Competing for Mangoes [20 points] Two firms produce and sell premium Alphonso mangoes. The two firms compete simultaneou

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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.
(a) [5 pts] What are the best response functions for Firm 1 and
Firm 2?
(b) [5 pts] What quantity of mangoes does Firm 1 produce? What
quantity does firm 2 produce? What are the profits to Firm 1?
Profits to Firm 2?
(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 1’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 1’s production of Q1=15
by producing Q2=15? If not, what quantity will Firm 2 choose?
Explain.