Law of Equi-Marginal Utility

The law helps a consumer decide how to spend their limited income on multiple goods to get the most satisfaction.
A consumer reaches maximum satisfaction when the last rupee spent on each good provides the same level of utility (satisfaction).

1. If you spend a rupee on X and get more satisfaction than spending it on Y, you should buy more X and less Y.
2. Keep switching spending from one good to another until every rupee gives you equal satisfaction, considering each good’s price.
3. Condition for Maximum Utility:     \[\frac{MU_X}{P_X}=\frac{MU_Y}{P_Y}\]
   where MU_X and MU_Y are marginal utilities, and P_X and P_Y are their respective prices.

1. Calculate MU/P for each good at every unit.
2. Compare combinations that match the budget.
3. Choose the combination where MU_X/P_X=MU_Y/P_Y and all money is used.
4. That’s the highest satisfaction (utility).

1) When a consumer spends money only on oranges, marginal utility from each additional rupee falls (e.g., first rupee = 10 utils, second = 8, then 6, then 4, then

2) Spending all ₹5 on oranges: total utility = 10 + 8 + 6 + 4 + 2 = 30 utils.

3) Instead, combining purchases of mangoes and oranges gives higher total utility.

• Best combination: ₹3 on oranges and ₹2 on mangoes is optimal, yielding 10 + 8 + 6 (oranges) + 8 + 6 (mangoes) = 38 utils.
• Other combinations (e.g., ₹3 mangoes + ₹2 oranges, or all on one) yield less total utility.

1. The diagram below shows equilibrium at the point where the marginal utility of spending on mangoes equals the marginal utility of oranges.
2. Shaded area E1PBC (right panel) = Gain in total utility by choosing more balanced spending.
3. Shaded area ECGF (left panel) = Loss in utility from unbalanced spending.
4. The intersection of MU lines shows the best allocation, maximising overall satisfaction.

• Modern economists state that maximum satisfaction is reached when the ratios of marginal utilities to their prices across all goods are equal.
• Key Formula:    \[\frac{MU_a}{P_a}=\frac{MU_b}{P_b}=\cdots=\frac{MU_n}{P_n}\]
  where MU = Marginal Utility and P = Price for different goods.

• The law of equi‑marginal utility explains how a rational consumer allocates limited income among many goods to get maximum satisfaction.​

  It states that a consumer reaches maximum satisfaction when the marginal utility per unit of money is equal for all goods, i.e. MU_A/P_A=MU_B/P_B=⋯=MUn/Pn.​

  This is an extension of the law of diminishing marginal utility to many commodities and is also called Gossen’s Second Law or the law of maximum satisfaction.​