Chapter 10: Problem 6
Consider a profit-maximizing firm in a competitive industry. For each of the following situations, indicate whether the firm should shut down production or produce where \(\mathrm{MR}=\) MC. LO10.5 a. \(P<\) minimum AVC. b. \(P>\) minimum ATC. c. Minimum AVC \(
Short Answer
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a. Shut down; b. Produce where MR = MC; c. Produce where MR = MC.
Step by step solution
01
Understanding Key Concepts
In a competitive industry, a firm should decide its production based on comparisons between price (P), average variable cost (AVC), and average total cost (ATC). The decision to shut down or produce is influenced by these costs. If price (P) is less than the minimum AVC, the firm should shut down in the short run because it cannot cover even its variable costs.
02
Case Analysis for Decision Making
Let's analyze each given situation:- **Case a:** When \( P < \text{minimum AVC} \). Here, the firm is unable to cover its variable costs, leading to a situation where the firm should shut down.- **Case b:** When \( P > \text{minimum ATC} \). At this price, the firm not only covers its total costs, which include both fixed and variable costs, but it also makes a profit. Therefore, the firm should continue production where \( \text{MR} = \text{MC} \).- **Case c:** When \( \text{minimum AVC} < P < \text{minimum ATC} \). Under these circumstances, the firm can cover its variable costs but not all of its fixed costs. The firm should produce where \( \text{MR} = \text{MC} \).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Shutdown Rule
The shutdown rule is a vital concept in economics, particularly for firms operating in competitive markets. It helps firms decide whether they should continue production or temporarily cease operations when facing unfavorable market conditions. This decision primarily hinges on the relationship between the market price and the firm's average variable costs (AVC).
If the market price (\(P\)) falls below the minimum average variable cost (\(AVC\)), the firm cannot cover its variable costs. In such cases, the shutdown rule suggests that the firm should halt production in the short run to minimize losses. This is because continuing to produce would result in greater losses than shutting down temporarily, as fixed costs would still need to be paid, but not met with associated revenues.
Once market conditions improve and prices rise above the minimum AVC, the firm can resume production with the aim of eventually reaching or surpassing the breakeven point.
If the market price (\(P\)) falls below the minimum average variable cost (\(AVC\)), the firm cannot cover its variable costs. In such cases, the shutdown rule suggests that the firm should halt production in the short run to minimize losses. This is because continuing to produce would result in greater losses than shutting down temporarily, as fixed costs would still need to be paid, but not met with associated revenues.
Once market conditions improve and prices rise above the minimum AVC, the firm can resume production with the aim of eventually reaching or surpassing the breakeven point.
Average Variable Cost (AVC)
The average variable cost (AVC) is crucial for determining short-term production decisions. It represents the variable cost per unit of output, calculated by dividing the total variable costs (TVC) by the quantity of output produced (\(Q\)):
\[\text{AVC} = \frac{\text{TVC}}{Q}\]
Variable costs include expenses that fluctuate with the level of production, such as labor and raw materials. Unlike fixed costs, which remain constant regardless of production levels, variable costs vary according to output changes.
In the context of the shutdown rule, the AVC plays a critical role. If the price is below the minimum AVC, the firm may not be able to even cover these costs, thus stopping production is the best strategy to minimize losses. Conversely, if the price per unit exceeds AVC, the firm can continue to cover variable costs, and should consider only shutting down if prices drop profoundly.
\[\text{AVC} = \frac{\text{TVC}}{Q}\]
Variable costs include expenses that fluctuate with the level of production, such as labor and raw materials. Unlike fixed costs, which remain constant regardless of production levels, variable costs vary according to output changes.
In the context of the shutdown rule, the AVC plays a critical role. If the price is below the minimum AVC, the firm may not be able to even cover these costs, thus stopping production is the best strategy to minimize losses. Conversely, if the price per unit exceeds AVC, the firm can continue to cover variable costs, and should consider only shutting down if prices drop profoundly.
Average Total Cost (ATC)
Average total cost (ATC) gives a comprehensive overview of the costs associated with producing a good. It is calculated by summing the total fixed costs (TFC) and total variable costs (TVC) and dividing by the quantity produced (\(Q\)):
\[\text{ATC} = \frac{\text{TFC} + \text{TVC}}{Q}\]
ATC is a key metric for determining long-term profitability. It encompasses both variable and fixed costs, offering insights into the overall cost structure of a firm. When the market price exceeds ATC, the firm is not only covering all its costs but is also generating profit.
In contrast, if the price falls between AVC and ATC, the firm covers its variable costs but not the entirety of its fixed costs. This situation means the firm is operating under a loss, but it should continue to produce where marginal revenue equals marginal costs (\(MR = MC\)), as long as potential future profits justify the current losses.
\[\text{ATC} = \frac{\text{TFC} + \text{TVC}}{Q}\]
ATC is a key metric for determining long-term profitability. It encompasses both variable and fixed costs, offering insights into the overall cost structure of a firm. When the market price exceeds ATC, the firm is not only covering all its costs but is also generating profit.
In contrast, if the price falls between AVC and ATC, the firm covers its variable costs but not the entirety of its fixed costs. This situation means the firm is operating under a loss, but it should continue to produce where marginal revenue equals marginal costs (\(MR = MC\)), as long as potential future profits justify the current losses.
Marginal Revenue (MR)
Marginal revenue (\(MR\)) is the additional revenue earned from selling one more unit of output. For firms in perfectly competitive markets, the marginal revenue is equal to the market price because firms are price takers:
Each additional unit sold contributes the same amount to total revenue as the market price of the good. To maximize profits, firms compare marginal revenue with marginal cost (\(MC\)). They should continue producing as long as MR is equal to MC.
When MR equals MC, the revenue from selling an additional unit exactly offsets the cost of producing it. Producing beyond this point would mean the cost of additional units exceeds the revenue they generate, leading to a decline in total profits. Thus, equality between MR and MC guides firms to the optimal level of production.
Each additional unit sold contributes the same amount to total revenue as the market price of the good. To maximize profits, firms compare marginal revenue with marginal cost (\(MC\)). They should continue producing as long as MR is equal to MC.
When MR equals MC, the revenue from selling an additional unit exactly offsets the cost of producing it. Producing beyond this point would mean the cost of additional units exceeds the revenue they generate, leading to a decline in total profits. Thus, equality between MR and MC guides firms to the optimal level of production.
Marginal Cost (MC)
Marginal cost (\(MC\)) is an essential concept in determining the optimal level of production for profit maximization. It indicates the cost of producing one extra unit of output. Calculated by the change in total cost (\(TC\)) resulting from a one-unit increase in output, MC is represented as:
\[\text{MC} = \frac{\Delta \text{TC}}{\Delta Q}\]
In perfectly competitive markets, firms aim to produce at a level where marginal cost equals marginal revenue (\(MR = MC\)). This is the equilibrium condition for maximizing profits. If MC is less than MR, the firm should increase production as it would increase profits.
Conversely, if MC exceeds MR, the firm should reduce output to avoid losses. These adjustments help firms align production with demand conditions and market prices to optimize performance efficiently.
\[\text{MC} = \frac{\Delta \text{TC}}{\Delta Q}\]
In perfectly competitive markets, firms aim to produce at a level where marginal cost equals marginal revenue (\(MR = MC\)). This is the equilibrium condition for maximizing profits. If MC is less than MR, the firm should increase production as it would increase profits.
Conversely, if MC exceeds MR, the firm should reduce output to avoid losses. These adjustments help firms align production with demand conditions and market prices to optimize performance efficiently.
