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If the firm shuts down, it must incur its fixed costs (FC) in the short run. In this case, the firm's fixed cost is \( \$ 1,600,000 \) per day. In other words, shuts down, the firm would suffer losses of \( \$ 1,600,000 \) per day until its fixed costs end (such as the expiration of a building lease). This firm's shutdown price-that is, the price below which it is optimal for the firm to shut down-is

Ask by Guerrero Ray. in the United States
Mar 16,2025

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The shutdown price for the firm is the lowest price at which it can cover its variable costs. If the market price is below this point, the firm should shut down to minimize losses, incurring only its fixed costs of \$1,600,000 per day.

Solución

Assume that the firm's total cost consists of fixed costs (FC) and variable costs (VC). In the short run, fixed costs must be paid regardless of production, so if the firm shuts down it loses its fixed costs (here, \(\$1{,}600{,}000\) per day). However, if the firm operates, it will incur both fixed and variable costs. The shutdown rule tells us that a firm should produce only if the market price \(P\) is at least as high as the average variable cost (AVC). In other words, the firm should produce if \[ P \geq \text{AVC} \] and shut down (produce zero output) if \[ P < \text{AVC}. \] Thus, the “shutdown price” is defined as the minimum point of the average variable cost curve: \[ P_{\text{shutdown}} = \min (\text{AVC}). \] If the market price falls below this level, the firm cannot cover its variable costs over and above the sunk fixed costs, and it is optimal to cease production temporarily, incurring only its fixed costs.

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Interestingly, the shutdown price can be determined by looking at variable costs and the contribution margin. If the price falls below the average variable cost (AVC), the firm would not be able to cover its variable costs; hence, it is better to shut down. This means the shutdown price is directly linked to the firm’s ability to cover these variable expenses without further losses. In practice, many firms will closely monitor their pricing strategies around this shutdown point. For instance, businesses in the hospitality sector may reduce operating hours during off-peak seasons to avoid losses. Recognizing when to shift strategies can be critical in managing costs effectively while still positioning themselves to capitalize when demand picks up again!

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