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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.7P

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