Grades 35
Concepts
Assessment Activity

Why is the derivative of the cost function the most precise estimate of marginal cost? (Hint: because the limit approaches zero with the derivative.)

An analyst has estimated the total cost of producing x items for a certain company as C(x) = 1800 + 10x + 0.02x^{2} and the demand for producing x items for a certain company as p = 60 + 0.01x. Find the number of items the company should produce to maximize profit or minimize loss. How much will the company profit from producing such a quantity?

An analyst found that the company’s marginal cost is less than the marginal revenue associated with producing 5000 units of a good for the previous year. What implications does this data have for the company to maximize profit this year?

The company should produce less than 5,000 units.

The company should produce more than 5,000 units.

The company should produce 5,000 units.

There are no implications in regards to level of production.

The company should produce less than 5,000 units.

An analyst found that the company’s marginal cost is equal to the marginal revenue associated with producing 5000 units of a good. What implications does this information have for profit maximization?

The company should produce less than 5,000 units.

The company should produce more than 5,000 units.

The company should produce 5,000 units.

There are no implications in regards to level of production.

The company should produce less than 5,000 units.

An analyst found that the company’s marginal cost is more than the marginal revenue associated with producing 5000 units of a certain good. What implications does this information have for profit maximization?

The company should produce less than 5,000 units.

The company should produce more than 5,000 units.

The company should produce 5,000 units.
 There are no implications in regards to level of production.

The company should produce less than 5,000 units.
Overview
Profit maximizing firms use marginal analysis to determine whether to produce an additional unit of output or to employ an extra resource. In its most basic sense marginal cost is simply a measure of the rate of change between the total costs and the quantity of output (or in another context the amount of a variable input). Using the metric of cost this lesson explores the concept of slope from an economic point of view.
The lesson uses Marginal Costs and Marginal Revenue as context for the underlying meaning of the derivative function. Students make the connection between the difference quotient and marginalism leading to the application of derivatives to find marginal functions. Students also apply their findings to a firm’s marginal functions to decide how much the firm should produce to maximize profit.
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