Final answer:
The best production method is determined by comparing the total costs of each method. Method 1 should be used with the original cost of labor, as it has the lowest total cost. Even if the cost of labor rises, Method 1 would still have the lowest total cost.
Step-by-step explanation:
The best production method is determined by comparing the total costs of each method. We can calculate the total cost for each method by multiplying the number of units of labor and capital by their respective costs, and summing the results.
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
Therefore, the firm should use Method 1 because it has the lowest total cost of $9,000.
If the cost of labor rises to $200/unit, the total cost for each method would change as follows:
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
Based on the new costs, the firm should still use Method 1 because it still has the lowest total cost of $14,000.