Question 5 A manufacturing company produces the quantity q of a product that depends on L units of labour and a capital amount K as given by the equation 1 q = 6 (L)²² (K) ² Challong Labour costs are $10 per labour unit and capital costs are $20 per unit of capital and the total cost budget is $3,000. (a) Find the optimal solution using Lagrange Multipliers. (b) Demonstrate the following economic principle for the optimal solution found in (a) that The marginal productivity of labour / The marginal productivity of capital = (29) / (32) = Cost per unit of labour / Cost per unit of capital (c) Recompute the optimal values for L and K when the budget is increased by $1 and check that this allows for the production of an extra λ units where A is the Lagrangian multiplier.

Question 5 A manufacturing company produces the quantity q of a product that depends on L units of labour and a capital amount K as given by the equation 1 q = 6 (L)²² (K) ² Challong Labour costs are $10 per labour unit and capital costs are $20 per unit of capital and the total cost budget is $3,000. (a) Find the optimal solution using Lagrange Multipliers. (b) Demonstrate the following economic principle for the optimal solution found in (a) that The marginal productivity of labour / The marginal productivity of capital = (29) / (32) = Cost per unit of labour / Cost per unit of capital (c) Recompute the optimal values for L and K when the budget is increased by $1 and check that this allows for the production of an extra λ units where A is the Lagrangian multiplier.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Step 1: a. Finding optimal solution using Lagrange multiplier

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Step 4: Proving equilibrium condition using the optimal solution.

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