Question

2. ABC Corp wants to produce whatever output it wishes to sell at minimum cost. Its production function is y = z 1/3 1 z 2/3 2 , where y is output and z1 ≥ 0 and z2 ≥ 0 are inputs. It is a price taker in input markets so its total cost, C, equals w1z1 + w2z2, where w1 > 0 and w2 > 0 are input prices. Fix output at y0.

(i) Use Lagrange’s Method to find ABC’s cost-minimizing input demand functions, z c i (w1, w2, y0), i = 1, 2 and its total cost function C(w1, w2, y0). Use µ as the symbol for the Lagrange multiplier.

(ii) Prove C1(w1, w2, y0) = z c 1 (w1, w2, y0). (iii) Interpret the Lagrange multiplier µ(w1, w2, y0).

Answer 1

ii) Lagrange Multiplier , imply the rate of change of optimal minimized value of total cost , with respect to output level target y0

So, if Output target rises by 1, then Minimum cost level changes by Lagrangian Multiplier value