Grades 9-12
Risk and Return Concept Video
Video
This lesson creates a connection between derivatives and marginalism. Students will be engaging in a set of scaffolding activities that explore the Marginal Cost Function, Marginal Revenue Function, and the implications that these functions have on production. A short video clip will provide an example of why the intersection of Marginal Cost and Marginal Revenue yields maximum profit.
90 minutes
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.
Ex. for production of 1^{st} item.
Ex. for production of 2^{nd} item.
www.youtube.com/watch?v=W-GEZAthjCk
Stop the video at 1:31 — Ask students to think about what implications marginal revenue and marginal cost have in relation to how many apples a farmer should pick.
Grades 9-12
Video
Grades 9-12
Lesson
Grades 9-12
Lesson
Grades 9-12
Lesson
Grades 9-12
Activity