Question

Label the curves in the following graph. a. At each market price, \(P_{1}, P_{2}\), and \(P_{3}\), at what output level would the firm produce? b. What profit would be earned if the market price was \(P_{1}\) ? c. What are the shutdown and break-even prices?

Short answer

Answer: The output levels are \(Q_{1}\), \(Q_{2}\), and \(Q_{3}\) respectively, where the Marginal Cost (MC) curve intersects with each market price. Question: What is the profit earned when the market price is \(P_{1}\)? Answer: The profit earned at market price \(P_{1}\) can be calculated using the formula: \(\text{Profit} = (P_{1} \times Q_{1}) - (\text{ATC at } Q_{1} \times Q_{1})\). Question: What are the shutdown and break-even prices? Answer: The shutdown price is the market price at which the Average Variable Cost (AVC) curve is at its minimum. The break-even price is the market price at which the Average Total Cost (ATC) curve is at its minimum.

Step-by-step solution

Identify the relevant curves

We will examine the graph representing the costs and revenues of a firm operating in a competitive market. These curves include Marginal Cost (MC), Average Variable Cost (AVC), and Average Total Cost (ATC). As we don't have the actual graph, it is important to understand the concepts: - MC curve: Represents the additional cost incurred by producing one more unit. - AVC curve: Represents the cost per unit of output, excluding fixed costs. - ATC curve: Represents the cost per unit of output, including both fixed and variable costs. Also, we have three different market prices: \(P_{1}\), \(P_{2}\), and \(P_{3}\).

Output level at each market price

Now, let's determine the output level at each market price, assuming the firm makes optimal production decisions. In a competitive market, the firm will produce the quantity where the Marginal Cost (MC) is equal to the market price. So, at each market price, locate the point on the graph where the MC curve intersects with the market price and read the corresponding output level on the x-axis. Let's denote these output levels as \(Q_{1}\), \(Q_{2}\), and \(Q_{3}\) for \(P_{1}\), \(P_{2}\), and \(P_{3}\) respectively.

Profit earned when the market price is \(P_{1}\)

To find the profit earned when the market price is \(P_{1}\), we need to find the difference between Total Revenue (TR) and Total Cost (TC) for the optimum output level \(Q_{1}\). The Total Revenue at \(Q_{1}\) is equal to \(P_{1} \times Q_{1}\). To find the Total Cost, we need to find the Average Total Cost (ATC) at \(Q_{1}\) from the graph. The Total Cost would be equal to ATC multiplied by \(Q_{1}\). The profit can be calculated as follows: \(\text{Profit} = TR - TC = (P_{1} \times Q_{1}) - (\text{ATC at } Q_{1} \times Q_{1})\).

Shutdown and break-even prices

Shutdown price is the market price at which the firm will choose to stop production to minimize its losses. This occurs when the market price is equal to the minimum average variable cost (AVC) reached in the graph. Locate this point on the graph, and read the corresponding price where the AVC curve is at its minimum. Break-even price is the market price at which the firm covers all its costs (including fixed costs) and makes zero profit. This occurs when the market price is equal to the minimum average total cost (ATC) reached in the graph. Locate this point on the graph, and read the corresponding price where the ATC curve is at its minimum.

Key concepts

Marginal Cost (MC)

Understanding Marginal Cost (MC) is crucial for making effective production decisions in a competitive market. MC represents the additional cost incurred by producing one more unit of a good or service. As production increases, MC can initially decrease due to economies of scale, but it typically increases after a certain point because of the law of diminishing returns.

For a firm trying to determine the ideal level of output, the MC curve is vital. The rule of thumb is to continue producing until the MC of producing an additional unit is equal to the price that unit can be sold for, which means until Marginal Cost matches market price. This intersection indicates the most profitable production quantity because it's where the incremental revenues from selling one more unit equals the incremental cost of producing it.

To illustrate, with given market prices such as \(P_{1}\), \(P_{2}\), and \(P_{3}\), the corresponding output levels would be found where MC intersects with these prices. For example, if the MC curve crosses \(P_{1}\), the firm should produce at that output level to maximize its profits or minimize losses at that particular price.

Average Variable Cost (AVC)

Average Variable Cost (AVC) is another important concept in analyzing production decisions. It expresses the average amount of variable costs (costs that change with the level of output) per unit of output. The AVC does not include any of the fixed costs (costs that remain the same regardless of output), which makes it critical for determining short-term financial decisions.

When a firm considers whether it should continue operations or shut down temporarily, AVC plays a central role. If the market price falls below the AVC, the firm cannot even cover its variable costs, so it would minimize losses by halting production, which is known as the shutdown condition. For example, in the exercise provided, if \(P_{1}\) is below the minimum AVC, the firm would choose to shut down because it cannot cover its variable costs — let alone make a profit.

Knowing the shutdown point is essential for a firm to avoid incurring additional losses when market conditions are unfavorable. This could also provide valuable insights for pricing and output adjustments to stay competitive and solvent.

Average Total Cost (ATC)

Average Total Cost (ATC) is the sum of all production costs (fixed and variable) divided by the number of units produced. ATC gives a comprehensive view of the cost per unit, factoring in the entirety of production expenses.

In the context of the given exercise, determining the profit at market price \(P_{1}\) involves calculating the ATC at the output level that corresponds to \(P_{1}\). By multiplying this ATC by the number of units (\(Q_{1}\)), a firm can ascertain its total costs. Subtracting this figure from the total revenue (\(P_{1} \times Q_{1}\)) yields the profit. If \(P_{1}\) is higher than ATC at \(Q_{1}\), the firm makes a profit; if it equals ATC, the firm breaks even.

The break-even point is where the market price equals the minimum ATC. For a firm operating in a competitive market, knowing the break-even price is strategic for guiding them on how to price their products and also when making long-term decisions regarding investments in production capacity or technology, to reduce costs and improve profitability over time.