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Independence of Marginal Utility from Income in Quasi-Linear Preferences
A key characteristic of the quasi-linear utility function, , is that the marginal utility of the good is not affected by the individual's income, . Mathematically, this means the partial derivative of utility with respect to , which is , is a function of alone and does not depend on .
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Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
Ch.10 Market successes and failures: The societal effects of private decisions - The Economy 2.0 Microeconomics @ CORE Econ
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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 wherexis a specific good andmis money speA consumer's preferences for a specific good
xand moneym(representing all other consumption) are described by the utility functionu(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 functionu(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 goodxwill 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), wherexis the quantity of a specific good andmis 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) + mis referred to as 'quasi-linear' because while it is typically non-linear with respect to goodx, 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
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A Common Specification for v(t) in Quasi-Linear Utility (v(t) = βt^α)
Angela's Specific Utility Function ()
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Utility Function of Angela's Friend ()
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A farmer's production of grain (y) is described by the function y = g(h), where h is the number of hours worked per day. This function is known to be increasing and strictly concave for all h > 0. Which of the following statements must be true?
Willingness to Pay with Quasi-Linear Preferences
Consider a consumer whose preferences for a specific good (x) and money for all other goods (m) can be represented by the utility function u(x, m) = 20√x + m. If this consumer's income significantly increases, while the price of good x remains constant, their marginal willingness to pay for an additional unit of good x will also increase.
Deriving the Income-Independence Property
Match each utility function, where
xis a specific good andmrepresents money for all other goods, with the correct description of its marginal utility for goodx.Interpreting Consumer Behavior
A consumer's preferences for a specific product (good x) and money available for all other goods (m) are represented by a utility function. The consumer is known to experience diminishing marginal utility for good x. For which of the following utility functions will the consumer's marginal utility for good x be independent of their level of income (m)?
Predicting Consumer Behavior
For a consumer with preferences represented by the utility function
u(x, m) = v(x) + m, wherexis a specific good andmis money for other goods, the marginal rate of substitution betweenxandmdepends only on the quantity of ____.An economist is analyzing a consumer's preferences, represented by the utility function u(x, m) = 10ln(x) + m, where 'x' is the quantity of a specific good and 'm' is the money available for all other goods. The economist wants to determine if the additional satisfaction the consumer gets from one more unit of good 'x' depends on their level of income 'm'. Arrange the following steps in the correct logical sequence to conduct this analysis.
Consider a consumer whose preferences for a specific good (x) and money for all other goods (m) can be represented by the utility function u(x, m) = 20√x + m. If this consumer's income significantly increases, while the price of good x remains constant, their marginal willingness to pay for an additional unit of good x will also increase.