Calculus-Based Methods for Analyzing Indifference Curves
Calculus provides multiple methods for analyzing indifference curves. One approach is to rearrange the indifference curve equation to express one good as an explicit function of the other, and then differentiate to find the slope. An alternative and often more general technique is implicit differentiation. This method is applied directly to the utility function and considers how one good (e.g., consumption) must change in response to a small change in the other (e.g., free time) to keep the utility level constant. For a more rigorous mathematical treatment of these techniques—including the use of derivatives to determine properties like quasi-linearity, calculate the MRS, and apply implicit differentiation—readers can consult Sections 14.1, 15.1, 17.1, and 17.3 of 'Mathematics for Economists: An Introductory Textbook' by Malcolm Pemberton and Nicholas Rau (4th ed., 2015 or 5th ed., 2023).
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An individual's preferences for two goods, Good X (on the horizontal axis) and Good Y (on the vertical axis), are represented by a map of indifference curves. Point A and Point B are both located on the same indifference curve, labeled U1. Point C is located on a different indifference curve, labeled U2, which is positioned further from the origin than U1. Based on this information, which statement accurately describes the individual's preferences?
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- Bundle A: 3 cups of coffee, 10 hours of leisure
- Bundle B: 4 cups of coffee, 10 hours of leisure
- Bundle C: 3 cups of coffee, 12 hours of leisure
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- Bundle A: 16 hours of free time and an income of $100.
- Bundle B: 15 hours of free time and an income of $120.
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- Bundle C: 16 hours of free time and an income of $110.
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An individual is choosing between combinations of two goods: concert tickets and restaurant meals per month. They are currently consuming a bundle of 4 tickets and 10 meals. When asked, they state they would be equally happy with a bundle of 5 tickets and 7 meals. They also say they would be just as satisfied with 3 tickets and 15 meals. Which set of points represents three bundles that lie on the same indifference curve for this individual?
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- Bundles A and B both lie on the indifference curve I1.
- Bundle C lies above and to the right of the curve I1.
- Bundle D lies below and to the left of the curve I1.
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Learn After
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