Answer :
To determine the number of workers the iron ore company would want to hire given the price of iron ore is [tex]$4 per ton and the wage rate is $[/tex]40 per day, we need to calculate the marginal revenue product (MRP) for each additional worker and compare it to the wage rate.
Step-by-Step Solution:
1. Understand the table data:
The table provides the total output of iron ore produced by a varying number of workers.
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Workers} & \text{Total Output of Iron Ore} \\ \hline 0 & 0 \\ \hline 1 & 30 \\ \hline 2 & 49 \\ \hline 3 & 65 \\ \hline 4 & 75 \\ \hline 5 & 80 \\ \hline \end{array} \][/tex]
2. Calculate the Marginal Product of Labor (MPL):
The MPL is the additional output produced by an additional worker. We find it by subtracting the total output of the previous worker(s).
[tex]\[ \begin{align*} \text{MPL}_1 &= 30 - 0 = 30 \\ \text{MPL}_2 &= 49 - 30 = 19 \\ \text{MPL}_3 &= 65 - 49 = 16 \\ \text{MPL}_4 &= 75 - 65 = 10 \\ \text{MPL}_5 &= 80 - 75 = 5 \\ \end{align*} \][/tex]
3. Calculate the Marginal Revenue Product (MRP):
MRP is found by multiplying the MPL by the price of iron ore ([tex]$4 per ton). \[ \begin{align*} \text{MRP}_1 &= 30 \times 4 = 120 \\ \text{MRP}_2 &= 19 \times 4 = 76 \\ \text{MRP}_3 &= 16 \times 4 = 64 \\ \text{MRP}_4 &= 10 \times 4 = 40 \\ \text{MRP}_5 &= 5 \times 4 = 20 \\ \end{align*} \] 4. Comparison of MRP with Wage Rate: The company will hire workers as long as the MRP of the next worker is greater than or equal to the wage rate ($[/tex]40 per day).
- For the 1st worker: MRP = [tex]$120 \geq $[/tex]40 → Hire
- For the 2nd worker: MRP = [tex]$76 \geq $[/tex]40 → Hire
- For the 3rd worker: MRP = [tex]$64 \geq $[/tex]40 → Hire
- For the 4th worker: MRP = [tex]$40 \geq $[/tex]40 → Hire
- For the 5th worker: MRP = [tex]$20 < $[/tex]40 → Do not hire
Based on this comparison, the company would hire up to 4 workers, as the 5th worker's MRP does not justify their wage.
Therefore, the iron ore company would want to hire 4 workers.
Step-by-Step Solution:
1. Understand the table data:
The table provides the total output of iron ore produced by a varying number of workers.
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Workers} & \text{Total Output of Iron Ore} \\ \hline 0 & 0 \\ \hline 1 & 30 \\ \hline 2 & 49 \\ \hline 3 & 65 \\ \hline 4 & 75 \\ \hline 5 & 80 \\ \hline \end{array} \][/tex]
2. Calculate the Marginal Product of Labor (MPL):
The MPL is the additional output produced by an additional worker. We find it by subtracting the total output of the previous worker(s).
[tex]\[ \begin{align*} \text{MPL}_1 &= 30 - 0 = 30 \\ \text{MPL}_2 &= 49 - 30 = 19 \\ \text{MPL}_3 &= 65 - 49 = 16 \\ \text{MPL}_4 &= 75 - 65 = 10 \\ \text{MPL}_5 &= 80 - 75 = 5 \\ \end{align*} \][/tex]
3. Calculate the Marginal Revenue Product (MRP):
MRP is found by multiplying the MPL by the price of iron ore ([tex]$4 per ton). \[ \begin{align*} \text{MRP}_1 &= 30 \times 4 = 120 \\ \text{MRP}_2 &= 19 \times 4 = 76 \\ \text{MRP}_3 &= 16 \times 4 = 64 \\ \text{MRP}_4 &= 10 \times 4 = 40 \\ \text{MRP}_5 &= 5 \times 4 = 20 \\ \end{align*} \] 4. Comparison of MRP with Wage Rate: The company will hire workers as long as the MRP of the next worker is greater than or equal to the wage rate ($[/tex]40 per day).
- For the 1st worker: MRP = [tex]$120 \geq $[/tex]40 → Hire
- For the 2nd worker: MRP = [tex]$76 \geq $[/tex]40 → Hire
- For the 3rd worker: MRP = [tex]$64 \geq $[/tex]40 → Hire
- For the 4th worker: MRP = [tex]$40 \geq $[/tex]40 → Hire
- For the 5th worker: MRP = [tex]$20 < $[/tex]40 → Do not hire
Based on this comparison, the company would hire up to 4 workers, as the 5th worker's MRP does not justify their wage.
Therefore, the iron ore company would want to hire 4 workers.