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 \(=M C) .\) This firm is making a _____ and should _____ production. 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

Understanding the Given Information

The fixed cost for the firm is \(\\(10,000\) per month, and the variable cost per battery is higher than the price, sitting at \(\\)105\) against \(\$100\) per battery sold. The firm is producing 500 batteries where marginal revenue \(=\) marginal cost.

Calculate Monthly Revenue

To find the total revenue, multiply the number of batteries produced and sold by the market price: \(500 \times 100 = \$50,000\).

Calculate Total Variable Cost

Calculate the total variable cost by multiplying the number of batteries produced by the average variable cost: \(500 \times 105 = \$52,500\).

Calculate Total Cost

To find the total cost, sum the fixed cost and total variable cost: \(10,000 + 52,500 = \$62,500\).

Determine Profit or Loss

Subtract the total cost from the total revenue to find the profit or loss: \(50,000 - 62,500 = -\$12,500\), indicating a loss.

Decide on Production

Since the firm is making a loss and the price is less than the average variable cost (\(100 < 105\)), the firm should shut down to minimize losses to the fixed cost amount of \$10,000, avoiding unnecessary variable costs.

Key concepts

Fixed Costs

In economics, fixed costs are expenses that remain consistent regardless of the production level or output quantity. For our car battery firm, this means that they must pay $10,000 every month in fixed costs, even if they produce no batteries at all.

Fixed costs include expenses like rent, salaries of full-time employees, and insurance. These costs do not change with the amount of production and are often considered sunk costs once paid.

In the context of a perfectly competitive market, understanding fixed costs helps businesses determine their break-even point. They can calculate how much they need to produce or sell to cover these costs and start making a profit.

Variable Costs

Variable costs are those that change with the level of output produced. Unlike fixed costs, which remain steady, variable costs increase as production grows and decrease when production falls.

For our firm, the cost of producing each car battery is $105, which is their average variable cost. This means that as they produce more batteries, their total variable costs increase proportionally. To calculate total variable costs, the firm multiplies the quantity of batteries produced by the average variable cost (AVC). In this case, for 500 batteries, it amounts to $52,500.

Understanding variable costs is crucial for determining short-term financial strategies and pricing. A firm in a perfectly competitive market must ensure that the market price covers its variable costs to justify remaining in production.

Marginal Revenue

Marginal Revenue (MR) refers to the additional revenue that a firm earns from selling one more unit of a good or service. In perfect competition, where the firm is a price taker, MR equals the market price.

For our battery firm, the market price is $100 per battery, meaning that the marginal revenue from each battery sold is also $100. This is calculated by multiplying the price per unit by the number of additional units sold.

In a perfectly competitive environment, firms maximize profit where MR equals Marginal Cost (MC). Hence, at this optimal output level, firms should continue production unless market conditions like price or costs demand reevaluation.

Average Variable Cost

Average Variable Cost (AVC) is calculated by dividing total variable costs by the quantity of output produced. It helps firms understand how much of their costs are attributable to each unit produced.

For our car battery firm, the AVC is $105 per battery, which means each battery costs this amount in variable expenses alone.

Comparing AVC to the market price is essential for decision-making. If the market price falls below the AVC, as in our example where the price is $100 but the AVC is $105, the firm experiences a loss on each unit sold. In such cases, the firm should halt production to prevent further losses. This decision minimizes losses to a level equal to the fixed costs, as continuing production would add unnecessary variable costs.