Question

Consider the following for in a perfectly competitive market. The current market price is $18 per unit. The firm’s total cost function is C = 45 +3Q + 2Q² , where Q is the number of units produced and sold.

1. Determine this firm’s profit-maximizing output level in the short-run.
2. At this output level, what is the profit (loss) generated by this firm?
3. If the firm is making a loss, should it continue producing in the short-run?
4. If the firm’s fixed cost increases from 45 to 65, determine this firm’s new profit-maximizing output level in the short-run. What general conclusions can be derived from this result?

E. Draw the appropriate diagram to demonstrate your results in parts (A) – (D). use the numbers you calculated in the above parts.

Answer 1

Price of th market is P = $18
Cost is given as, C = 45 + 3Q + 2Q²
A) In short run, a competitive market will be in equilibrium where P = MC.
MC = dC/dQ = 3 + 4Q
In equilibrium, 3 + 4Q = 18
or, 4Q = 15
or, Q = 15/4 = 3.75

Profit maximizing level of output = 3.75 units.

B) Profit = Revenue - Cost
Revenue = P * Q = 18 * 3.75 = $67.5
Cost = 45 + (3*3.75) + (2*3.75*3.75)
= 45 + 11.25 + 28.125
= $84.375

Profit = $67.5 - $84.375 = -$16.875 (loss)

C) As the firm is making losses in the short run, it will not continue the production and the firm will shut down.

D) Now given the fixed cost increases from 45 to 65.
Cost function can be rewritten as, C = 65 + 3Q + 2Q²
MC = 3 + 4Q
Hence profit maximising output will be same at Q = 3.75
Since fixed costs are independent of output, thus any change in fixed cost will not depict any change in equilibrium.
But under this case, loss will increase.

Profit = Revenue - Cost
Revenue = P * Q = 18 * 3.75 = $67.5
Cost = 65 + (3*3.75) + (2*3.75*3.75)
= 65 + 11.25 + 28.125
= $204.375
Profit = $67.5 - $204.375 = -$136.875 (loss)
Still the firm faces loss and at a greater margin.Hence it will close down.

E)