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plants, A and B. The marginal cost functions of each are 1. A firm produces output in two MCA 25 +0.020A and MCB 15+ 0.02Qs T Please show all workings. Thank you.
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Answer #1

Answer

Given

MCa=25+0.02Qa

MCb=15+0.02Qb

demand function

Q=6350-25P

Q=Qa+Qb

P=254-0.04Q

P=254-0.04*(Qa+Qb)

Since firms want to maximize its total profit

TR=P*Q={254-0.04(Qq+Qb)}*(Qa+Qb)

TR=254*(Qa+Qb)-0.04*(Qa+Qb)^2

MRa=dTR/dQa=254-0.08*(Qa+Qb)

MRb=dTR/dQb=254-0.08*(Qa+Qb)

MRa=MCa

254-0.08*(Qa+Qb)=25+0.02Qa

0.1Qa+0.08Qb=229 Eq 1

MRb=MCb

254-0.08*(Qa+Qb)=15+0.02Qb

0.08Qa+0.1Qb=239 Eq2

From equation 1 and 2 we find that

Qa=1050

Qb=1550

Total Output Q = Qa+Qb=1050+1550=2600

Price P= 254-0.04Q=254-0.04*2600=$150

Qa=1050

Qb=1550

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