Question

You produce widgets. Currently you produce four widgets at a total cost of \(\$ 40\). a. What is your average total cost? b. Suppose you could produce one more (the fifth) widget at a marginal cost of \(\$ 5 .\) If you do produce that fifth widget, what will your average total cost be? Has your average total cost increased or decreased? Why? c. Suppose instead that you could produce one more (the fifth) widget at a marginal cost of \(\$ 20 .\) If you do produce that fifth widget, what will your average total cost be? Has your average total cost increased or decreased? Why?

Short answer

a. The average total cost for four widgets is \(\$10\) per widget. b. If the fifth widget costs an additional \(\$5\), the new average total cost becomes \(\$9\) per widget, which has decreased. c. If the fifth widget costs an additional \(\$20\), the new average total cost becomes \(\$12\) per widget, which has increased.

Step-by-step solution

Calculate Current Average Total Cost

To find the average total cost (ATC) for the original four widgets, divide the total cost by the number of widgets produced. The total cost is given as \(\$40\), and the number of widgets is 4. The formula to calculate the ATC is: \[\text{ATC} = \frac{\text{Total Cost}}{\text{Number of widgets}}\]

Determine New Average Total Cost for Fifth Widget at \(5

To calculate the new ATC after producing a fifth widget at a marginal cost of \(\$5\), add the marginal cost to the total cost, and divide by the new total number of widgets. The formula is: \[\text{New ATC} = \frac{\text{Total Cost} + \text{Marginal Cost}}{\text{New Number of widgets}}\]. Then compare the new ATC to the original to determine if it has increased or decreased.

Determine New Average Total Cost for Fifth Widget at \)20

To determine the new ATC after producing a fifth widget at a marginal cost of \(\$20\), use the same method as in step 2, but with the new marginal cost. Compare the new ATC to the original to determine if it has increased or decreased and explain why based on the changes in total cost and the number of widgets.

Key concepts

Marginal Cost

Marginal cost is a fundamental concept in microeconomics that refers to the extra cost incurred for producing one additional unit of a good or service. It's a reflection of changes in the total cost when production output is increased by one unit. Consider this: when a company is already producing widgets, as in our exercise, deciding whether to make another widget requires understanding how much more it would cost.

This incremental cost can influence decision-making. For instance, if the cost of producing the next widget is lower than what customers are willing to pay for it, the company may decide to increase production for profit maximization. In the given exercise, the decision to produce the fifth widget would involve comparing the marginal cost to the average total cost to see how it affects profitability.

Total Cost

Total cost in production economics embodies the entirety of expenses associated with producing a certain level of output. It includes both fixed costs (which remain constant regardless of output level) and variable costs (which fluctuate with production volume). For a widget manufacturer, the total cost might include the fixed costs of the factory lease and machinery, plus variable costs like labor and raw materials.

The exercise demonstrated how to calculate the total cost for a specific number of widgets. Understanding total cost is necessary for pricing strategies and for determining the viability of production levels. In most scenarios, the goal is to manage and reduce total costs effectively for maximizing profits.

Production Costs Economics

Production costs in economics are the costs associated with creating goods or services, and they are pivotal for any business model. They are divided into direct costs (like raw materials and direct labor) and indirect costs (like utilities and rent), which together contribute to the total cost of production.

In the exercise, we focus on how producing an additional widget affects these costs. Keeping the production costs in check is essential as they directly affect the pricing of products, competitive positioning, and the company's bottom line. Moreover, understanding production costs helps in setting financial goals and assessing the efficiency of production processes.

Cost Analysis

Cost analysis is a critical activity within microeconomics and managerial accounting that involves assessing the various costs of production. It aids businesses in making informed decisions regarding pricing, investment in production means, cost-cutting measures, and overall financial planning.

In our exercise, cost analysis would involve examining how producing another widget, with the fifth widget's marginal cost at either \(\$5\) or \(\$20\), influences the average total cost and ultimately the company's decision on whether to produce more units. Through careful analysis, a company can spot trends, efficiencies, or waste, and adjust strategies accordingly to optimize profitability.