Final answer:
The firm should continue to produce in the short run because the price of the good exceeds the average variable cost, allowing the firm to cover all variable costs and contribute to fixed costs, thus minimizing its losses.
Step-by-step explanation:
The question relates to whether a perfectly competitive firm should continue production in the short run when it is producing 3,000 units at a total cost of $36,000, with fixed costs of $20,000, and selling each unit at $10. To determine this, we compare the price to the firm's average variable cost (AVC) and average total cost (ATC). In this case, the firm's variable costs (VC) are total cost minus fixed costs, which is $36,000 - $20,000 = $16,000. The AVC is then VC divided by quantity, which is $16,000 / 3,000 = $5.33 per unit.
Since the price ($10) is greater than AVC ($5.33), the firm covers all its variable costs and contributes to fixed costs. As long as the price exceeds AVC, the firm should continue producing in the short run because it is minimizing its loss. If the firm were to shut down, it would lose its entire fixed cost of $20,000, whereas by continuing to produce, the loss is smaller as some of the fixed costs are covered by the revenue from production.