Table 18-8
The following table shows the production function for a particular business. The numbers represent the various labor and output combinations the firm may choose for its output on a daily basis.

-Refer to Table 18-8.Suppose this firm charges a price of $5 per unit of output and pays workers a wage equal to $160 per day.How many workers should this firm hire to maximize its profit?

Question

Table 18-8
The following table shows the production function for a particular business. The numbers represent the various labor and output combinations the firm may choose for its output on a daily basis.
 
-Refer to Table 18-8.Suppose this firm charges a price of $5 per unit of output and pays workers a wage equal to $160 per day.How many workers should this firm hire to maximize its profit?

Quizplus · Accepted Answer

To maximize its profit, the firm needs to produce at the point where marginal revenue (MR) equals marginal cost (MC). The marginal revenue is given by the price, which is $5 per unit. The marginal cost can be calculated by taking the first derivative of the production function with respect to the labor input, which gives the marginal product of labor (MPL). Then, we can calculate the marginal cost as the wage divided by the MPL.
For example, at 3 workers, MPL=10 (from the table), so MC= $160/10 =$16/unit. Since MR=$5, the firm should produce at a level where MPL= MC, which is at 4 workers, where MPL=MC=$20/unit. At this level, the firm can produce 80 units of output and earn a profit of (80 x $5) - (4 x $160) = $320. Therefore, the best choice is to hire 4 workers to maximize the firm's profit.

Table 18-8 The Following Table Shows the Production Function for a Particular