To determine the preferred asset, analyze mean and variance for higher expected return and lower risk, and apply second-order stochastic dominance by comparing CDFs for expected utility. A utility-maximizing choice is found where marginal utilities per dollar are equal, ensuring efficient allocation of wealth on the consumption budget constraint.
To decide which asset is preferred between X and Y based solely on mean and variance, one would need the specific mean (expected return) and variance (risk measure) of each asset. Generally, the preference is for the asset with the higher mean and lower variance; however, the final choice may also depend on the investor's risk tolerance.
According to the second-order stochastic dominance criterion, one would compare the cumulative distribution functions (CDFs) of X and Y. If the CDF of X is always to the right of the CDF of Y, then Y dominates X in the sense of second-order stochastic dominance. Essentially, one asset stochastically dominates another if it yields a higher expected utility regardless of the utility function, provided it is a function that displays risk aversion.
In the context of utility-maximizing choice on a consumption budget constraint, one could analyze the opportunity set and the indifference curves to find the optimal choice. An asset that allows a consumer to reach a higher indifference curve, while staying within their budget constraint, is preferred. The utility-maximizing choice lies where the marginal utility per dollar spent is equal across all goods, which ensures that the last dollar spent on each good provides the same increase in utility.