Final answer:
The indifference curve associated with the bundle (4, 4) in the utility function U = X⁰·⁵Y⁰·⁵ is the set of all (X, Y) combinations where X⁰·⁵ * Y⁰·⁵ = 2. This represents all the bundles of goods X and Y that provide the same utility to the consumer as the bundle (4, 4).
Step-by-step explanation:
Indifference Curves and Utility Functions
A consumer's utility function U = X⁰·⁵Y⁰·⁵ describes their preferences for different combinations of goods X and Y, where utility is a numerical representation of their satisfaction. An indifference curve is a graph that shows all combinations of goods that give the consumer the same level of utility.
For the bundle (4, 4), where X = 4 and Y = 4, we can calculate the total utility and then determine the indifference curve that contains all the combinations of X and Y that provide that same level of utility using the given utility function.
The indifference function can be found by setting the utility equation equal to the total utility at the point (4, 4), which is U = 4⁰·⁵ * 4⁰·⁵ = 2. Therefore, the indifference curve associated with the bundle (4, 4) is the set of all (X, Y) combinations such that X⁰·⁵ * Y⁰·⁵ = 2. This result is critical for understanding consumer choice and the theory of consumer behavior within the field of microeconomics.