Table 18-9

-Refer to Table 18-9.This table describes the number of baseballs a manufacturer can produce per day with different quantities of labor.Each baseball sells for $5 in a competitive market and the firm pays each unit of labor a wage equal to $320 per day.How many units of labor should the firm hire to maximize profit?

Question

Table 18-9
 
-Refer to Table 18-9.This table describes the number of baseballs a manufacturer can produce per day with different quantities of labor.Each baseball sells for $5 in a competitive market and the firm pays each unit of labor a wage equal to $320 per day.How many units of labor should the firm hire to maximize profit?

Quizplus · Accepted Answer

To maximize profit, the firm should produce where marginal revenue (MR) equals marginal cost (MC). First, we need to calculate the total revenue (TR) for each level of labor. TR is equal to the quantity produced multiplied by the price:

TR = Price x Quantity

At 0 units of labor, the quantity produced is 0. Therefore, TR = $0.

At 1 unit of labor, the quantity produced is 8 baseballs. Therefore, TR = $40.

At 2 units of labor, the quantity produced is 14 baseballs. Therefore, TR = $70.

At 3 units of labor, the quantity produced is 18 baseballs. Therefore, TR = $90.

At 4 units of labor, the quantity produced is 20 baseballs. Therefore, TR = $100.

At 5 units of labor, the quantity produced is 20 baseballs. Therefore, TR = $100.

Next, we need to calculate the total cost (TC) for each level of labor. TC is equal to the wage rate multiplied by the number of units of labor:

TC = Wage Rate x Labor

At 0 units of labor, TC = $0.

At 1 unit of labor, TC = $320.

At 2 units of labor, TC = $640.

At 3 units of labor, TC = $960.

At 4 units of labor, TC = $1280.

At 5 units of labor, TC = $1600.

Now, we can calculate the marginal revenue (MR) and marginal cost (MC) for each level of labor. MR is equal to the change in total revenue divided by the change in quantity produced. MC is equal to the change in total cost divided by the change in quantity produced.

At 1 unit of labor, MR = $40 - $0 = $40, MC = $320 - $0 = $320.

At 2 units of labor, MR = $70 - $40 = $30, MC = $640 - $320 = $320.

At 3 units of labor, MR = $90 - $70 = $20, MC = $960 - $640 = $320.

At 4 units of labor, MR = $100 - $90 = $10, MC = $1280 - $960 = $320.

At 5 units of labor, MR = $100 - $100 = $0, MC = $1600 - $1280 = $320.

The firm should produce where MR = MC to maximize profit. This occurs at 4 units of labor, where MR = MC = $320. Therefore, the firm should hire 4 units of labor to maximize profit.

Table 18-9 -Refer to Table 18-9.This Table Describes the Number of Baseballs