Derivation of the MRS for a Quasi-Linear Utility Function

Slope of a Quasi-Linear Indifference Curve

Quasi-Linear Utility and Vertically Parallel Indifference Curves

An individual's preferences for hours of free time, t, and units of consumption, c, can be described by the function u(t, c) = 4√t + c. Which equation below correctly represents the specific combination of t and c that yields a constant utility level of 20?

Deriving a Specific Indifference Curve Equation

An individual's preferences for free time (t) and consumption (c) are represented by a quasi-linear utility function of the form u(t,c) = v(t) + c. For a fixed utility level of u₀ = 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 (t) and consumption (c) are represented by the utility function u(t, c) = 2t² + c. A student claims that one of this individual's indifference curves is described by the equation c = 2t² - 100. Is this claim correct?

Modeling a Freelancer's Choices

An individual's preferences for free time (t) and consumption (c) are given by the utility function u(t, c) = 10ln(t) + c. The equation for the indifference curve that corresponds to a utility level of 25 can be written as c = ____.

An individual's preferences for free time (t) and consumption (c) are represented by the utility function u(t, c) = 2√t + c. Consider two different bundles of goods: Bundle A, which provides a utility level of 40, and Bundle B, which provides a utility level of 45. If both bundles contain the exact same amount of free time (t*), what is the difference in the amount of consumption between Bundle B and Bundle A (i.e., c_B - c_A)?

Relationship Between Indifference Curves for Quasi-Linear Preferences

You are given an individual's preferences represented by a utility function of the form u(t, c) = v(t) + c, where t is free time and c is consumption. Arrange the following steps in the correct logical order to derive the equation for a single indifference curve, expressed with consumption (c) as a function of free time (t).

An individual's preferences for free time (t) and consumption (c) are represented by a quasi-linear utility function. One of this individual's indifference curves is described by the equation c = 100 - 8√t. Which of the following functions correctly represents the underlying utility function u(t, c) that could generate this curve?