Question

Suppose a shoe manufacturer has an average fixed cost of \(\$ 0.50\) per shoe at an output of 10,000 shoes. If he expanded production to 12,500 shoes, what would his average fixed costs be?

Short answer

When the shoe manufacturer expands production to 12,500 shoes, the new average fixed cost per shoe would be $0.40.

Step-by-step solution

Find the total fixed cost at an output of 10,000 shoes

To find the total fixed cost, we should multiply the average fixed cost per shoe by the number of shoes produced: Total Fixed Cost = Average Fixed Cost per Shoe × Number of Shoes

Calculate total fixed cost

Using the given average fixed cost of $0.50 per shoe and an output of 10,000 shoes, we can calculate the total fixed cost: Total Fixed Cost = $0.50 × 10,000 = \$5,000

Calculate average fixed cost at an output of 12,500 shoes

To find the new average fixed cost, we need to divide the total fixed cost by the new number of shoes produced: New Average Fixed Cost = Total Fixed Cost / New Number of Shoes

Determine the new average fixed cost

We know the total fixed cost is \$5,000 and the new number of shoes produced is 12,500. Using these values, we can find the new average fixed cost: New Average Fixed Cost = $5,000 / 12,500 = \$0.40 The average fixed cost per shoe when expanding production to 12,500 shoes would be $0.40.

Key concepts

Understanding Fixed Costs in Economics

In the realm of economics, fixed costs are expenses that do not change regardless of the level of production or output. These are costs that a company incurs even when there is no production taking place. Examples include rent, insurance, and salaries of permanent employees. The shoe manufacturer from our exercise, for instance, deals with fixed costs such as the rent of the factory and the machinery used for manufacturing the shoes.

It is important to distinguish between fixed costs and variable costs, the latter being expenses that vary with production levels like raw materials and hourly wages. Understanding the fixed costs is essential for businesses as it helps in price setting and can influence decisions on whether to increase or decrease production levels.

Production Costs Insights

Production costs are the combined expenses that are involved in the creation of a good or service. These costs are typically categorized into two parts: fixed costs, which we've covered above, and variable costs. For our shoe manufacturer, along with the fixed costs, they will have variable costs such as the leather and fabric used, as well as utility bills that might vary based on how much is produced.

When production costs are managed efficiently, a business can price its products competitively and maximize profits. An interesting part of production costs is understanding how these costs behave at different output levels, which directly links to the concept of economies of scale.

Economies of Scale Explained

Economies of scale refer to the cost advantage experienced by a firm when it increases its level of output. The idea is that as production scales up, the average cost per unit of output decreases. This happens because fixed costs are spread over a larger number of units.

Going back to our shoe manufacturer, when they increased production from 10,000 to 12,500 shoes, the average fixed cost per shoe decreased from \(0.50 to \)0.40. This is a direct result of economies of scale. The more shoes they make, the less each shoe costs in terms of the fixed costs. Firms aim for economies of scale to reduce costs and increase competitive advantage. However, it's worth noting that economies of scale can only continue to a certain point, beyond which diseconomies of scale might set in, raising the average cost per unit.