Question

This section explained how a firm computes profit. Specifically, it computes total cost and total revenue and then finds the difference. Suppose a firm wants to compute its profit per unit. In other words, instead of computing how much profit it earns in total, it wants to know how much profit it earns per unit. How could the firm go about computing profit per unit? (Hint: The answer deals with average total cost.)

Short answer

A firm can compute profit per unit by subtracting the average total cost from revenue per unit (price). This is equivalent to dividing the total profit by the number of units produced.

Step-by-step solution

Compute Total Profit

The total profit of a firm is calculated by subtracting the total cost from total revenue. If $TR$ is total revenue and $TC$ is total cost, then total profit $TP$ can be represented as:\n$$TP=TR-TC$$

Define Profit per Unit

Profit per unit is essentially the average profit, which is calculated by dividing the total profit by the number of units produced. If $Q$ is the quantity of units produced, then profit per unit $PPU$ can be calculated as: \n$$PPU=TP/Q$$

Use Revenue and Cost per Unit

The profit per unit can also be obtained by subtracting the average total cost ($ATC$) from the Revenue per unit, also known as price ($P$). The average total cost is the total cost divided by the quantity of units produced. Therefore, profit per unit can also be calculated as: \n$$PPU=P-ATC$$

Key concepts

Understanding Total Cost

When it comes to understanding a business's financial health, knowing the total cost is essential. Essentially, the total cost includes all expenses incurred to produce goods or services. This can encompass raw materials, labor, overhead, and any other costs that contribute to the production process.

For a firm calculating profit per unit, scrutinizing the total cost provides a comprehensive view of the expense side of their operation. It’s calculated by summing direct and indirect costs. Direct costs are tied directly to production, like raw materials and labor, while indirect costs are not directly linked to production, but are necessary for operations, as in utilities or rent. The total cost formula is expressed as:
$$TC=TotalFixedCosts+TotalVariableCosts$$

Total Revenue and Its Role in Profitability

In the context of a firm's profit calculations, total revenue is the complete income received from selling goods or services. It is fundamental in determining whether a firm is profitable. Total revenue is simply the product of the price at which goods or services are sold and the number of units sold. The formula for total revenue is given by:
$$TR=P\times Q$$
where $P$ is the price per unit, and $Q$ is the quantity of units sold. Understanding total revenue helps a firm to analyze how changes in price or quantity affect their income, which is crucial when considering strategies for increasing profit per unit.

Deciphering Average Total Cost

Average total cost (ATC) represents the cost to produce one unit of output, which is a key factor when calculating profit per unit. It’s critical for businesses to know the ATC so they can set prices that cover costs and generate a profit.

The ATC is determined by dividing the total cost by the quantity of units produced, represented by the equation:
$$ATC=\frac{TC}{Q}$$
When the ATC is known, a firm can assess the profitability of each unit by comparing it to the selling price. If the price exceeds the ATC, the firm makes a profit on each unit; if it’s lower, the firm incurs a loss on each unit. Keeping close tabs on the ATC can lead to strategic decisions regarding pricing, production levels, and cost management with the aim of optimizing profit per unit.