General Utility Function for Consumption and Free Time

Karim's Specific Utility Function

Equation of an Indifference Curve

Using Alternative Utility Functions to Model Different Preferences

Consider two individuals, Alex and Ben, who consume two goods, apples (x) and bananas (y). Alex's preferences are represented by the utility function U_A(x, y) = x * y. Ben's preferences are represented by the utility function U_B(x, y) = 2 * (x * y) + 10. Based on these functions, which of the following statements is true?

Interpreting Utility Values

A consumer's preferences are represented by a utility function. If this function assigns a value of 80 to bundle A and a value of 40 to bundle B, it means that the consumer derives exactly twice as much satisfaction from bundle A as from bundle B.

An individual's preferences for two goods, coffee (x) and donuts (y), are represented by the utility function U(x, y) = x + 2y. Consider the following four consumption bundles:

• Bundle A: 4 coffees, 3 donuts
• Bundle B: 6 coffees, 2 donuts
• Bundle C: 2 coffees, 5 donuts
• Bundle D: 8 coffees, 1 donut

Which of the following correctly ranks these bundles from most preferred to least preferred?

The Role of a Utility Function

A consumer, Jordan, enjoys drinking coffee (C) but is completely indifferent to the number of sugar packets (S) available, as they always drink their coffee black. Jordan's satisfaction depends solely on the quantity of coffee consumed; more coffee is always preferred to less, regardless of the amount of sugar. Which of the following utility functions accurately represents Jordan's preferences?

A consumer has the following preferences over bundles of two goods, pizza (P) and soda (S):

1. They prefer the bundle (4P, 2S) over the bundle (3P, 3S).
2. They are indifferent between the bundle (3P, 3S) and the bundle (2P, 5S).

Which of the following utility functions is inconsistent with this consumer's stated preferences?

A consumer's preferences for two goods, books (B) and movies (M), are represented by the utility function U(B, M) = B + 3M. Analyze this function. Which of the following statements accurately describes the consumer's preferences?

Evaluating the Validity of Utility Functions

A utility function mathematically represents a consumer's preferences for different bundles of goods. Analyze each of the following utility functions, where 'x' and 'y' represent the quantities of two different goods. Match each function to the description of preferences it best represents.