Isoquants and the Marginal Rate of Technical Substitution (MRTS)

An isoquant (from "iso" meaning equal and "quant" meaning quantity) is a curve showing all the different combinations of two factors — typically labour ($L$) and capital ($K$) — that produce the SAME level of output. Just as an indifference curve shows combinations of two goods giving equal satisfaction, an isoquant shows combinations of two inputs giving equal output; for this reason isoquants are sometimes called "equal product curves" or "iso-product curves."

Isoquants share four key properties:

1. Downward sloping (negative slope): to keep output constant, using LESS of one factor must be compensated by using MORE of the other — the two move in opposite directions along a single isoquant.
2. Convex to the origin: as more labour is substituted for capital along an isoquant, progressively LESS capital can be given up for each additional unit of labour — the two factors are not perfect substitutes for each other.
3. A higher isoquant represents a higher level of output: an isoquant further from the origin uses more of both factors (or more of one without less of the other) and therefore always represents a greater output than one closer to the origin.
4. No two isoquants can intersect: an intersection would imply that the same combination of labour and capital simultaneously produces two DIFFERENT levels of output, which is impossible.

The rate at which one factor can be substituted for another while keeping output unchanged is called the Marginal Rate of Technical Substitution (MRTS) — the amount of capital that must be given up to gain one additional unit of labour, output held constant:

Consider the following isoquant schedule, all combinations producing exactly 100 units of output: