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.
