If the inverse market demand function facing a duopoly is  what are the Nash-Cournot equilibrium quantities if the marginal cost of Firm 1 is m and that of Firm 2 is  where x > 0? Which firm produces more and which has the higher profit?

Consider a Stackelberg duopoly:There are two firms in an industry with demand Q = 1 − Pd.The “leader” chooses a quantity qL to produce. The “follower” observes qL and chooses a quantity qF.Suppose now that the cost function is Ci(qi) = qi2  for i = L, F. (a) Find the subgame perfect equilibrium. (b) Compare the equilibrium you found with the Nash equilibrium if the game was simultaneous (i.e., Cournot competition). Is the Nash equilibrium of the Cournot game also a Nash equilibrium of the sequential game? Why or why not?

If firm 1 and firm 2 are the oligopolistic firms in bottled spring water production in Nomansland. The market demand is given by ? = 5000 −20?, Qd is the number of kilolitres demanded per month while P is the price of kilolitres of bottled water. The marginal cost of a kilolitre of bottled water is R10.How do I Find the Cournot equilibrium quantities and price? and how do I Find the Cournot profits and the monopolist profits?

Consider the following normal form representation of the standard competition between firm A and firm B. Each firm can choose either standard A or standard B. Their payoffs are given as follows: Firm B A В A Firm A В 1 1 3 1 (1) (10 points) What's Nash equilibrium (NE) in this game? If there are more than one, find them all. But there is no NE, state that there is no NE. (2) (10 points) If you find a NE (or multiple Nash equilibria), is it (or are they) Pareto efficient?

2. 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.

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1.6. Consider the Cournot duopoly model where inverse demand is P(Q) = a - Q but firms have asymmetric marginal costs: c₁ for firm 1 and c2 for firm 2. What is the Nash equilibrium if 0 a+c₁?

1. 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 B

a and b

Q. 3