Q1) Cournot model with three firms. Assume that demand for a good is given by p= a-bQ (Q = total quantity demanded) and that there are 3 firms competing in quantity with a constant marginal cost c < a.
Write down the maximization problem of a representative firm in the market. Solve for the reaction function of this firm: how the optimal quantity produced depends on the quantity produced by the other two firms in the market.
To verify that you have found the correct reaction function, compute the optimal q1 if q2=40, q3=60, a=4, b=0.01, and c=2 (This is not necessarily in equilibrium)
What is q1?
Q2) In the three-firm case, what will be the equilibrium price and the total quantity produced in the market?
To verify that you have found the correct equilibrium, compute p and Q if a=4, b= 0.01, and c=2
What is p?
What is Q?