Two firms compete by choosing price. Their demand functions are Q, = 20 - P, + P2 and Q2 = 20 + P1 - P2. where P, and P2 are the prices charged by each firm, respectively, and Q, and Q2 are the resulting demands. Note that the demand for each good depends only on he difference in prices; if the two firms colluded and set the same price, they could make that price as high as they wanted, and earn infinite profits. Marginal costs are zero. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.) Each firm will charge a price of $. (Enter a numeric response rounded to two decimal places.) Each firm will produceunits of output. n turn, each firm will earn profit of $ Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will each sell, and what will be profits?

Two firms compete by choosing price. Their demand functions are Q, = 20 - P, + P2 and Q2 = 20 + P1 - P2. where P, and P2 are the prices charged by each firm, respectively, and Q, and Q2 are the resulting demands. Note that the demand for each good depends only on he difference in prices; if the two firms colluded and set the same price, they could make that price as high as they wanted, and earn infinite profits. Marginal costs are zero. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.) Each firm will charge a price of $. (Enter a numeric response rounded to two decimal places.) Each firm will produceunits of output. n turn, each firm will earn profit of $ Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will each sell, and what will be profits?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Two firms compete in selling homogeneous goods. They choose their output levels q1 and q2 simultaneously and face demand curve P=80-6Q, where Q=q1+q2. The total cost function of firm 1 is C1=8q1 and the total cost function of firm 2 is C2=32q2+2/3. a) Find and draw the reaction curves of the two firms. b) Compute equilibrium quantities, price and profits. Suppose now that firm 2, thanks to a technological innovation, becomes more efficient. The new total cost function of firm 2 is C2= 8q2 c) Compute the new equilibrium quantities, price and profits.
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Consider a market for crude oil production. There are two firms in the market. The marginal cost of firm 1 is 20, while that of firm 2 is 20. The marginal cost is assumed to be constant. The inverse demand for crude oil is P(Q)=200-Q, where Q is the total production in the market. These two firms are engaging in Cournot competition. Find the production quantity of firm 1 in Nash equilibrium. If necessary, round off two decimal places and answer up to one decimal place.
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QUESTION 14 Consider the following simultaneous move game between two firms. Each firm can charge either a low or a high price. The numbers represent the profit of each firm at each period. Firm 1 High Price Low Price r≥ 40% r≥ 20% Firm 2 High Price Low Price 30,30 0,55 r≥ 50% full cooperation cannot be achieved in this game. Or≤ 20% 55,0 This game is repeated infinity times, and at each period both players must choose their actions simultaneously. In this case, cooperation at the high price will be possible if the interest rate, r, is r≤ 50% r≤ 40% The players are deciding whether or not to cooperate - specifically, whether or not to follow this cooperation strategy: "Each player will play 'high price' as long as no one has played 'low price' before. If someone has played 'low price' before, then each player will play 'low price' forever." 25, 25
Part 3,4, and 5
Consider two firms, referred to as firms 1 and 2, who compete in a market by choosing quantities produced and face the following inverse demand: P(Q) 10-20 Each firm has a marginal cost of production of $4.00. Suppose these firms collude by agreeing to produce quantities to maximize their joint profits. Firm 1 sticks to the agreement, but firm 2 does not. If firm 2 can secretly change its produced quantity, how much would it produce?
Suppose the airline industry consisted of only two firms: American and Texas Air Corp. Let the two firms have identical cost functions, C(q) = 40g. Assume that the demand curve for the industry is given by P= 160 - Q and that each firm expects the other to behave as a Cournot competitor. Calculate the Cournot-Nash equilibrium for each firm, assuming that each chooses the output level that maximizes its profits when taking its rival's output as given. What are the profits of each firm? (Round all quantities and dollar amounts to two decimal places.) When competing, each firm will produce 40 units of output. In turn, each firm will earn profit of $ 1600. What would be the equilibrium quantity if Texas Air had constant marginal and average costs of $10 and American had constant marginal and average costs of $40? If Texas Air had constant marginal and average costs of $10 and American had constant marginal and average costs of $40, American would produce units and Texas Air Corp. would…
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Consider a duopoly with homogenous goods where Firm 1 has the following production function: Q1 = F1(L,K) = L1/2 K1/2, where Q and K are measured in units and L in hours. Firm 2 uses labour and capital as well but has a different production function, given by Q2 = F2(L,K) = L1/3 K2/3. You may assume that the market for labour and capital is perfectly competitive and the current wage rate is £40 and the rental rate on capital is £10. Both firms sell their products on the same market with inverse demand function P = 52 – (Q1 + Q2), where P is measured in pound sterling. Which production function(s) exhibit(s) decreasing returns to scale? Suppose Firm 1 wishes to produce 6 units. What is the cost minimising input mix for Firm 1? Suppose Firm 2 wishes to produce 4 units. What is the cost minimising input mix for Firm 2? Assume both firms now have the option to produce either 4 units or 6 units. We will consider the situation where both firms simultaneously, but independently,…