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Quasi-linear Preferences

General Form of a Quasi-Linear Utility Function

The general mathematical expression for a quasi-linear utility function is $u(x, m) = v(x) + m$ . In this form, $x$ represents a particular good (or a 'bad' if it negatively impacts utility), and $m$ represents an individual's income that is spent on other goods. The function is termed 'quasi-linear' because it is linear with respect to income ( $m$ ) but typically non-linear concerning good $x$ . This functional form has the important property that the marginal utility of good $x$ is independent of income. For the preferences to be considered well-behaved, $v(x)$ must be an increasing function, so its first derivative must be positive ( $v'(x) > 0$ ), and it is generally assumed to be concave.

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Mathematically Deriving the Pareto Efficiency Curve for the Angela-Bruno Interaction
Angela's Specific Utility Function (u(t, c) = 4√t + c)
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Specific Function for Utility from Free Time (v(t) = 4√t)
Marginal Utility of Free Time for a Quasi-Linear Function
Indifference Curve Equation for a Quasi-Linear Function
Equivalence of Convex Quasi-Linear Preferences and Concavity of v(t)
Measuring Utility in Consumption Units via Quasi-Linear Preferences
Utility Function of Angela's Friend (u(t, c) = c + 75 ln(t))
A General Form for v(t) in Quasi-Linear Utility (v(t) = βt^α)
Independence of Marginal Utility from Income in Quasi-Linear Preferences
Marginal Utility of Income in a Quasi-Linear Function
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, u(x, m), represents quasi-linear preferences where x is a specific good and m is money spent on all other goods?
A consumer's preferences for a specific good x and money m (representing all other consumption) are described by the utility function u(x, m) = 10√x + m. By analyzing the properties of this function, which statement accurately describes the consumer's behavior or preferences?
Consider a consumer whose preferences for a specific good, x, and money available for all other goods, m, can be represented by the utility function u(x, m) = 20 * ln(x) + m. According to this model, if the consumer's income increases, their willingness to pay for an additional unit of good x will also increase.
A utility function of the form u(x, m) = v(x) + m is said to represent 'well-behaved' quasi-linear preferences. For this to be true, the utility from good x must be increasing (meaning its first derivative, v'(x), is positive), and there must be diminishing marginal utility for good x (meaning its second derivative, v''(x), is negative), for all x > 0. Which of the following specifications for v(x) satisfies both of these conditions?
Analyzing Preferences with a Quasi-Linear Model
Modeling Consumer Preferences for Different Goods
An individual's preferences are modeled by a utility function u(x, m), where x is the quantity of a specific good and m is the amount of money available for all other goods. Match each utility function to the statement that correctly describes its marginal utility properties.
A utility function of the form u(x, m) = v(x) + m is referred to as 'quasi-linear' because while it is typically non-linear with respect to good x, it is perfectly linear with respect to the variable ______, which represents an individual's income available for other goods.
Evaluating Model Suitability for Different Goods
Critical Evaluation of the Quasi-Linear Utility Model

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