Final answer:
To calculate the total cost of each method of production, we need to multiply the cost of labor by the number of units of labor and the cost of capital by the number of units of capital for each method. The firm should use Method 1 because it has the lowest total cost. If the cost of labor rises, Method 1 still remains the method with the lowest total cost.
Step-by-step explanation:
To calculate the total cost of each method of production, we need to multiply the cost of labor by the number of units of labor and the cost of capital by the number of units of capital for each method. Based on the given information and assuming that each unit of labor and capital is used for only one method, the total cost for each method would be:
- Method 1: $100 per unit of labor * 50 units of labor + $400 per unit of capital * 10 units of capital = $5000 + $4000 = $9000
- Method 2: $100 per unit of labor * 20 units of labor + $400 per unit of capital * 40 units of capital = $2000 + $16000 = $18000
- Method 3: $100 per unit of labor * 10 units of labor + $400 per unit of capital * 70 units of capital = $1000 + $28000 = $29000
The firm should use Method 1 because it has the lowest total cost of $9000.
If the cost of labor rises to $200/unit, the total cost for each method would be:
- Method 1: $200 per unit of labor * 50 units of labor + $400 per unit of capital * 10 units of capital = $10000 + $4000 = $14000
- Method 2: $200 per unit of labor * 20 units of labor + $400 per unit of capital * 40 units of capital = $4000 + $16000 = $20000
- Method 3: $200 per unit of labor * 10 units of labor + $400 per unit of capital * 70 units of capital = $2000 + $28000 = $30000
In this case, the firm should still use Method 1 because it remains the method with the lowest total cost of $14000.