Elements of Numerical Mathematical Economics with Excel

6.7. Isoquants and the constrained production optimization with two inputs

Let us go back now to the original firm, consisting of finding the optimal inputs combination to maximize the obtainable output, subject to the total costs the firm must sustain.

The problem is described as follows (see Section 6.4: Problem 6.4-1 with its Dual 6.4-2):

{ max { x i } y ( x 1 , x 1 , ⋯ , x n ) s . t . ∑ i = 1 n p i x i = C with x i ≥ 0 ( isocost line )

and it is a standard constrained problem that can be solved either analytically via the Lagrange multipliers or geometrically using ...