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Explain why the marginal cost curve intersects the average total cost curve at the level of output where average total cost is at a minimum.

Short Answer

Expert verified
The marginal cost curve intersects the average total cost curve at the level of output where average total cost is at a minimum because MC influences the ATC. When MC is less than ATC, it brings the average down and when MC is more than ATC, it brings the average up. Thus, the ATC reaches its minimum when MC equals ATC.

Step by step solution

01

Identifying what is Average Total Cost (ATC) and Marginal Cost (MC)

ATC is the total cost of production divided by the number of goods produced while MC is the cost of producing one more unit. The ATC is usually U shaped because it initially decreases with an increase in output due to economies of scale and later increases due to diseconomies of scale. The MC also tends to follow a U shape; it decreases at first due to increasing marginal returns and then increases due to diminishing marginal returns.
02

Relationship between ATC and MC

MC is an additional cost incurred in producing one more unit. If MC is less than ATC, it brings the average down. Conversely, when MC is more than ATC, it pulls the average up. This means that the ATC decreases when MC is less than ATC and starts increasing when MC is more than ATC.
03

MC intersects ATC at its minimum point

MC intersects ATC at the minimum point of the ATC curve because ATC decreases when MC is less than ATC and starts increasing when MC is more than ATC. This implies that the MC curve will intersect the ATC curve at its minimum point as at this point onwards the MC becomes higher than ATC and the ATC starts increasing after reaching a minimum value.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Marginal Cost
Marginal Cost (MC) is an essential concept in economics, especially when analyzing the cost structure in production. It refers to the cost of producing one more unit of a good. Understanding MC helps businesses decide how much to produce in order to maximize profit.
  • When the MC is lower than the price of the product, increasing production can increase profit.
  • MC is typically represented as a U-shaped curve. Initially, as production increases, MC decreases due to increasing marginal returns. Eventually, it starts to rise because of diminishing marginal returns.
In practical terms, knowing the MC helps in decision making, particularly in determining the optimal level of production. For example, a company needs to gauge the cost implications of producing extra units before expanding production to ensure they are not incurring unnecessary expenses.
Average Total Cost
Average Total Cost (ATC) is another important concept that helps businesses understand their overall cost structure. ATC is calculated by dividing the total cost of production by the number of units produced. This gives an idea of the cost per unit.
  • Similar to the MC, the ATC generally follows a U-shaped curve.
  • The ATC decreases with an increase in output initially due to economies of scale. However, it increases after a certain point due to diseconomies of scale.
The interaction between MC and ATC is crucial:
  • If the MC is less than the ATC, it means each additional unit is cheaper than the average, lowering the ATC.
  • Conversely, if the MC is more than the ATC, it increases the average.
The point where the MC intersects ATC marks the minimum point of the ATC curve, indicating the most cost-efficient level of production.
Economies of Scale
Economies of scale refer to the cost advantages that businesses experience when production becomes efficient. As the scale of production increases, the cost per unit of output generally decreases. This happens because fixed costs are spread over a larger number of goods, and operational efficiencies improve.
  • Examples of fixed costs include rent, salaries, and equipment.
  • Improving operational efficiency can involve streamlined processes and technology adoption.
However, economies of scale are limited and eventually lead to diseconomies of scale when a company grows beyond its optimal size. At this point, costs start to increase per unit due to factors such as increased complexity, management inefficiencies, or higher costs of coordination.
  • Understanding where these efficiencies end is important for businesses to avoid unnecessary cost spikes.
Overall, the concept of economies of scale helps explain why the ATC curve is U-shaped: it initially decreases due to economies of scale and then increases when diseconomies of scale set in.

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Most popular questions from this chapter

Explain how the events listed in (a) through (d) would affect the following costs at Southwest Airlines: 1\. Marginal cost 2\. Average variable cost 3\. Average fixed cost 4\. Average total cost a. Southwest signs a new contract with the Transport Workers Union that requires the airline to increase wages for its flight attendants. b. The federal government starts to levy a \(\$ 20\) -perpassenger carbon emissions tax on all commercial air travel. c. Southwest decides on an across-the-board 10 percent cut in executive salaries. d. Southwest decides to double its television advertising budget.

What is the production function? What does the shortrun production function hold constant?

Is Jill Johnson correct when she states the following: "I am currently producing 10,000 pizzas per month at a total cost of \(\$ 50,000\). If I produce 10,001 pizzas, my total cost will rise to \(\$ 50,011\). Therefore, my marginal cost of producing pizzas must be increasing." Draw a graph to illustrate your answer.

In the ancient world, a book could be produced either on a scroll or as a codex, which was made of folded sheets glued together, something like a modern book. One scholar has estimated the following variable costs (in Greek drachmas) of the two methods: $$ \begin{array}{l|c|l} \hline \text { Scroll } & \text { Codex } \\ \hline \begin{array}{l} \text { Cost of writing } \\ \text { (wage of a scribe) } \end{array} & 11.33 \text { drachmas } & 11.33 \text { drachmas } \\ \hline \text { Cost of paper } & 16.50 \text { drachmas } & 9.25 \text { drachmas } \\ \hline \end{array} $$ Another scholar points out that a significant fixed cost was involved in producing a codex: In order to copy a codex \(\ldots\) the amount of text and the layout of each page had to be carefully calculated in advance to determine the exact number of sheets \(\ldots\) needed. No doubt, this is more time-consuming and calls for more experimentation than the production of a scroll would. But for the next copy, these calculations would be used again. a. Suppose that the fixed cost of preparing a codex was 58 drachmas and that there was no similar fixed cost for a scroll. Would an ancient book publisher who intended to sell 5 copies of a book be likely to publish it as a scroll or as a codex? What if the publisher intended to sell 10 copies? Briefly explain. b. Although most books were published as scrolls in the first century C.E., by the third century, most were published as codices. Considering only the factors mentioned in this problem, explain why this change may have taken place.

(Related to the Apply the Concept on page 376) Small business owner Jay Goltz described several decisions he made to reduce the fixed costs of his businesses, including replacing halogen lamps with LED lamps. Goltz noted, "I'm guessing that many business owners could save a lot more than pennies on their fixed costs, and those savings ... fall right to the bottom line." a. Why are the costs of electricity used to power the lights used in Mr. Goltz's businesses fixed costs? b. Explain why Goltz wrote that reducing fixed costs results in savings that "fall right to the bottom line."

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