Cost Minimization Point

The cost minimization point is the combination of inputs that allows a company to produce a given level of output at the lowest possible cost.

In the long run, it is graphically depicted with isoquant curves and isocost lines.

Isoquants illustrate all input combinations yielding a specific output level, while isocost lines display all input combinations purchasable at a given cost.

The point at which the isocost line is tangent to the isoquant shows the combination of inputs a company should use to achieve a specific output. At this point, the cost is minimal. Here, the slope of the isocost line is equal to the slope of the isoquant curve.

The slope of the isocost line is the negative of the relative price of the inputs. For the isoquant, the slope is the Marginal Rate of Technical Substitution or MRTS, which is the negative of the marginal product of labor divided by the marginal product of capital.

This equation can be rearranged to represent the ratios of the input's marginal products to their price.

This condition states that at the cost minimization point, the marginal product per dollar spent must be equal for all inputs. It's also known as the "equal marginal principle" in production.