Question

If p= 12 - 2Q and C= 24 + 2Q + 0.5Q², what is the profit per unit?

Answer 1

the firm produces at MR=MC

MC is the change in total cost and found by differentiation

MC=dTC/dQ=2+Q .......... by first differentiation of cost function

TR=P*Q=12Q-2Q^2

MR is the change in total revenue and a change in function found by differentiation

MR=dTR/dQ=12-4Q

equating both

2+Q=12-4Q

5Q=10

Q=2

P=12-2*2=8

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Average total cost =total cost /Q=C/Q=(24+2Q+0.5Q^2)/Q=24/Q+2+0.5Q

Q=2

ATC=24/2+2+0.5*2

ATC=15
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Profit per unit =P-ATC
=8-15
=-$7
the per unit profit is -$7