Question

A firm produces 125 units of a good. Its variable costs are 400 dollar, and its total costs are 700 dollar Answer the following questions: a. What do the firm's fixed costs equal? b. What is the average total cost equal to? c. If variable costs were 385 dollar when 124 units were produced, then what was the total cost equal to at 124 units?

Short answer

a. The firm's fixed costs equal 300 dollar. b. The average total cost equals 5.6 dollar per unit. c. The total cost at 124 units equals 685 dollar.

Step-by-step solution

Calculate Fixed Costs

Fixed costs are calculated by subtracting the variable costs from the total costs. So Fixed costs = Total costs - Variable costs = 700 dollar - 400 dollar = 300 dollar

Calculate Average Total Cost

The average total cost equals the Total cost divided by Quantity. So Average Total Costs = Total Costs / Quantity = 700 dollar / 125 units = 5.6 dollar per unit.

Calculate Total Cost at 124 units

The total cost is the sum of variable cost and fixed cost. We know from part a that fixed cost is 300 dollar. Variable cost at 124 units is given as 385 dollar. So Total cost = Fixed costs + Variable costs = 300 dollar + 385 dollar = 685 dollar

Key concepts

Fixed Costs Calculation

Understanding the calculation of fixed costs is crucial in the field of economics and business management. Fixed costs are the expenses that do not change with the amount of goods or services produced; they are 'fixed' over a specified period of time. Examples include rent, salaries of permanent staff, and insurance payments.

To calculate fixed costs, as shown in the textbook exercise, you subtract the total variable costs from the total costs of production. Using the formula:
\[\begin{equation} Fixed\text{ }Costs = Total\text{ }Costs - Variable\text{ }Costs \text{ }\end{equation}\],where variable costs vary with production levels. In the exercise, with a total cost of \$700 and variable costs of \$400, the firm's fixed costs amount to \$300. This step is pivotal as it sets the stage for other calculations such as breaking even and projecting profits.

Average Total Cost

Moving on to the average total cost (ATC), this concept helps in understanding the cost per unit of production. ATC is calculated by dividing the total cost by the quantity of output produced. This gives businesses insight into the efficiency of their production process. An optimal ATC is when a firm maximizes its production efficiency.To calculate ATC, use the formula: \[\begin{equation} Average\text{ }Total\text{ }Cost = \frac{Total\text{ }Costs}{Quantity}\text{ }\end{equation}\],As the exercise illustrates, with a total cost of \$700 to produce 125 units, the ATC equates to \$5.6 per unit. Knowing the ATC is significant for pricing decisions and to compare against the selling price to determine profitability per unit.

Efficiency and Pricing

By understanding ATC, firms can identify at which point they can achieve economies of scale—producing enough to lower the ATC and increase competitiveness through lower pricing or higher margins.

Total Cost Determination

Lastly, total cost determination is about finding the sum of all costs associated with production. The total cost includes both fixed and variable costs. This total cost figure is essential for companies to calculate profitability and make cost-related decisions.The formula for determining total cost is:\[\begin{equation} Total\text{ }Cost = Fixed\text{ }Costs + Variable\text{ }Costs \text{ }\end{equation}\],In the provided exercise, once the fixed cost is known to be \$300, determining the total cost at a different production level (124 units) is straightforward — simply add the fixed costs to the variable costs at that level of production (\$385), resulting in a total cost of \$685. This practice underscores the importance of clear cost breakdowns for budgeting and forecasting purposes.

Adapting to Production Changes

A firm needs to be able to adjust its strategies according to changes in production and costs. Knowing how to calculate the total cost at different production levels supports strategic decisions regarding scaling production up or down.