Isocost

[1][2] Although similar to the budget constraint in consumer theory, the use of the isocost line pertains to cost-minimization in production, as opposed to utility-maximization.

The slope is: The isocost line is combined with the isoquant map to determine the optimal production point at any given level of output.

A line joining tangency points of isoquants and isocosts (with input prices held constant) is called the expansion path.

[3] The cost-minimization problem of the firm is to choose an input bundle (K,L) feasible for the output level y that costs as little as possible.

, and the absolute value of the slope of an isoquant is the marginal rate of technical substitution (MRTS), we reach the following conclusion: If the isoquants are smooth and convex to the origin and the cost-minimizing input bundle involves a positive amount of each input, then this bundle satisfies the following two conditions: The condition that the MRTS be equal to w/r can be given the following intuitive interpretation.

Suppose w rises, so that the maximum amount of labor that can be employed at the same cost will decrease, that is, the intercept of the isocost line on the L axis will decrease; and because r remains unchanged, the intercept of the isocost line on the K axis will remain unchanged.