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 market price for the firm's product increases to $5,how many units of labor will the firm employ at a wage rate of $200?

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 market price for the firm's product increases to $5,how many units of labor will the firm employ at a wage rate of $200?

Quizplus · Accepted Answer

To determine the quantity of labor the firm will employ at a wage rate of $200, we need to use the marginal revenue product (MRP) formula. MRP is equal to the additional revenue generated by each additional unit of labor. In a competitive market, MRP is also equal to the product price times the marginal product of labor (MPL).

At a price of $2 per unit, we can calculate the MRP at each level of labor input:

- MRP of 3 units of labor: $2 x (370 - 0) = $740
- MRP of 4 units of labor: $2 x (490 - 370) = $240
- MRP of 5 units of labor: $2 x (570 - 490) = $160
- MRP of 6 units of labor: $2 x (600 - 570) = $60
- MRP of 7 units of labor: $2 x (620 - 600) = $40

As we see, diminishing returns to labor result in diminishing MRP, after the 4th unit of labor. There is no point to employ more than 4 units of labor at the wage of $200. But when the market price increases to $5 per unit, the MRP formula changes accordingly:

- MRP of 3 units of labor: $5 x (370 - 0) = $1850
- MRP of 4 units of labor: $5 x (490 - 370) = $600
- MRP of 5 units of labor: $5 x (570 - 490) = $400
- MRP of 6 units of labor: $5 x (600 - 570) = $150
- MRP of 7 units of labor: $5 x (620 - 600) = $100

Now the firm will prefer to employ more labor, up to the point where MRP = wage rate. At a wage rate of $200, this occurs at 5 units of labor, where MRP = $400. So the firm will choose to employ 5 units of labor when the market price is $5 per unit.