Analysis of a Consumer's Preferences for Consumption and Free Time

A consumer's preferences for consumption (c) and free time (t) are represented by the quasi-linear utility function u(t, c) = 4√t + c. By expressing an indifference curve as an explicit function c(t) and using differentiation, what can you conclude about the shape of the consumer's indifference curves?

Determining Indifference Curve Convexity via Differentiation

An analyst wants to determine the shape of the indifference curves for a consumer whose preferences for consumption (c) and free time (t) are represented by the utility function u(t, c) = 2t^(1/2) + c. The method involves expressing the indifference curve as an explicit function c(t) and using differentiation. Arrange the following steps in the correct logical order to complete this analysis.

Consider a consumer whose preferences for consumption (c) and free time (t) are represented by the utility function u(t, c) = ln(t) + c. A correct analysis of this function's indifference curves would conclude that the consumer's willingness to give up consumption for an additional unit of free time increases as they have more free time.

A consumer's preferences for consumption (c) and free time (t) are represented by a quasi-linear utility function. For each utility function provided, match it to the correct mathematical expression for the second derivative of its indifference curve (d²c/dt²), which is used to determine the curve's convexity.

A consumer's preferences for consumption (c) and free time (t) are represented by the utility function u(t, c) = 10√t + c. To analyze the shape of the indifference curves, one can express an indifference curve as an explicit function c(t) and find its second derivative, d²c/dt². For this utility function, the value of the second derivative at t = 4 is ____.

Economic Interpretation of Indifference Curve Shape

An analyst examines a consumer's preferences for consumption (c) and free time (t) using the utility function u(t, c) = 10t - t² + c. Their analysis concludes: "Because the second derivative of the indifference curve equation, d²c/dt², is a positive constant (2), the indifference curves are convex, which implies a diminishing marginal rate of substitution for all positive values of free time (t)."

Which of the following statements provides the most accurate evaluation of the analyst's conclusion?

Evaluating the Analysis of a Non-Monotonic Utility Function