Given the Cobb-Douglas utility function U=X1/2Y1/2, which bundle is most preferred among Bundle A (2,4), Bundle B (3,4), and Bundle C (2,5)?

To determine which bundle is most preferred when given the Cobb-Douglas utility function U = X1/2Y1/2, we evaluate the utility derived from each bundle by substituting the values of X and Y into the utility function.

For Bundle A (2, 4):

• U_A = (2)^(1/2) * (4)^(1/2) = √2 * √4 = √2 * 2 = 2√2 ≈ 2.83

For Bundle B (3, 4):

• U_B = (3)^(1/2) * (4)^(1/2) = √3 * √4 = √3 * 2 = 2√3 ≈ 3.46

For Bundle C (2, 5):

• U_C = (2)^(1/2) * (5)^(1/2) = √2 * √5 = √10 ≈ 3.16

When we compare the utility values:

• U_A ≈ 2.83
• U_B ≈ 3.46
• U_C ≈ 3.16

Bundle B provides the highest utility at approximately