Question

The quantity, Q. of a product manufactured by a company is given by Q=aK⁰.⁶ L⁰⁴ where a is a positive constant, K is the quantity of capital and L is the quantity of labor used. Capital costs are 548 per unit, labor costs are $12 per unit, and the company wants costs for capital and labor combined to be no higher than $360. Suppose you are asked to consult for the company, and learn that 6 units each of capital and labi being used. (a) What do you advise? Should the company use more or less labor? More or less capital? If so, by how much? Enter the exact answers. The company should (b) Complete the sentence below to sell your advice to the board of directors. Round your answer to two decimal places. the quantity of capital and the quantity of labor will increase production by \% while halding costs to $360.

Answer 1

The best production method is Method 1 due to its lowest total cost, both before and after the increase in labor costs.

Step-by-step explanation:

To determine the best production method, considering differing costs for labor and capital, we will calculate the total cost of each method. Initially, with labor costing $100/unit and capital at $400/unit, we have the following total costs:

• Method 1: (50 units of labor × $100/unit) + (10 units of capital × $400/unit) = $5,000 + $4,000 = $9,000
• Method 2: (20 units of labor × $100/unit) + (40 units of capital × $400/unit) = $2,000 + $16,000 = $18,000
• Method 3: (10 units of labor × $100/unit) + (70 units of capital × $400/unit) = $1,000 + $28,000 = $29,000

Method 1 offers the lowest total cost and would be the optimal choice. If labor costs increase to $200/unit, we re-calculate:

• Method 1: (50 units of labor × $200/unit) + (10 units of capital × $400/unit) = $10,000 + $4,000 = $14,000
• Method 2: (20 units of labor × $200/unit) + (40 units of capital × $400/unit) = $4,000 + $16,000 = $20,000
• Method 3: (10 units of labor × $200/unit) + (70 units of capital × $400/unit) = $2,000 + $28,000 = $30,000

Even with increased labor costs, Method 1 still remains the most cost-effective.