The Law of Equi-Marginal Utility (Gossen's Second Law, also called the law of substitution or maximum satisfaction) states that a rational consumer maximises total satisfaction when income is allocated so that the marginal utility per rupee spent is equal across all goods.

The governing condition

For two goods $X$ and $Y$, the consumer is in equilibrium when:

subject to the budget constraint that total spending equals income ($P_x Q_x + P_y Q_y = M$).

The economic reasoning

If $\frac{MU_x}{P_x} > \frac{MU_y}{P_y}$, the last rupee spent on $X$ yields more satisfaction than the last rupee on $Y$. The consumer therefore transfers spending from $Y$ to $X$. As more $X$ is bought its $MU_x$ falls (law of diminishing marginal utility) and as less $Y$ is bought its $MU_y$ rises — until the two ratios become equal and no further reallocation can raise total utility.

One-line worked illustration …