An industry consists of two firms with identical costs C(q) = 5q + q2/2. The market demand is Q = 125 - p. Explain your answers and provides examples.
- Solve for the collusive output per firm (q*).
- Solve for the output if one firm cheats on the collusive agreement optimally (q**).
- Solve for the Cournot output per firm (q***).
- Set up the normal form representation problem of this game where each firm could make three choices, q*, q**, q***. You will need to calculate profits under the nine possible outcomes.
- Find the unique Nash Equilibrium.
- What is the equilibrium price, quantity per firm, and profit per firm, if instead we use the Stackelberg Leader Model where firm one is the leader?