Question

One unit of Commodity A is produced by combining 1 unit of land, 2 units of labor, and 5 units of capital. Similarly, one unit of Commodity B is produced by 2 units of land, 3 units of labor, and 4 units of capital. Assuming that the price of commodities A, B, and C are respectively Pa = N270, Pb = N160, and Pc = N190, find the total rent (R), the wages (W), and interest of the three resources.

a) R = N200, W = N75, I = N125
b) R = N150, W = N110, I = N130
c) R = N225, W = N70, I = N95
d) R = N180, W = N120, I = N160

Answer 1

The best production method when labor costs $100 per unit and capital costs $400 per unit is Method 1 with the lowest cost of $9000. If the cost of labor rises to $200 per unit, Method 1 still remains the best production method with a new total cost of $14000.

Step-by-step explanation:

To determine the best production method, we need to calculate the total costs for each production method given the cost per unit of labor and capital. Initially, hiring labor for the winter costs $100 per unit and capital costs $400 per unit.

• 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 the initial costs, the best production method is Method 1 with the lowest cost of $9000.

If the cost of labor rises to $200 per unit, we should re-calculate the total costs:

• 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

With the increased labor cost, Method 1 still remains the best production method but now with a total cost of $14000.