3. Consider a two-stage game of R&D competition. The players are firm i and j, each produces with different marginal cost c; and cj, where i, j = 1, 2 and i ‡ j. The rules are the firms first invest, denoted by I, and I;, in cost-reducing innovation, they then engage in Cournot competition in the output market by deciding qk, k = i, j and i # j simultaneously. The payoffs to the firms are their profits. (a) write out the objective function for firm i and j at the R&D stage and that at the output stage. (b) Assuming that p'(Q) < 0 and p'(Q)+p"(Q)qi <0 for all 0≤ qk ≤ >0 and Q, show that 1 p"Q+3p' (c) dvi dli < 0. əqi p"qj+2pi aci pi(p"Q+3p') = <0 2 əqi acj == p"qi+p' p'(p"Q+3p') aQ aci = show, in the R&D stage, that the first-order conditions are = [p' (Q(C₁, c)) ³9/(c) — 1] qi(c. c) = Jaj(cuci) aci — 1] qi(C₁, Cj) = qp¹ (1i,1, čį, ēj) = 0. And Ij=constant (d)--) In a closed economy, show that the total differentiation of the national welfare function is dW = −p'(q¡dqi+qjdqj) — q₁dc₁ — qjdc¡ – dl¡ – dlj. - -

3. Consider a two-stage game of R&D competition. The players are firm i and j, each produces with different marginal cost c; and cj, where i, j = 1, 2 and i ‡ j. The rules are the firms first invest, denoted by I, and I;, in cost-reducing innovation, they then engage in Cournot competition in the output market by deciding qk, k = i, j and i # j simultaneously. The payoffs to the firms are their profits. (a) write out the objective function for firm i and j at the R&D stage and that at the output stage. (b) Assuming that p'(Q) < 0 and p'(Q)+p"(Q)qi <0 for all 0≤ qk ≤ >0 and Q, show that 1 p"Q+3p' (c) dvi dli < 0. əqi p"qj+2pi aci pi(p"Q+3p') = <0 2 əqi acj == p"qi+p' p'(p"Q+3p') aQ aci = show, in the R&D stage, that the first-order conditions are = [p' (Q(C₁, c)) ³9/(c) — 1] qi(c. c) = Jaj(cuci) aci — 1] qi(C₁, Cj) = qp¹ (1i,1, čį, ēj) = 0. And Ij=constant (d)--) In a closed economy, show that the total differentiation of the national welfare function is dW = −p'(q¡dqi+qjdqj) — q₁dc₁ — qjdc¡ – dl¡ – dlj. - -

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

QUESTION 13 Consider a market where two firms (1 and 2) produce differentiated goods and compete in prices. The demand for firm 1 is given by D₁(P₁, P2) = 140 - 2p1 + P2 and demand for firm 2's product is D2 (P1, P2) 140 - 2p2 + P1 Both firms have a constant marginal cost of 20. What is the Nash equilibrium price of firm 1? (Only give a full number; if necessary, round to the lower integer; no dollar sign.)
PART C D
Q2
a. Consider the game faced by the British and Dutch managers when both are given contracts that compensate them with (1)/(2) of 1% of revenue. The strategic form game is shown. Find the Nash equilibria. b. Now consider the game between the British and Dutch shareholders as to what kind of contracts to give their managers. Assume that they simultaneously choose between a contract that gives the manager 1% of profit and one that gives him (1)/(2) of 1% of revenue. Assume, as before, that the shareholders’ payoff is profit (and we ignore the trivial amount that they pay to their managers). After a pair of contracts is selected, the two contracts are revealed to both managers, and the managers then choose between supply levels of low, moderate, and high. Find all SPNE.
2. Consider an infinitely repeated game in which, in each period, two firms with zero costs choose quantities and prices are given by: p1 = 1 - q1 - q2/2, p2 = 1 - q2 - q1/2. Firms have a common discount factor of 8 = 1/2. a) Explain what a trigger strategy is and determine whether the firms can attain the joint profit maximising outcome in a subgame perfect equilibrium using trigger strategies. b) Explain what a stick and carrot strategy is and discuss whether it is possible to attain the joint-profit maximising outcome in a subgame perfect equilibrium using stick and carrot strategies.
1. which compete in quantities (Cournot -Nash equilibrium = C) 2. which compete in quantities with the first firm (the Leader) choosing the output first (Stackelberg competition = S). 3. which collude and choose quantities in order to maximize the joint profits (behave like two plants of a multiplant monopoly = M).
8)Consider a market in which 5 companies operate, whose marginal and average costs are equal to c. The demand function is given by P(Q)= 1-Q, where P is the price and Q indicates the total quantity. Assume that companies compete with Cournot in choosing production levels. Assume that the game is repeated an infinite number of periods, that companies adopt trigger strategies and that the punishment is represented by Nash Reversion. 1)What is the value of the discount factor that allows companies to sustain tacit collusion in a balanced situation? 2) Assume now that companies are able to discover the defection of a rival company with K periods of delay. What do you think the effect on the sustainability of collusion can be? 3) Do you think that in this market collusion would be more easily sustainable if the companies compete with Bertrand? 4) If in a price-competitive market (Bertrand) N symmetrical companies operate, what would be the critical value of the discount factor that would…
Please help with #4- A and B
There are two firms in the market (duopoly). These two firms are competingsimultaneously. The first firm chooses its output level (x) by predicting the second firm’soutput (y). Let c denote the total cost function c(x) = x and c(y) = y. Also, let’s assumethat the inverse demand function is p(Y) = 7 - Y where Y = x + y. (1) Obtain the reactionfunction of the first firm. (2) Find the equilibrium (output and profit of each firm) whentwo firms simultaneously compete
Consider oligopoly models with two firms who have identical marginal costs. The size of the deadweight loss differs depending on whether firms compete according to Bertrand or Cournot.(a) True. (b) False.
Suppose that Firm 1 and Firm 2 are Stackelberg competitors in the market for popsicles. Firm 1 is the leader and Firm 2 is the follower. They have the same cost functions such that MC = 4. Market demand for popsicles is given by QD = 38 – 0.5P. Use this information to answer questions #1 and #2. 1. How many popsicles will Firm 1 produce in the SPE of this game? a. 91 6 b. q1 = 9 12 91 d. 91 с. 18 e. q1 = 36 %3D 2. If these firms were Cournot competitors, then compared to the outcome in #1 (Hint: No calculations necessary.) a. Firm 1 would earn more profit, and Firm 2 would earn less profit. b. Firm 1 would earn less profit, and firm 2 would earn more profit. c. Both firms would earn less profit. d. Both firms would earn more profit. The firms' profits would be the same, but industry-wide profit would be lower.