1. Consider the market for tomatoes, which are considered to be homogenous products. There are only two
producers in the market. The cost functions of producer 1 and producer 2 are given by TC1 (q1) = q1
and TC2 (q2) = 4q2; respectively. Let the demand be p = 10 – Q: Find the profit level of each producer
in a Cournot-Nash equilibrium.
2. Consider a Cournot game with homogenous products. There are N firms in the market, and N is fixed. The
demand function is given by p (Q) = 100 – Q and the cost function is given by TC (q) = 2q: First,
find a competitive equilibrium outcome (the market price, quantity of each firm, and profit). Then, calculate the
price, quantity, and profit in the Cournot-Nash equilibrium. What is the relationship between the competitive
equilibrium outcome and the outcome in the Cournot-Nash equilibrium when N is large?
3. Consider the market for potatoes, which are considered to be homogeneous products. There are two identical
producers in the market. Demand is given by Q(p) = 15 – p. Their marginal cost is 3. What is the Bertrand-Nash
equilibrium?

Sample Solution