Final answer:
The indifference function associated with the bundle X = 4 and Y = 2, for the utility function U = X^0.5Y^0.5, is Y = 8 / X. This equation represents the indifference curve for the given bundle, encapsulating all combinations of goods X and Y that provide the same level of utility.
Step-by-step explanation:
The student has presented a utility function U = X0.5Y0.5, which is a Cobb-Douglas utility function, and asks for the indifference curve associated with a given bundle where X = 4 and Y = 2. The indifference curve represents all combinations of goods X and Y that give the consumer the same satisfaction or utility. To find the equation of the indifference curve for the utility level obtained from the bundle X = 4 and Y = 2, we must first calculate the utility level at this bundle:
U = 40.5 × 20.5 = 2 × 1.414 = 2.828
Next, we set the utility function equal to this utility level to find the indifference curve:
2.828 = X0.5Y0.5
This can be rearranged to solve for Y in terms of X:
Y = (2.828 / X0.5)2
× = 8 / X
Therefore, the indifference function associated with the bundle X = 4 and Y = 2 is Y = 8 / X.