Answer: 1 unit of X and 2 units of Y
Explanation: Total utility is the complete satisfaction you get from maximising usage of a quantity of a good or service. However another element also needs to be considered, and that is marginal utility. Marginal utility is the satisfaction you get from consuming an additional quantity of a good or service.
Both these factors are important as they determine how much of each product the consumer should buy. To maximise total utility, the consumer must use the full $10 income. But the question still stands as to which combination of products should the consumer purchase.
To make it fair the consumer should start by purchasing one of X and one of Y, and keep taking one of each (starting with X) to keep it fair. However after taking one of X, worth $2, and one of Y, worth $4, there is only $4 left. That means that if the consumer then takes one of X there will be $2 left, disallowing the consumer to afford X, and thus making the purchases unfair. Therefore in terms of meeting the marginal utlility, it is better to then swop to purchasing Y with the remaining $4, and maximising the consumer's total utility.
