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Homework answers / question archive / Question 1 a) Are the cournot Nash equilibrium profits the largest that duopolists can earn in an oligopolistic market? [4 marks] b) Explain intuitively what the duopolists must do to earn monopoly profits in an oligopolistic market? [6 marks] c) If the duopolists are playing a one-time game in (b), is the monopoly equilibrium output stable? Justify your answer? [4 marks] d) If the game in (b) is repeated, does commitment enhance profits in a strategic environment? [6 marks] QUESTION 2 The inverse market demand in a homogeneous product Cournot duopoly is given by ? = 140− 5(?1 +?2)
Question 1 a) Are the cournot Nash equilibrium profits the largest that duopolists can earn in an oligopolistic market? [4 marks]
b) Explain intuitively what the duopolists must do to earn monopoly profits in an oligopolistic market? [6 marks]
c) If the duopolists are playing a one-time game in (b), is the monopoly equilibrium output stable? Justify your answer? [4 marks]
d) If the game in (b) is repeated, does commitment enhance profits in a strategic environment? [6 marks]
QUESTION 2
The inverse market demand in a homogeneous product Cournot duopoly is given by ? = 140− 5(?1 +?2). and marginal costs are ??1(?1)= 10?1 and ??2(?2)=20
A. Determine the reaction function for each firm. [4+4 marks]
B. Use a graph to depict the Cournot Nash equilibrium. [3marks]
C. Calculate each firm's equilibrium output. [5marks]
D. Calculate the equilibrium market price. [4marks]
E. Calculate the profit each firm earns in equilibrium. [5marks]
[Total: 25 Marks]
QUESTION 3
A. Consider a situation where Bubuche Ltd is the only producer in the industry and the market demand curve for the producer is given by; ?=260−0.5?. This firm has a total cost that can be expressed as; ?? = 100? + ? 2+ 50.
i. Given the above information, what is this monopolist’s profit maximizing price and output? [5marks]
ii. Given the above information, calculate this single price monopolist’s profit.
iii. At the profit maximizing quantity, what is this monopolist’s average total cost of production (ATC)? [5marks]
iv. What is the monopolist’s efficient price and output? [5marks]
v. Calculate the profit at efficient level, given the answer(s) in (IV) above.
[5marks]
Answer to Question 1
a) No, the cournot Nash equilibrium profits are not the highest that the duopolies can earn in a oligopolistic market.
b) The duopolies can collude to earn monopoly profits. If they collude, they act as one single monopoly, and thus can have control over either price or quantity, which leads to higher profits. For example, they can agree to produce a smaller quantity which leads to higher prices.
c) If it is a one time game, the monopoly equilibrium output is not stable. Usually, the duopolies reduce the quantity supplied in order to raise prices and earn higher profit per unit. There is incentive for each duopolies to break the contract and produce more than the contract amount. The one producing higher will earn more profits.
d) If the game in part b) is repeated, then commitment does enhance profits. The duopolies can employ a punishment strategy in order to enhance cooperation. In this strategy, if one party deviates, the other will respond to the deviation such that it harms the other duopolist. Once, cooperation is attained, both duopolies enjoy the maximum payoff available in the game.
