Marginal Utility per Unit of Spending

Marginal utility alone is not enough when goods have different prices. A 30-unit gain costing 15 uses more scarce budget than a 20-unit gain costing 5. The useful comparison is marginal utility per unit of spending:

This ratio asks how much extra satisfaction the next currency unit buys at the margin.

Allocate the next unit of budget

Suppose the next noodle meal gives 40 units of MU and costs 10, while the next fruit cup gives 24 and costs 4:

Buying the fruit cup first produces more utility from the scarce budget. After buying it, use the MU of the next fruit cup. Diminishing marginal utility changes the ratios after every unit, so optimization is an iterative comparison rather than a permanent ranking of goods.

The equal-marginal principle

For divisible goods and an interior optimum, the consumer allocates spending until

Why? If X yields 5 utility units per currency unit while Y yields 3, moving a little spending from Y to X raises total utility. Reallocation continues until the ratios are equal, unless a boundary is reached.

The condition can also be written

The consumer's willingness to trade Y for X at the margin matches the market's required tradeoff. Graphically, an indifference curve is tangent to the budget line.

Discrete goods and corner choices

Meals, tickets, and phone plans may not be divisible. Exact equality may be impossible, and spending the final few currency units may not improve utility. In that case, use MU per price to guide the search, then compare nearby complete feasible baskets.

An optimum can also be at a corner, where the consumer buys none of one good. This is not a failure of rationality. It occurs when one good's adjusted marginal benefit never catches up before the budget is exhausted, or when goods are indivisible.

The model predicts that a price change alters the ratio even if preferences do not change. Consumers then reallocate spending, which helps explain downward-sloping individual demand.

Allocate a small budget step by step

Suppose tea costs 6 and its successive marginal utilities are 30, 18, and 12. Noodles cost 10 and give 40, 30, and 15. At the start, the next tea gives 5 utility per currency unit and noodles give 4, so buy tea first.

After that purchase, the next tea ratio falls to $18/6=3$, while the first noodles remain at 4. The ranking changes, so buy noodles next. A good allocation process repeatedly updates the next available ratios; it does not rank whole product categories once and keep that order forever.

Why equal ratios describe balance

If the final tea unit gives 3 utility per yuan while the final noodles unit gives 5, moving a small amount of spending from tea to noodles raises total utility. An interior allocation cannot be optimal while such an improvement remains. Balance occurs when the ratios are equal or constraints prevent further adjustment.

Whole units require a final check

With indivisible meals and tickets, exact equality may be impossible. A greedy sequence based on the highest ratio can also leave unusable money. After following the marginal rule, compare nearby complete baskets that satisfy the budget. This is not abandoning marginal analysis; it is adapting it to a lumpy choice set.

Common mistakes include comparing raw MU instead of MU per price, using average utility, and comparing the first unit repeatedly instead of the next unit.