Marginal Rate of Substitution (MRS)

Introduction to Mathematical Extensions for Economic Analysis

Variable Slope of a Curve

Approximation of a Derivative by a Finite Difference

Marginal Utility

Implicit Differentiation in Economics

Composite Function Rule (Chain Rule)

Delta (Δ) Symbol

A coffee shop is considering staying open for an additional hour, from 4 PM to 5 PM. The table below shows their total revenue and total costs for different hours of operation. Based on an analysis of the change from the 4th to the 5th hour, what is the most logical decision and why?

Production Decision at a Small Firm

Decision on Studying

A software company has invested $5 million in developing a new product. Due to unexpected competition, the projected future revenue from the product has dropped to$3 million. The company estimates it will cost an additional $1 million to complete the product. Based on a rational analysis of incremental changes, the company should abandon the project because the total cost ($6 million) will exceed the total revenue ($3 million).

Marginal vs. Average Analysis in Decision-Making

A rational decision-maker thinks at the margin by comparing the additional benefits and additional costs of a small change. For each scenario below, match it with the correct marginal comparison that should guide the decision.

Rational individuals make decisions at the margin. This means they will choose to take an action only if the additional, or marginal, benefit of the action is at least as great as the marginal ____.

A firm is considering whether to produce one additional unit of a good. Arrange the following steps in the logical order a rational decision-maker would follow when thinking at the margin.

Fertilizer Application Decision

A company's total cost of producing widgets is shown in the table below. What is the marginal cost of producing the 3rd widget?