Suppose that two identical firms produce tooth brushes and that they are the only firms in the market. Their costs are the same, with MC=$20. Q _S is the output of Firm Shiny and Q _B the output of Firm Bright. Price is determined by the following demand curve:

P = 140 – Q

where Q = Q _S + Q _B . If both firms independently and strategically choose their outputs, they each maximise profits at 40 units, but if a single firm served this market, market price would be $80 to maximize profit.

Based on the above, and assuming there are 2 firms, calculate the profit of each firm at equilibrium. 

Suppose both firms cooperate to set output. Calculate each firm’s profit.

If Shiny abides by the agreement, but Bright cheats and increases production by 15 units, what are each firm’s profits? What will the Nash equilibrium be in light of your answer to a, b and c? 

How much money would Bright be willing to spend to force Shiny out of this market? Carefully explain your reasoning, with numbers.