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2. Competing for Mangoes [20 points] Two firms produce and sell premium Alphonso mangoes. The two firms compete simultaneously in quantities. Both Firm 1 and Firm 2 produce with the same cost function: TC1(Q1)=20+30Q1 and TC2(Q2)=20+30Q2. Demand for the mangoes follows P=60-(1/2)Q, where Q=Q1+Q2.
(c) [5 pts] Suppose Firm 1 proposes to Firm 2 that they collude and both produce 15 (Q1=Q2=15). Compare Firm 1 and Firm 2's profits under this arrangement: would both firms be better off than in part (b)? Explain.
(d) [5 pts] Is Firm l's proposal to Firm 2 a Nash equilibrium if Firm 1 and Firm 2 only compete against each other in the market once? That is, will Firm 2 respond to Firm l's production of Qı=15 by producing Q2=15? If not, what quantity will Firm 2 choose? Explain.
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