Overview
This lecture explains the difference between discrete and continuous quantities in economic models and how to interpret questions involving each, especially in demand and benefit calculations.
Discrete vs. Continuous Quantities
- Discrete quantities are whole, countable units (e.g., 1, 2, 3 cups of coffee).
- Continuous quantities allow non-integer values (e.g., 2.678 units).
- Average consumption over several periods can justify non-integer values (e.g., 2.2 cups/day on average).
- Units of measure can be in thousands or millions, making non-integer numbers practical.
Interpreting Questions & Assumptions
- The type of quantity (discrete or continuous) affects how you solve problems and calculate areas under curves.
- If a table is given, assume quantities are discrete.
- If an equation or formula is given, assume continuous (non-integer) quantities are possible.
- For computer-graded questions, using the correct assumption is crucial for correct answers.
Modeling and Precision in Economics
- Economic models are simplifications; exact predictions are not possible, only approximations.
- Economists don't claim highly precise answers (e.g., exactly 37.47 units).
Calculating Benefits: Tables vs. Curves
- With discrete quantities, total benefit is the sum of individual unit values (e.g., 4 + 3 + 2 + 1 = 10).
- With continuous quantities, total benefit is the area under the demand curve (triangle formula: base × height ÷ 2).
- The total benefit differs depending on the assumption (e.g., 10 vs. 12.5).
Best Practices for Problem Sets & Exams
- Instructor will try to specify if quantities are discrete or continuous.
- Non-linear tables suggest you should not try to fit a continuous linear function.
- Be alert to context clues; use the continuous assumption with equations and discrete with tables unless told otherwise.
Key Terms & Definitions
- Discrete Quantity — A countable, whole number unit (e.g., 1, 2, 3).
- Continuous Quantity — A measurement that can take any value, including fractions (e.g., 2.768).
- Demand Curve — Graphical or mathematical representation of quantity demanded at various prices.
- Total Benefit — The sum of willingness to pay for all units consumed.
- Area Under the Curve — Represents total benefit in continuous models.
Action Items / Next Steps
- Pay attention to whether questions use tables or equations to determine the correct assumption for quantity type.
- Watch for explicit instructions on discrete vs. continuous assumptions in exams and problem sets.