Let market demand in the trinkets industry be given by Q(P) = 55−P. There are only two firms in the industry, and the total cost function for each firm be given by C(qi) = 10 + 25q, where i = 1, 2.
1. Write down the market’s (inverse) demand function, that is, price as a function of each firm’s output, q1 and q2.
2. Write down the profit maximization problem of each firm. If both firms are Cournot competitors, what are they maximizing over?
3. Solve each firm’s maximization problem, write down each firm’s first order condition, and derive find the best-response function of each firm.
4. Suppose firm 2 produces nothing, that is, q2 = 0. What is firm 1’s optimal output level? How does this quantity with the monopoly output level?
5. Find each firm’s Cournot-Nash equilibrium output, profit, and the resulting equilibrium price in the market.
6. What is consumer surplus in equilibrium? How does it compare with consumer surplus under perfect competition?
7. Calculate the total surplus in this Cournot-Nash equilibrium. Is the equilibrium outcome Pareto efficient? If not, calculate the Dead-Weight-Loss (DWL) in this market.
8. Suppose that, observing profits made by incumbent firms, 6 new firms, identical to the first two, enter the market as Cournot competitors. How do equilibrium prices, quantities, and profits change? (Note: now there are 8 identical firms competing in the market for trinkets).
9. Are consumers better off? In other words, does their consumer surplus rise, fall, or stay the same? Explain your answer.
10. A ninth and identical firm is thinking about entering the market too. Explain why it will, upon further reflection, decide not to do so.