Learn Before
Variable Slope of a Curve
When a function is represented graphically by a curve rather than a straight line, its slope is not constant and will differ at various points. This principle is essential for understanding concepts that rely on non-linear relationships, such as the diminishing marginal rate of substitution along a convex indifference curve, where the slope changes continuously.
0
1
Tags
Social Science
Empirical Science
Science
CORE Econ
Economics
Economy
Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
Ch.3 Doing the best you can: Scarcity, wellbeing, and working hours - The Economy 2.0 Microeconomics @ CORE Econ
Related
Marginal Rate of Substitution (MRS)
Introduction to Mathematical Extensions for Economic Analysis
Variable Slope of a Curve
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?
Hours Open Total Revenue Total Cost 4 $200 $120 5 $240 $150 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?
Quantity of Widgets Total Cost 0 $10 1 $15 2 $22 3 $32 4 $45 Numerical Approximation of a Derivative
Learn After
Imagine a graph where the vertical axis represents the total output of a factory and the horizontal axis represents the number of hours it operates per day. The relationship is shown as a curve that rises steeply at first, then begins to level off. Three points are labeled on this curve: Point A is near the beginning where the curve is very steep, Point B is in the middle where the slope is moderate, and Point C is near the end where the curve is almost flat. The slope of the curve at any point represents the additional output generated per additional hour of operation. Which statement correctly analyzes the relationship shown on the graph?
Interpreting Production Trade-offs
Interpreting a Trade-off Curve
Explaining Changing Trade-offs
A graph shows the relationship between the total satisfaction a person gets from eating slices of pizza. The horizontal axis measures the number of slices eaten, and the vertical axis measures total satisfaction. The graph is a curve that starts at the origin, rises steeply for the first few slices, and then becomes progressively flatter as more slices are eaten. Three points are identified on this curve: Point A (after the 1st slice), Point B (after the 4th slice), and Point C (after the 8th slice). Match each point to the statement that best describes the additional satisfaction gained from eating one more slice at that stage.
A graph shows the total cost of production (vertical axis) versus the quantity of units produced (horizontal axis). The line on the graph is a curve that becomes progressively steeper as more units are produced. This graphical representation implies that the cost to produce each additional unit is falling.
Analyzing Production Trade-offs
A graph displays a student's final exam score (vertical axis) as a function of the total hours they studied (horizontal axis). The graph is a curve that becomes progressively flatter as study hours increase. This indicates that the additional points gained on the exam from each extra hour of studying ________ as the total study time increases.
A graph shows the total crop yield from a field (vertical axis) based on the amount of fertilizer applied (horizontal axis). The relationship is represented by a curve that starts at the origin, rises, and then becomes progressively flatter. The slope at any given point represents the additional yield gained from one more unit of fertilizer. Arrange the following points on the curve in order from where the slope is STEEPEST to where it is FLATTEST.
Evaluating a Business Decision