Final answer:
The optimal choice for a consumer is to equalize the marginal utility per dollar spent across all goods. For example, José will keep purchasing the good with the highest marginal utility per dollar until the marginal utilities per dollar spent are equal for all goods within his budget.
Step-by-step explanation:
The consumer's optimal choice in allocating budget across different goods is defined by the principle that the marginal utility per dollar spent should be equal for all goods. If we consider the example of José purchasing movies and T-shirts, we can see this principle in action. José will compare the marginal utility per dollar for each good. Initially, the movie provides a higher marginal utility per dollar (2.3) compared to the T-shirt (1.6), so he purchases the movie first.
As he continues to buy more movies, the marginal utility per dollar for each additional movie decreases. He keeps purchasing movies until the marginal utility per dollar of the sixth movie equals the marginal utility per dollar of the first T-shirt. At this point, provided he has enough budget, he will buy both. The utility maximization occurs when the ratio of marginal utility to the price of good 1 is equal to the ratio of the marginal utility to the price of good 2, ensuring efficient allocation of his budget across goods X and Y.
The consumer's optimal choice occurs when the marginal utility per dollar spent on good X is equal to the marginal utility per dollar spent on good Y. This condition maximizes the utility obtained from the total budget spent on a combination of goods or services.