Final answer:
The profit-maximizing firm should choose Method 1 both before and after the increase in the cost of labor, as it presents the lowest total production cost in each scenario.
Step-by-step explanation:
To determine the best production method that a profit-maximizing firm should choose, we need to calculate the total costs of each method given the price per unit of labor and capital. Initially, if hiring labor for the winter costs $100/unit and a unit of capital costs $400, the calculations for each method would be:
Method 1: (50 units of labor × $100) + (10 units of capital × $400) = $5000 + $4000 = $9000
- Method 2: (20 units of labor × $100) + (40 units of capital × $400) = $2000 + $16000 = $18000
- Method 3: (10 units of labor × $100) + (70 units of capital × $400) = $1000 + $28000 = $29000
With these costs, the firm would choose Method 1 as it has the lowest total cost.
If the cost of labor rises to $200/unit, the new calculations would be:
Method 1: (50 units of labor × $200) + (10 units of capital × $400) = $10000 + $4000 = $14000
- Method 2: (20 units of labor × $200) + (40 units of capital × $400) = $4000 + $16000 = $20000
- Method 3: (10 units of labor × $200) + (70 units of capital × $400) = $2000 + $28000 = $30000
Even after the rise in labor costs, the firm would still choose Method 1 as the most cost-effective way to produce 1,000 units of output.