Question

Determine the best level of output for a perfectly competitive firm that sells its 

product at P = $4 and faces TC = 0.04Q3

– 0.9Q2 + 10Q + 5. Will the firm produce this level of 

output? Why?

Answer 1

Total Revenue(TR) =Price $\times$ Q

TR=4Q

Profit =Total Revenue(TR) - Total Costs (TC)

Profit =$4Q–(0.04Q^{3} –0.9Q^{2} +10Q +5)$

Profit =$–0.04Q^{3} +0.9Q^{2} –6Q–5$

$\frac{dP} {dQ}$ =$–0.12Q^{2} +1.8Q –6$

$\frac{dP} {dQ} =0$

$–0.12Q^{2} +1.8Q–6$

$–Q^{2} +15Q-50=0$

$Q(–Q+10)-5(10–Q) =0$

$(Q–5)(Q–10)=0$

$(Q=5) and (Q=10)$

For Q=5;Profit=

$–0.04(5)^{3} +0.9(5)^{2} –6(5)–5$

= –17.5

For Q=10;Profit =$–0.04(10)^{3} +0.9(10)^{2} –6(10)–5$

= –15

The firm would be operating at a loss hence the firm should not produce this level of output evidenced by the sell of the firm’s output at $4 per unit gives negative profits.