Question

A perfectly competitive firm that makes car batteries has a fixed cost of \(\$ 10,000\) per month. The market price at which it can sell its output is \(\$ 100\) per battery. The firm's minimum AVC is \(\$ 105\) per battery. The firm is currently producing 500 batteries a month (the output level at which MR = MC). This firm is making a and should production LO 10.5 a. profit; increase b. profit; shut down c. loss; increase d. loss; shut down

Short answer

The firm is making a loss and should shut down (option d).

Step-by-step solution

Understand the Concepts

In a perfectly competitive market, a firm will produce where its marginal revenue (MR) equals its marginal cost (MC). The decision to continue operating in the short run depends on the price, minimum average variable cost (AVC), fixed costs, and resulting profit or loss.

Determine Revenue and Costs

The firm produces 500 batteries, and the price per battery is \(100. Therefore, total revenue is calculated as: \( \text{Total Revenue} = 500 \times 100 = \\)50,000 \). The fixed cost is \\(10,000, and the minimum AVC is \\)105 per battery.

Calculate Variable and Total Costs

The variable cost at minimum AVC is \( \text{Variable Cost} = 500 \times 105 = \\(52,500 \). The total cost is the sum of fixed and variable costs: \( \text{Total Cost} = 10,000 + 52,500 = \\)62,500 \).

Calculate Profit or Loss

The profit or loss is calculated by subtracting the total cost from the total revenue: \( \text{Profit/Loss} = 50,000 - 62,500 = -\$12,500 \). The firm makes a loss.

Analyze the Shutdown Decision

Since the market price \( \\(100 \) is less than the minimum AVC \( \\)105 \), the firm cannot cover its variable costs. Therefore, it should shut down production to minimize its losses.

Key concepts

Marginal Revenue

Marginal Revenue (MR) is a critical concept in understanding how firms decide their level of production. In a perfectly competitive market, MR is equal to the market price, since each additional unit sold adds exactly the sales price to total revenue. This implies that the firm is a price taker and cannot influence the market price. Understanding MR helps determine the quantity of output a firm will supply. Because MR equals the price in perfect competition, firms will continue producing as long as the price is greater than or equal to the marginal cost (MC). In this context, the car battery firm faces a price of \(100\) per battery. Therefore, its MR is also \(100\) for every additional battery sold. The firm aims to produce where MR equals MC, maximizing their profit potential in the process.

Average Variable Cost

Average Variable Cost (AVC) refers to the cost per unit that varies with the level of output. This includes costs like materials and labor that increase as more output is produced. For a firm to continue operating in the short-term, the market price must at least cover the AVC. If the market price falls below AVC, the firm will incur losses on each unit produced, making it unsustainable to produce even in the short-term.In the exercise, we've been given that the minimum AVC is \(105\) per battery, which is higher than the selling price of \(100\) per battery. This gap between price and AVC indicates that the firm cannot cover its variable costs, which triggers the need for reevaluating the shutdown decision.

Shutdown Decision

The shutdown decision is crucial for firms operating in competitive markets. When a firm's revenue falls short of covering its variable costs, continuing production would only increase losses. Therefore, it is often advisable to halt production temporarily.In this specific example, the firm is unable to cover its minimum AVC of \(105\) with the current selling price of \(100\). This imbalance means the firm faces an unavoidable loss of \(12,500\) if it continues to operate. Therefore, in the short run, shutting down until conditions improve—such as an increase in market price—is a smarter financial decision. Shutting down would mean only incurring fixed costs, as opposed to both fixed and variable costs.

Fixed Costs

Fixed costs are expenses that don't change with the level of output produced. In this case, the firm incurs a fixed cost of \(10,000\) per month. These costs need to be paid regardless of whether the firm produces any output. Examples include expenses like rent, salaries for permanent staff, or machinery depreciation.In the short run, fixed costs remain constant. They are critical because while they don't impact the decision to produce in the immediate short term—since they must be paid regardless—they influence long-term strategic decisions. For the car battery firm, deciding to shut down operations temporarily does not save these fixed costs, but stops additional losses from stacking up by eliminating variable costs.