Question

Assume a competitive firm faces a market price of

​$60​, a cost curve​ of: C​ = 0.003q³​+ 50q ​+ 1000​,

The​ firm's profit-maximizing output level is ___ units ​(enter your response rounded to two decimal places​), and the per unit profit at this output level is ​$____ ​(enter your response rounded to two decimal places—include the minus sign if necessary).

This firm will▼ _______ (shut down or produce) in the​ short-run. The firm will realize▼________(economic profit or economic loss)​ , and ▼ ______ (must or may or may not) have a business profit.

In the​ long-run, if circumstances do not​ change, this firm will ▼_______ (shut down or produce).

Answer 1

Profit maximizing level where P = MC ( because this is a competitive firm)

MC = d(C)/dQ

MC = d(  0.003q³​+ 50q ​+ 1000) / dQ

MC = 0.009q² +50

Put P = MC

60 = 0.009q² + 50

10 = 0.009q²

10/0.009 = q²

q = 33.33

Per unit profit = (P-ATC)

ATC = C/Q = 0.003q² + 50 + 1000/q

Put q = 33.33

ATC = 0.003(33.33)² + 50 + 1000/33.33

ATC = 83.35

Per unit profit = P - ATC = 60- 83.35 = -23.35

The​ firm's profit-maximizing output level is 33.33 units ​(enter your response rounded to two decimal places​), and the per unit profit at this output level is ​- $23.35

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The firm will shut down in the short run if AVC is more than price

AVC = VC/Q [ VC = 0.003q³ + 50q]

AVC = 0.003q² + 50

AVC = 0.003(33.33)² + 50 = 53.33

As AVC is less than $60 so the firm will produce in the short run.

This firm will produce in the​ short-run. The firm will realize economic loss​ , and may or may not have a business profit.

In the​ long-run, if circumstances do not​ change, this firm will shut down.