Equivalence of Convex Quasi-Linear Preferences and Concavity of v(t)

A consumer's preferences are represented by a quasi-linear utility function of the form u(t, m) = v(t) + m, where t is the quantity of a good and m is money spent on all other goods. For the indifference curves associated with these preferences to be convex (bowed-in toward the origin), which of the following forms for v(t) would be appropriate, assuming t > 0?

Deriving the Convexity Condition for Quasi-Linear Preferences

For a consumer with quasi-linear preferences represented by the utility function u(t, m) = t^3 + m, where t is the quantity of a good and m is money, the indifference curves will be convex for all positive quantities of good t.

Analyzing Consumer Behavior with Quasi-Linear Preferences

A consumer's preferences are represented by a quasi-linear utility function of the form u(t, m) = v(t) + m. Match each of the following functional forms for v(t) to the corresponding shape of the indifference curves they generate for t > 0.

The Economic Intuition of Convexity in Quasi-Linear Preferences

For a consumer with quasi-linear preferences represented by the utility function u(t, m) = v(t) + m, the indifference curves will be convex if the marginal utility of good t, represented by v'(t), is a(n) ________ function of t.

Comparative Analysis of Convexity in Quasi-Linear Preferences

Constructing Utility Functions with Specific Preference Properties

An economist is analyzing a consumer's preferences, which can be described by a quasi-linear utility function of the form u(t, m) = v(t) + m, where t is the quantity of a specific good and m represents money for all other goods. To determine if the consumer's indifference curves are convex (i.e., exhibit a diminishing marginal rate of substitution), the economist must follow a specific analytical procedure. Arrange the following steps into the correct logical sequence.