Question

A firm has a fixed cost of \(\$ 100,000\), and variable \(\cos\) is \(\$ 90,000\) at an output of one. How much is margina cost at an output of one? (LO2) a) \(\$ 10,000\) b) \(\$ 90,000\) c) \(\$ 100,000\) d) \(\$ 190,000\) e) There is insufficient information to answer the question.

Short answer

The correct answer is (b) $90,000.

Step-by-step solution

Understand the Concepts

In this problem, we have fixed costs (FC) and variable costs (VC). Fixed costs remain constant regardless of the level of production, while variable costs change with production levels. Marginal cost (MC) is calculated as the change in total cost (TC) when increasing the output level by one unit. The formula for the total cost is: TC = FC + VC.

Calculate Total Cost at Output of One

Using the formula for total cost (TC), we can calculate the total cost for the firm when the output is one: \(TC_1 = FC + VC_1\) \(TC_1 = \$100,000 + \$90,000\) \(TC_1 = \$190,000\)

Calculate Marginal Cost at Output of One

Now we will calculate the marginal cost using the definition of marginal cost. Since the firm is already producing one unit, the variable cost for the first unit is the additional cost incurred to produce that one unit. In this case, the marginal cost is equal to the variable cost for producing one unit: MC at an output of one: \(MC_1 = VC_1\)

Choose the Correct Answer

Now, we compare the calculated MC with the options given in the exercise: a) $10,000 b) $90,000 c) $100,000 d) $190,000 e) There is insufficient information to answer the question. The calculated MC_1 = \(90,000, which matches option (b). So, the correct answer is (b) \)90,000.

Key concepts

Fixed Costs

Fixed costs are one of the two main types of business expenses, with the former being expenses that do not change with the level of production. These are the costs that a company must pay regardless of how much or how little it produces. Fixed costs can include rent or mortgage payments on business property, salaries for permanent staff, and insurance premiums.

For example, our exercise mentions a fixed cost of \(\$100,000\), which needs to be paid by the firm irrespective of how many units are produced, even if it produces only a single unit. Understanding the implication of fixed costs is crucial for pricing strategies and for determining break-even points in a business.

Variable Costs

In contrast to fixed costs, variable costs vary with production volume. This means that as a company produces more units, the total variable costs increase. But likewise, if the company reduces production, the variable costs decrease. Some common examples of variable costs include raw materials, direct labor costs, and utilities such as electricity, which might fluctuate depending on the operational intensity.

Reflecting on our problem, the variable cost given for producing the first output is \(\$90,000\). This cost will potentially change if the output level is adjusted. Variable costs are significant when calculating marginal costs because they directly affect the incremental expenses associated with producing additional units.

Total Cost Calculation

Total cost in business and economic analysis incorporates both fixed and variable costs. It represents the total economic cost of production and is calculated as the sum of all costs required to produce any given level of output.

In our example, the total cost (TC) calculation formula is expressed as \(TC = FC + VC\). When the firm produces one unit, as given in the exercise, total costs amount to \(\$190,000\). This information becomes essential when attempting to assess the overall expenditure of a business and is pivotal for performing break-even analysis, determining profitability, and making important financial decisions.