Answer
the market equilibrium is at Qd=Qs
620-5P=170+5P
10P=450
P=45
Q=620-5*45
=395
the market quantity is 395
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the firm produces at MC=P
MC=change in total cost =first differentiation of total cost =dTC/dQ=4+4Q
4+4Q=45
4Q=41
Q=10.25 ......... the quantity maximize profit is 10.25, and P=45
TR=P*Q=10.25*45=461.25
TC=5+4*10.25+2*10.25^2
=256.125
Profit=TR-TC
=461.25-256.125
=205.125
profit is $205.125
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