Chapter 4 · Test 1
Continuity
Limits of functions, continuity tests, and economic discontinuities.
What you will learn
- Choose a parameter for continuity
- Evaluate a removable limit
- Classify a discontinuity
Reasoning habits that help
- At a joining point, continuity requires the two branch values and the function value to agree.
- A hole at one point does not prevent a limit from existing when nearby values approach a single number.
- Continuity classification compares the side limits and function value to identify smooth, removable, jump, or unbounded behavior.
Where economists use these methods
- Continuity restrictions help join tax schedules, benefit formulas, and piecewise policy rules without artificial jumps.
- Limits describe marginal behavior near a point even when an economic formula is undefined exactly at that point.
- Economists inspect continuity to distinguish smooth responses from threshold jumps, isolated formula artifacts, and unbounded model behavior.