Question

A competitive firm has a market price of $55, a cost curve of: C=0.004q^3 + 30q + 750.

What is the firm's profit maximizing output level (to the nearest tenth) and the profit (to the nearest penny) at this output level?

In this case, the firms will (enter/exit). This will cause the market supply to (shift left/shift right). This will continue until the price is equal to the minimum average cost of ( ) (round your answer to the nearest penny). At this price level the profit will be (zero/the level of variable cost/the level of fixed cost/cannot be determined).

Answer 1

MC = dC/dq = 0.012q² + 30

(I) Setting P = MC,

0.012q² + 30 = 55

0.012q² = 25

q² = 2,083.33

q = 45.6

(II) Profit = TR - TC

TR = P x q = 55 x 45.6 = 2,508

TC = 0.004 x (45.6)³ + 30 x 45.6 + 750 = 379.28 + 1,368 + 750 = 2,497.28

Profit = 2,508 - 2,497.28 = 10.72

(III) Since profit is positive, the firms will enter. This will cause the market supply to shift right. This will continue until the price is equal to the minimum average cost of 54.77**. At this price level the profit will be zero (since in long run equilibrium, each firm earns zero profit).

**Average cost (AC) = C/q = 0.004q² + 30 + (750 / q)

AC is minimum when AC = MC.

0.004q² + 30 + (750 / q) = 0.012q² + 30

0.008q² = 750 / q

0.008q³ = 750

q³ = 93,750

q = 45.43

Minimum AC = MC = 0.012 x 45.43 x 45.43 + 30 = 24.77 + 30 = 54.77