Final answer:
To maximize utility with a given income, a consumer should ensure that the marginal utility per dollar spent is the same for all goods purchased. This achieves a balance where the satisfaction gained from the last dollar spent on each good is equal, optimizing overall satisfaction within the consumer's budget constraints.
Step-by-step explanation:
A consumer with a given income will maximize utility when each good is purchased in amounts such that the marginal utility per dollar spent is the same for all goods. To achieve utility maximization, consumers apply the rule that at the optimal choice, the ratio of the marginal utility to the price of each good should be equal. This general rule ensures that consumers are making the most out of their budget by equating the pleasure or satisfaction (utility) gained from the last unit of currency spent on each good or service.
The concept is based on the premise that rational consumers seek to reach the highest level of satisfaction possible within their budget constraints. By comparing the marginal utility gains and losses of moving to different combinations of goods on their budget line, they can find the point where the utility-per-dollar is equalized across goods, which indicates that no further utility gains can be achieved by reallocating the budget.