Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Question
Chapter 15, Problem 15.3P
b)
To determine
Graphical representation of Nash equilibrium and isoprofit.
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Students have asked these similar questions
1. The market (inverse) demand function for a homogeneous good is P(Q) = 10 - Q. There are
two firms: firm 1 has a constant marginal cost of 2 for producing each unit of the good, and
firm 2 has a constant marginal cost of 1. The two firms compete by setting their quantities of
production, and the price of the good is determined by the market demand function given the
total quantity.
a. Calculate the Nash equilibrium in this game and the corresponding market price
when firms simultaneously choose quantities.
b. Now suppose firml moves earlier than firm 2 and firm 2 observes firm 1 quantity
choice before choosing its quantity find optimal choices of firm 1 and firm 2.
Let ci be the constant marginal and average cost for firm i (so that firms may have different marginal costs). Suppose demand is given by P=1-Q.
Calculate the Nash equilibrium quantities assuming there are two firms in a Cournot market. Also compute market output, market price, firm profits, industry prof- its, consumer surplus, and total welfare.
Represent the Nash equilibrium on a best-response function diagram. Show how a reduction in firm 1’s cost would change the equilibrium. Draw a representative isoprofit for firm 1.
Three firms compete in the style of Cournot. The inverse demand is P(Q) = a - Q. Scenario 1: All three firms have the same constant marginal cost MC = c. Scenario 2:
Firm 1 has MC = 0.5c, Firm 2 has MC = c, and Firm 3 has MC = 1.5c. Assume that a > 3c. Which of the following is correct? (Price means the price in Nash equilibrium.)
O Price in scenario 1> Price in scenario 2
O Price in scenario 2> Price in scenario 1
O Price in scenario 1 = Price in scenario 2
O Any of the first three options is possible depending on the value of a
O Any of the first three options is possible depending on the value of a and c.
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- Assume firms' marginal and average costs are constant and equal to c and that inverse market demand is given by P = a - bQ where a, b > 0. Suppose now the market is served by k firms that choose quantities for their identical products simultaneously. Calculate: i. ii. iii. iv. The Nash equilibrium quantities for the Cournot firms as functions of k. 2 Market output and price as a function of k Firm profit as a function of k Using your answers in i, ii, iii and iv, describe what happen to firm output, market output, market price and firm profit as the number of firms increases.arrow_forwardThe market demand function is Each firm has a marginal cost of m = $0.28. Firm 1, the leader, acts before Firm 2, the follower. Solve for the Stackelberg-Nash equilibrium quantities, prices, and profits. The Stackelberg-Nash equilibrium quantities are The Stackelberg-Nash equilibrium price is Profits for the firms are and 92 p = $ π2 $ = Q=7,000 1,000p. 91 and units units. (Enter your responses as whole numbers.) (Enter your response rounded to two decimal places.) π₁ = $ (Enter your responses rounded to two decimal places.)arrow_forward2. An industry contains two firms that have identical cost functions C(q)=10+2q. The inverse demand function for the market is P=50-2Q where Q is the total industry output. Assuming the firms compete in quantities: Find the firms' best response functions. b. Solve for the Cournot Nash Equilibrium of the game. What is the total industry output in equilibrium? What is the equilibrium price? с. i. If both firms could collude, what would the industry output and price be? Suppose they decide that each firm produces half of the industry output found in part (i). Is this agreement self-enforcing? Explain. ii. a.arrow_forward
- 10Two firms produce differentiated products. The demand for each firm’s product is as follows: Demand for Firm 1: q1 = 20 – 2p1 + p2 Demand for Firm 2: q2 = 20 – 2p2 + p1 Both firms have the same cost function: c(q) = 5q. Firms compete by simultaneously and independently choosing their prices and then supplying enough to meet the demand they receive. Please compute the Nash equilibrium prices for these firms.arrow_forward1. Best responses in a Cournot Oligopoly Firm A and Firm B sell identical goods Total market demand for the good is: The inverse demand function is therefore 1 P(QM) = 780 -Q=780 -0.02222QM 45 QM is total market production (i.e., combined production of firm's A and B. That is: Q(P) = 35, 100- 45P 2M = A +QB As a result, the inverse demand curve for each firm is: P(QA, QB) = 780- -1/32₁-752 45 Unlike the example in class, the two firms have different costs. = 4000A TCA (QA) TCB (QB) = 260QB = 780 -0.022220A -0.02222QB a. Using the demand function and the cost functions above, what is firm A's profit function. b. Using the profit function above and assuming that firm B produces Qg, calculate what firm A's best response is to firm B’s decision to produce QB- Note: Firm A's best response should be a function of Barrow_forwardThe inverse market demand curve for salmon is given by P(Y) = 100 – 2Y, and the total cost function for any firm in the industry is given by TC(y) = 4y. a. Suppose that two Cournot firms operated in the market. What would be the reaction function for Firm 1 and the reaction function of Firm 2? (Notes: The marginal cost is not zero). If the firms were operating at the Cournot equilibrium point, what would the industry output and price be? b. For the Cournot case, draw the two reaction curves and indicate the equilibrium point on the grapharrow_forward
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