The table below shows a competitive firm's short-run production function.Labor is the firm's only variable input,and market price for the firm's product is $2 per unit. $\begin{array}{cccc}
\text {Units of Labor } & \text { Units of Output} \
3 &370\
4 &490\
5 &570\
6 &600\
7&620\
\end{array}$

If the wage rate is $200,the firm should

Question

The table below shows a competitive firm's short-run production function.Labor is the firm's only variable input,and market price for the firm's product is $2 per unit. $\begin{array}{cccc}
  \text {Units of Labor   } & \text {  Units of Output}  \
3 &370\
4 &490\
5 &570\
6 &600\
7&620\
\end{array}$

If the wage rate is $200,the firm should

Quizplus · Accepted Answer

To determine whether the firm should shut down or produce, we need to compare the average revenue product (ARP) with the wage rate. ARP is calculated by dividing total revenue by the number of units of labor employed.

At 3 units of labor, the firm produces 370 units of output. The total revenue at a price of $2 per unit is 370 x $2 = $740. ARP is therefore $740/3 = $246.67. We can repeat this calculation for each level of employment and record the results in the following table:

| Units of Labor | Units of Output | Total Revenue | ARP   |
|----------------|----------------|---------------|-------|
| 3              | 370            | $740          | $246.67 |
| 4              | 490            | $980          | $245    |
| 5              | 570            | $1140         | $228    |
| 6              | 600            | $1200         | $200    |
| 7              | 620            | $1240         | $177.14 |

We can see that at 3 units of labor, ARP is $246.67, which is greater than the wage rate of $200. This means that the firm should hire 3 units of labor. Similarly, at 4 units of labor, ARP is $245, which is also greater than the wage rate, so the firm should hire 4 units of labor. At 5 units of labor, however, ARP drops to $228, which is less than the wage rate, so the firm should only hire 4 units of labor.

Therefore, the optimal level of employment for the firm is 4 units of labor, which corresponds to a total output of 490 units and total revenue of $980. Because total revenue exceeds the total variable cost (which is the wage rate times the number of units of labor), the firm is making a profit and should continue to produce.