Question

What is the rule relating the ratio of marginal utility to prices of two goods at the optimal choice? Explain why, if this rule does not hold, the choice cannot be utility-maximizing.

Short answer

Marginal utility of two goods change with quantities consumed.

Step-by-step solution

Step 1. Introduction:

The general rule can also be expressed as the ratio of the prices of the two commodities must be equal to the ratio of the marginal utilities. It is written as:

$\frac{{\mathrm{P}}_1}{{\mathrm{P}}_2}=\frac{{\mathrm{MU}}_1}{{\mathrm{MU}}_2}$

Step 2. Explanation:

At the utility-maximizing point, dividing the price of good 1 by the price of good 2 equals the marginal utility of good 1 divided by the marginal utility of good 2. Along with the budget constraint, the total price of the two goods stays unchanged, so the price ratio does not alter. The marginal utility of the two commodities, however, varies with the quantity consumed. The utility ratio between two goods should be one if optimal choice is made. Alternatively, additional utility could be gained by substituting one good for the other. The problem of determining consumer equilibrium, or the combination of goods and services that maximizes an individual's total utility, boils down to weighing the trade-offs between one affordable combination and all other affordable combinations.