The consumer’s money income should be allocated so that the last dollar spent on each product yields the same amount of extra (marginal) utility.
How should the $10 income be allocated?
UTILITY MAXIMIZING COMBINATION
Algebraic Restatement of the Utility Maximization Rule
MUx/Px = MUy/Py = MUz/Pz
8 utils$1=16 utils$2
MARGINAL UTILITY-PRICE RATIO:
The ratio of the marginal utility obtained from consuming a good to the price of the good. This ratio is particularly important in determining consumer equilibrium, which is reached when the marginal utility-price ratios are the same for all goods. Equality between all marginal utility-price ratios is the rule of consumer equilibrium which is satisfied with utility maximization. The marginal utility-price ratio indicates the satisfaction derived from the last dollar spent on a good. A consumer maximizes utility be equating the marginal utility-price ratio for each good purchased and consumed. If the ratios are not equal, then utility can be increased by changing the combination of goods consumed. Consumer Equilibrium
When consumers make choices about the quantity of goods and services to consume, it is presumed that their objective is to maximize total utility. In maximizing total utility, the consumer faces a number of constraints, the most important of which are the consumer’s income and the prices of the goods and services that the consumer wishes to consume. The consumer’s effort to maximize total utility, subject to these constraints, is referred to as the consumer’s problem. The solution to the consumer’s problem, which entails decisions about how much the consumer will consume of a number of goods and services, is referred to as consumer equilibrium.