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

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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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Most popular questions from this chapter

Devra Gartenstein, a restaurant owner, made the following observation about preparing food: "Cooks become increasingly less productive as a kitchen becomes increasingly crowded." a. What do economists call the problem she is describing? What are its implications for the marginal product of labor for cooks? b. Do restaurant owners have a solution to this problem in the long run? Briefly explain.

(This problem is somewhat advanced.) Using symbols, we can write that the marginal product of labor is equal to \(\Delta Q / \Delta L .\) Marginal cost is equal to \(\Delta \mathrm{TC} / \Delta Q .\) Because fixed costs by definition don't change, marginal cost is also equal to \(\Delta \mathrm{VC} / \Delta \mathrm{Q} .\) If jill Johnson's only variable cost (VC) is labor cost, then her variable cost equals the wage multiplied by the quantity of workers hired, or \(w \mathrm{~L}\) a. If the wage Jill pays is constant, then what is \(\Delta V C\) in terms of \(w\) and \(L ?\) b. Use your answer to part (a) and the expressions given for the marginal product of labor and the marginal cost of output to find an expression for marginal cost, \(\Delta \mathrm{TC} / \Delta \mathrm{Q},\) in terms of the wage, \(w,\) and the marginal product of labor, \(\Delta Q / \Delta L\) c. Use your answer to part (b) to determine Jill's marginal cost of producing pizzas if the wage is \(\$ 750\) per week and the marginal product of labor is 150 pizzas. If the wage falls to \(\$ 600\) per week and the marginal product of labor is unchanged, what happens to Jill's marginal cost? If the wage is unchanged at \(\$ 750\) per week and the marginal product of labor rises to 250 pizzas, what happens to Jill's marginal cost?

Is it possible for average total cost to be decreasing over a range of output where marginal cost is increasing? Briefly explain.

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.

What are implicit costs? How are they different from explicit costs?

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