Causation

Quasi-Linear Utility and Vertically Parallel Indifference Curves

A key characteristic of indifference curves derived from a quasi-linear utility function is that they are vertical shifts of one another. This can be demonstrated by expressing the indifference curve equation as a function of consumption, cc, in terms of free time, tt. For two different utility levels, u1u_1 and u0u_0, the vertical distance between their respective indifference curves at any given value of tt is calculated as (u1v(t))(u0v(t))(u_1 - v(t)) - (u_0 - v(t)), which simplifies to the constant value u1u0u_1 - u_0. Since this vertical distance does not depend on tt, the curves are parallel in the vertical direction.

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Updated 2026-05-02

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