AP MicroeconomicsProduction & Costs
Least-Cost Rule
The least-cost rule says a firm minimizes the cost of any output when the marginal product per dollar is equal across all inputs: MPL/PL = MPK/PK.
A firm produces a given output most cheaply when the extra output per dollar spent is the same for every input. If MPL/PL exceeds MPK/PK, labor gives more output per dollar, so the firm shifts spending toward labor; doing so lowers MPL (diminishing returns) and raises MPK until the ratios equalize. This is the cost-minimization condition that underlies the firm's cost curves, and it is distinct from the profit-maximizing hiring rule (MRP = MRC). Graphically it is the tangency of an isoquant and an isocost line.
Formula / Example
MP_L / P_L = MP_K / P_K (output per dollar equal across inputs)