Suppose that the manager of a firm operating in a perfectly competitive market has estimated the average variable cost function to be: AVC = 4.0 - 0.0024Q + 0.000006Q2 Fixed costs are $500. If the forecasted price of the firm's output is $4.00, how much output will the firm produce in the short run (round to the nearest unit) ?

267 output

Explanation:

The computation of the output produced in the short run is shown below:

As it is given that

AVC i. e average variable cost function = 4.0 - 0.0024Q + 0.000006Q^2

And,

FC i. e fixed cost = $500.

Plus we know that

Total variable cost i. e TVC = AVC * Q i. e Quantity

So,

AVC * Q = TVC

= 4Q - 0.0024Q^2 + 0.000006Q^3

And,

The total cost = Total variable cost + Fixed cost

So,

TC = TVC + FC

= 4Q-.0024Q^2 +.000006Q^3 + $500.

And, the MC i. e marginal cost is

= Total cost : Quantity

MC = 4 - 0.0048Q + 0.000018Q^2

MC = 4

So,

Price = MC i. e 4

4 -.0048Q +.000018Q^2 = 4

So after solving this Q is 266.67 i. e 267 output