equimarginal principle
Suppose you have ten dollars and you love both tacos and coffee. How should you split the money to feel as happy as possible? The trick is not to spend it all on whichever you like more overall, but to keep shifting dollars toward whichever gives you the bigger bang per dollar at the moment, until both choices feel equally worthwhile. That balancing rule is the equimarginal principle.
Formally, you get the most total utility from a fixed budget when the last dollar spent on each good yields the same marginal utility per dollar. In symbols, you arrange your spending so that MU(taco) divided by price(taco) equals MU(coffee) divided by price(coffee), and so on for every good. Here is the intuition with numbers: if a taco costs 2 dollars and gives 10 units of marginal utility, that is 5 units per dollar; if coffee costs 1 dollar and gives 8 units, that is 8 units per dollar. Coffee is the better deal at the margin, so you buy more coffee. As you do, coffee's marginal utility falls, until eventually the per-dollar payoffs even out and you have nothing left to gain by reshuffling.
This principle is the heart of consumer choice and quietly governs far more than shopping. Firms allocating a fixed budget across advertising, a student dividing study hours across subjects before an exam, even a government splitting funds across programmes are all, in theory, hunting for the point where the last unit of effort or money does equal good everywhere. Real people rarely do the arithmetic, but they often grope toward the same balance by trial and adjustment.
Before a test, you study chemistry until the next hour would raise your grade less than an hour spent on math; then you switch to math. You stop reshuffling when the last hour on each subject helps roughly equally, exactly the equimarginal idea.
Balance spending so the last dollar buys equal value everywhere.
The rule equalises marginal utility per dollar, not marginal utility itself. A pricier good should give more raw marginal utility at the optimum, because each unit of it costs more dollars.