firm 1’s and firm 2’s profits? What is the industry output? c) Suppose the inverse demand curve in a market is D(p) =a-bp, where D(p) is the quantity demanded and p is the market price. Firm 1 is the leader and has a cost function c1(y1)=cy1 while firm 2 is the follower with a cost function c2(y2 )=. Firm 1 sets its price to maximise its profit. Firm 1 correctly forecasts that the follower takes the price leader’s…
Suppose Giocattolo of Italy and American Toy Company of the United States are the only two firms producing toys for sale in the U.S. market. Each firm realizes constant long-term costs so that the average total cost (ATC) equals the marginal cost (MC) at each level of output. Thus, MCo = ATCO is the long-term market supply schedule for toys. Suppose Giocattolo and American Toy Company operate as competitors, and the cost schedules of each company are MCo = ATCO = $10. On the following graph, use the grey point (star symbol) to identify the competitive market equilibrium. Then, use the green triangle (triangle symbols) to identify consumer surplus in this case. Note: Select and drag the point from the palette to the graph. Dashed drop lines will automatically extend to both axes. Then select and drag the shaded region from the palette to the graph. To resize the shaded region, select one of the points and move to the desired position. ? PRICE (Dollars per toy) 20 18 16 14 10 00 6 4 2 0…
There are two identical firms in an industry, 1 and 2, each with cost function , i = 1,2. The industry demand curve is P = 100 − 5X where industry output, X, is the sum of the two firms’ outputs (X1 + X2). (a) If each firm makes its output decisions on the assumption that the other will not react to its choices (the Cournot assumption), what is the equilibrium output for each firm? What is the equilibrium price? (b) Suppose that each firm takes it in turn to choose its level of output, on the assumption that the other’s output level is fixed. Would the process of adjustment be stable? (c) Suppose that firm 1 introduces a cost-saving innovation, so that its cost curve becomes C1 = 8X1. Firm 2’s cost curve and the industry demand curve are unchanged. What happens to the equilibrium quantity produced by each firm and to market price?
Economics: Industrial Economics Question: In a market that operates under quantity competition there are 2 firms (Cournot duopoly). The inverse demand function is P = A - B Q. The cost structure of firm 1 is given by C1(q1) = F1 + c1 q1 and that of firm 2 is given by C2(q2) = F2 + c2 q2. Prior to competing, the two firms can engage in research at levels (x1, x2) respectively in order to lower their marginal costs. As a result, marginal costs are c1 = c - x1 - β2x2 and c2= C - x2 - β1 X1. where β1 = β2 > ½. Finally, the research costs are F1 = a1 (x1)^2 /2 and F2 = a2 (x2)^2 /2, where a1 > 0 and a2> 0. 1. The Nash Equilibrium research levels are Choices: A. Higher than the cooperative research levels for both firms. B. Higher than cooperative research levels for firm 1 but lower for... C. Lower than the cooperative research levels for both firms. D. Higher than cooperative research levels for firm 2 but lower for... 2. An increase in the value of a2 would Choices: A.…
Consider an industry comprised of three identical firms faced with a linear cost function given by: C(qi) = cqi; for i = 1; 2; 3. Let inverse market demand be given by: P(Q) = a - bQ; where Q = q1 + q2 + q3.a. Compute the Cournot equilibrium; that is, find prices, quantities, and profits.b. Suppose that firms 1 and 2 merge, converting the market into a duopoly consisting of the “superfirm” and firm 3. Compute the new Cournot equilibrium. Once again find prices, quantities, and profits.c. Suppose that all three firms merge. Compute quantities, prices, and profits for the cartel solution.d. Suppose that firm 1 and 2 represent two members of OPEC – Saudi Arabia and Venezuela, say – while firm 3 is a non-OPEC oil exporting country – Russia, say. Describe the dynamics of OPEC. (Hint: re-interpret the solution to part 2, as 1 firm deviating from the fully cartelized solution. Is it convenient to have a partial cartel?)
Consider an industry with 2 firms engaging in quantity competition and facing the market demand function as Q = 200 – 4P. Suppose each firm bears the same cost production as C(q) = 100 + 0.25q? when producing q units. a. Derive Firm 1's best response function, q1(q2), against Firm 2's output level choice, q2. b. Find the equilibrium output level of Firm 1 at the N.E. equilibrium. c. Find the deadweight loss caused by the duopoly. d. Find again the equilibrium output level of Firm 1 if it acts as the leader while Firm 2 as the follower.
Consider a market where two firms produce the same product, and compete by choosing the price to charge consumers. There are no capacity constraints and no fixed costs. Consumers purchase from the firm that charges the lowest price, Pmin Aggregate demand is given by Q(Pmin) = 600 – 30pmin. Both firms have marginal costs of c = 15. What is the aggregate quantity produced in this market? And what price do consumers pay? (a) p₁ = = 15, p2 = 20, Q = 150 (b) P1 = P2 = 15, Q = 150 (c) P₁ = P₂ = 20, Q = 0 (d) p₁ = 10, P2 = 15, Q = 300 (e) None of the above options is correct.

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