Question

If the short-run marginal and average variable cost curves for a competitive firm are given by SMC = 2 + 3Q and AVC = 2 + 2Q, how many units of output will it produce at a market price of 23?

Answer 1

A competitive firm will produce 7 units of output at a market price of $23 as the price is greater than the average variable cost, indicating that the firm should continue producing in the short-run.

Step-by-step explanation:

The question asks how many units of output a competitive firm will produce at a market price of $23 when given the short-run marginal cost (SMC) and average variable cost (AVC) equations. In a perfectly competitive market, a firm will produce where the price or marginal revenue (MR) is equal to the marginal cost (MC). Using the provided SMC equation (SMC = 2 + 3Q), we set the price equal to the SMC to find the quantity (Q):

23 = 2 + 3Q

Q = (23 - 2) / 3

Q = 21 / 3

Q = 7

So, the firm will produce 7 units. However, to confirm that the firm should indeed produce this quantity, we check if 23 (price) is greater than the AVC at 7 units. Using the AVC equation (AVC = 2 + 2Q), we find:

AVC at 7 units = 2 + 2(7) = 2 + 14 = 16

Since the market price of $23 is greater than the AVC of $16, the firm will produce in the short-run even if it makes economic losses (if P < ATC).