Cournot competition is one where firms simultaneously choose their optimal quantity produced instead of prices. Let the demand of the market be P(Q) = a - bQ. The manner in which we derive a solution is through examining what the best strategy each has given what they believe their competition would do.

i. What are the general assumptions of a cournot duopoly?

Ii. Set up the cournot model (Hint! Consider the case of a duopoly, outline number of firms, firms output, total/market output, market price and cost function).

iii. Set up the profit function for the market.

iv. What is Firm 1's profit maximization problem? (Hint, clearly state the residual market output).

v. What is Firm 2's profit maximization problem? (Hint, clearly state the residual market output).

vi. What is Firm 1's payoff?

vii Derive the reaction function for Firm 1.

viii: Derive the reaction function for Firm 2

ix. Let's assume we have a price-demand function P(Q) = 1 - Q and identical cost functions C1(q1) =₁²;C2(q2) = ₁ ²

• What is the total quantity available in the market?
• Define the profit function of Firm 1.
• Find Firm 1's Reaction Function
• Find Firm 2's Reaction Function
• Derive the Cournot-Nash equilibrium price and quantity.

xi. Let's assume we have a price-demand function P(Q) = 1 - Q and identical cost functions C1(q1) =₁²;C2(q2) = ₁². Use Stackelberg competition to solve Firm 2's profit maximization problem.