Question

Suppose the total cost of producing 10,000 tennis balls is \(\$ 30,000\), and the fixed cost is \(\$ 10,000\). a. What is the variable cost? b. When output is 10,000 , what are the average variable cost and the average fixed cost? c. Assume that the cost curves have the usual shape. Is the dollar difference between the average total cost and the average variable cost greater when the output is 10,000 tennis balls or when the output is 30,000 tennis balls? Explain.

Short answer

a. The variable cost is $20,000. b. The average variable cost is $2 and the average fixed cost is $1. c. The difference between the average total cost and average variable cost is greater when output is 10,000 tennis balls due to the larger average fixed cost per unit.

Step-by-step solution

Calculate Variable Cost

To find the variable cost, subtract the fixed cost from the total cost. That is, variable cost = total cost - fixed cost = $30,000 - $10,000 = $20,000.

Calculate Average Variable Cost and Average Fixed Cost

Average variable cost is the variable cost divided by the quantity, thus Average Variable Cost = Variable Cost / Quantity = $20,000 / 10,000 = $2. \n Similarly, Average Fixed Cost = Fixed Cost / Quantity = $10,000 / 10,000 = $1.

Discuss the Differences between Average Total Cost and Average Variable Cost

In order to analyze the difference between the average total cost and average variable cost, we need to understand that the average fixed cost decreases as the quantity increases and the average variable cost remains constant if variable cost doesn't vary with the output. Therefore, the difference between the average total cost (which is the sum of average variable cost and average fixed cost) and average variable cost would be smaller at 30,000 than it is at 10,000. This is due to the decrease in the average fixed cost as output increases.

Key concepts

Average Fixed Cost

When it comes to understanding cost analysis in production, one key concept is the Average Fixed Cost (AFC). Fixed costs are expenses that do not change with the level of output, such as rent, salaries, or equipment costs. Therefore, even if production levels vary, these costs remain constant.
To calculate the average fixed cost, you take the total fixed cost and divide it by the total quantity produced. Using our tennis ball example, where the fixed cost is \(10,000 and the production is 10,000 units, we find the AFC as follows:

• AFC = Fixed Cost / Quantity

This translates to:
\[ AFC = \frac{10,000}{10,000} = \\)1 \]
As production increases, the AFC decreases, because the fixed cost is being spread over more units. For example, if production triples to 30,000 units, the AFC would drop significantly, illustrating how economies of scale can reduce costs per unit.

Average Variable Cost

Average Variable Cost (AVC) is another crucial aspect of cost analysis in production. Unlike fixed costs, variable costs change with the level of output. These can include costs like raw materials, utilities based on usage, or direct labor expenses. To find the AVC, you divide the total variable cost by the number of units produced.
In the case of producing 10,000 tennis balls, if the variable cost is calculated as \(20,000, the AVC would be:

• AVC = Variable Cost / Quantity

This gives us:
\[ AVC = \frac{20,000}{10,000} = \\)2 \]
The AVC tells us how much it costs, on average, to produce one additional unit, excluding fixed costs. It tends to flatter out after reaching a certain level of production, assuming economies of scale are achieved and costs stabilize as output is increased.

Variable Cost Calculation

To understand production costs, it's important to know how to calculate variable costs accurately. Variable costs might include expenses that vary directly with output, like materials and some labor costs.
The general formula for finding variable costs in any scenario is:

• Variable Cost = Total Cost - Fixed Cost

For our specific example regarding tennis ball production, where the total cost is given as \(30,000 and the fixed cost is \)10,000, calculation would be:
\[ Variable Cost = 30,000 - 10,000 = 20,000 \]
Understanding this calculation helps in making critical business decisions, such as determining how changes in production levels can affect overall costs and profitability. It can be a driving factor in setting competitive pricing, managing resources, and planning for future production expansions.