Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Chapter 15, Problem 15.3P
b)
To determine
Graphical representation of Nash equilibrium and isoprofit.
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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.
Please solve it complete with details and explanation
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.
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- I NEED HELP WITH A AND Barrow_forwardQUESTION 10 Suppose there are two firms that produce an identical product. The demand curve for the product is given by P = 62 - Q where Q is the total quantity produced by the two firms. Both firms choose their individual quantities qı20 and q22 0 simultaneously. Each firm has a marginal cost of 37. What is the market price when both firms produce the quantities in the unique Nash equilibrium? Give your answer as a number to two decimal places.arrow_forward**Practice** Consider a market with three firms. Each firm has a different cost function. We assume C1(q1) = 7q1, C2(q2) = q2 + 1, and C3(q3) = 3q3.arrow_forward
- I need help with a and barrow_forward2. A homogenous good industry consists of two firms (firm 1 and firm 2). Their cost functions are cq and cq2, respectively, where c<2. The market demand function is p=10-Q, where Q=q₁+q₂. (a) Assume that the two firms play the Bertrand price game. Find the firms' choices in the Bertrand-Nash equilibrium. (b) Assume that the two firms play the Cournot quantity game. Find the firms' choices in the Cournot-Nash equilibrium. (c) Assume the two firms play the Stackelberg game with firm 1 as the leader. Find the firms' equilibrium choices in the Stackelberg equilibrium.arrow_forward5arrow_forward
- The 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_forwardSee image for questions partsarrow_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_forwardImage uploaded answer is not allowed please dear expertarrow_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_forward
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