Final answer:
Sanghoon and Linh have the same ordinal preference in choosing bundles of audiobooks and movie downloads because their utility functions, although different in representation, indicate that if one prefers one bundle to another, so will the other. This is due to the fact that the square root in Sanghoon's function does not affect the ordering, only the scale.
Step-by-step explanation:
Sanghoon and Linh have ordinal preferences for bundles of audiobooks and movie downloads, meaning they can rank different bundles based on the level of satisfaction (utility) they provide. The utility functions for both individuals, U = √BM for Sanghoon and U = BM for Linh, show different representations of utility but indicate the same preference ordering. In other words, if Sanghoon prefers bundle X to bundle Y, Linh will have the same preference, and vice versa. This is because the square root in Sanghoon's utility function does not alter the ordering of preferences. It only changes the scale of utility, not the ranking, and since ordinal utility is concerned with rankings rather than specific values, their preferences align for any given bundles.
For instance, consider two bundles: bundle A with 4 audiobooks and 2 movie downloads (A = 4, M = 2) and bundle B with 3 audiobooks and 3 movie downloads (A = 3, M = 3). Sanghoon's utility for A is U = √(4×2) = √8 and for B is U = √(3×3) = √9. Similarly, Linh's utility for A is U = 4×2 = 8 and for B is U = 3×3 = 9. Both Sanghoon and Linh would prefer bundle B over A because their calculations result in the highest utility for bundle B, showcasing the same ordinal preference.