Suppose that identical duopoly firms have constant marginal costs of $16 per unit. Firm 1 faces a demand function of 9, = 100 - 2p, + 1p2. where q, is Firm 1's output, p, is Firm 1's price, and p, is Firm 2's price. Similarly, the demand Firm 2 faces is 92 = 100 - 2p2 + 1p,. Solve for the Bertrand equilibrium. In equilibrium, p, equals $ 44 and p2 equals $ 44. (Enter numeric responses using integers.) At these prices, q1 equals and q2 equals The total quantity supplied is.

Suppose that identical duopoly firms have constant marginal costs of $16 per unit. Firm 1 faces a demand function of 9, = 100 - 2p, + 1p2. where q, is Firm 1's output, p, is Firm 1's price, and p, is Firm 2's price. Similarly, the demand Firm 2 faces is 92 = 100 - 2p2 + 1p,. Solve for the Bertrand equilibrium. In equilibrium, p, equals $ 44 and p2 equals $ 44. (Enter numeric responses using integers.) At these prices, q1 equals and q2 equals The total quantity supplied is.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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.…
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Suppose that identical duopoly firms have constant marginal costs of $0 per unit. Firm 1 faces ademand function of q1 = 100 – 2p1 + p2, where q1 is Firm 1’s output, p1 is Firm 1’s price, and p2 isFirm 2’s price. Similarly, the demand Firm 2 faces is q2 = 100 – 2p2 + p1. Please solve for theBertrand equilibrium.
Firm A and Firm B are the only two firms in a market where price is determined by the inverse demand function: P = 147 - Q. Q is the sum of Firm A and Firm B's output, so Q = 9A + 9B Firm A's total cost function is given by TCA(9A) = 39A Firm B's total cost function is given by TCB(9B) = 89B If these firms Cournot compete (simultaneously setting quantities), what will market price be when both firms are maximizing profits in equilibrium? (Note: The answer may not be a whole number, so round to the nearest hundredth)
2. Four firms (A, B, C, and D) play a pricing game (i.e. Bertrand). Each firm (i) may choose any price Pi from 0 to ¥, with the goal of maximizing its own profit. Firms A and B have MC = 10, while firms C and D have MC = 20. The firms serve a market with the demand curve Q = 100 – P. All firms produce exactly the same product, so consumers purchase only from the firm with the lowest price. If multiple firms have the same low price, consumers divide their quantities evenly among the low-priced firms. Assume the firms choose price simultaneously. a. There are many equilibria in this simultaneous-move pricing game. Provide one equilibrium combination of prices, and argue that no firm has a unilateral incentive to deviate from these prices. Now assume firm A chooses price first. Firm B observes this choice and then chooses its own price second. Firm C chooses price third, and firm D chooses price last. b. Again, there are many equilibria in this sequential-move pricing game.…
Suppose that firms in a two-firm industry choose quantities every month, and each month the firms sell at the market-clearing price determined by the quantities they choose. Each firm has a constant marginal cost, and the market demand curve is linear of the form P = a - bQ, where Q is total industry quantity and P is the market price. Suppose that initially each firm has the same constant marginal cost. Further suppose that each month the firms attain the Cournot equilibrium in quantities. a) Suppose that it is observed that from one month to the next Firm 1’s quantity goes down, Firm 2’s quantity goes up, and the market price goes up. A change in the demand and/or cost conditions consistent with what we observe is: i) The market demand curve shifted leftward in a parallel fashion. ii) The market demand curve shifted rightward in a parallel fashion. iii) Firm 1’s marginal cost went up, while Firm 2’s marginal cost stayed the same. iv) Firm 2’s…
If the inverse demand for bean sprouts were given by P(Y) = 430 − 2Y and the total cost of producing Y units for any firm were TC(Y) = 10Y and if the industry consisted of two Cournot duopolists, then in equilibrium each firm's production would be
What is the homogeneous-good duopoly Cournot equilibrium if the market demand function is Q=4,000-1,000p, and Firm l's and Firm 2's variable cost functions are V (q1) = 0.22qlandV (q2) = 0.22q2 , respectively. Select one alternative: Both firms produce 1300 units of outpuit. Both firms produce 1280 units of output. Both firms produce 1240 units of output. Both firms produce 1260 units of output.
6. Two identical firms that have the cost function C(q) = 4qj, where j = {1,2} are competing in a homogenous good market. The two firms make simultaneous decisions on price, and they face industry demand Q(P) = 20-p. What is the Bertrand-Nash equilibrium profit of each firm? Hints for (b) and (c): Solve for each firm j's output (q;) and use the fact that Ij = p;qj - Cj(qj). b. Now, suppose the two firms are deciding whether to set a collusive market price of $6 (this means that they would both charge $6). Solve for their profits under this pricing scheme. a. C. If one of the firms decides to deviate from the collusive scheme and undercut its rival's price by $1, how much profit would it earn?
Answer 4 and 4
E1 Find Bertrand equilibrium and its outputs for the following asymmetric duopoly:q 1(p1, p2) = 16 - p1 + 0.5 p2, C1(q1) = 4q1;q 2(p1, p2) = 16 + 0.5 p1 - p2, C2(q2) = 6q2.(Note that the average and marginal costs are: AC1=MC1 = c1 = 4, AC2=MC2 = c2 = 6)