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Indifference Curve Equation for a Quasi-Linear Function
For a quasi-linear utility function of the form , the equation representing a single indifference curve is obtained by setting the utility level to a constant, . This yields the formula . This equation can be rearranged to express consumption as a function of free time (i.e., ), which is a necessary step for either plotting the curve or directly calculating its slope.
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A consumer's preferences are described as 'quasi-linear' if the utility function is linear with respect to one good (typically representing all other consumption) and non-linear with respect to another. A key implication of this form is that the marginal utility of the non-linear good does not depend on the quantity of the linear good. Given this information, which of the following utility functions,
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An individual's preferences for free time (
t) and consumption (c) are represented by a quasi-linear utility function of the formu(t,c) = v(t) + c. For a fixed utility level ofu₀ = 50, match each specific utility function on the left to its corresponding indifference curve equation on the right.Consider an individual whose preferences for free time (
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