Final answer:
The best production method initially is Method 1, and it remains the most economical option even if labor costs double, making it the most cost-effective choice regardless of increased labor costs.
Step-by-step explanation:
To determine the best production method, we need to consider both capital and labor costs. With labor costing $100/unit and capital costing $400/unit, the total costs for each method are as follows: Method 1 (50 labor units, 10 capital units) totals $9,000; Method 2 (20 labor units, 40 capital units) totals $18,000; and Method 3 (10 labor units, 70 capital units) totals $29,000.
Thus, Method 1 is the most cost-effective initially. If the labor cost doubles to $200/unit, the total cost for each method becomes: Method 1 is $14,000, Method 2 is $16,000, and Method 3 is $21,000; making Method 1 still the most cost-effective option.
In scenarios where labor costs increase significantly, a firm may seek to use more capital-intensive production methods. However, based on the given costs, remaining with Method 1, which is more labor-intensive, continues to be the most economical choice despite the increased labor costs.