Question

Suppose an individual's preferences are described by the Cobb-Douglass utility function U = X⁰·⁵Y⁰·⁵ and consider the following three combinations (or bundles) of X and Y: Bundle A (4,3); Bundle B (5,2); Bundle C (1,6). Given the individual's preferences, rank the bundles from least-preferred to most-preferred.

Answer 1

Using the Cobb-Douglas utility function, Bundle A has the highest utility, followed by Bundle B, and Bundle C has the lowest, ranking them from most preferred to least preferred as A > B > C.

Step-by-step explanation:

To rank the bundles from least-preferred to most-preferred using the Cobb-Douglas utility function U = X⁰·⁵Y⁰·⁵, we need to calculate the total utility for each bundle by plugging the quantities of goods X and Y into the utility function.

• Bundle A: U = 4⁰·⁵ * 3⁰·⁵ = 2 * √3 ≈ 3.464
• Bundle B: U = 5⁰·⁵ * 2⁰·⁵ = √5 * √2 ≈ 3.162
• Bundle C: U = 1⁰·⁵ * 6⁰·⁵ = 1 * √6 ≈ 2.449

Comparing the computed utility values, Bundle A has the highest utility, followed by Bundle B, and Bundle C has the lowest. Therefore, the ranking from most preferred to least preferred is A > B > C.

To understand the step-by-step process of finding the choice with the highest total utility, you need to compare the marginal utility you gain and lose from different choices along the budget constraint. This process involves a personal assessment of preferences without depending solely on the numerical values of utility. Finding the utility-maximizing choice can vary; you may add up total utility, compare marginal utility gains and losses, or compare the ratios of marginal utility to price and choose where they are equal.