Question

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)?

Answer 1

267 output

Step-by-step 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