Table 30.2 shows how many hairstyling appointments a hair salon can schedule per week based on the number of stylists.In the spaces provided, compute the marginal physical product (MPP) of the hair stylists, total revenue, and marginal revenue product of the stylists, assuming that a hair stylist charges $60 per appointment.In Table 30.2, suppose a hairstylist is paid $600 per week.How many hairstylists should a profit-maximizing salon hire?

Question

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To find the marginal physical product (MPP), we need to calculate the additional appointments that each additional stylist can schedule. This is found by taking the difference of the number of appointments between each number of stylists:

MPP = ΔOutput / ΔInput

For example, when going from 1 stylist to 2, the MPP is 55 - 35 = 20.

Using this method, we can fill in the entire MPP column in Table 30.2, which ranges from 20 to 5 as the number of stylists increases.

To find total revenue, we simply multiply the number of appointments by the price per appointment ($60):

TR = Price x Output

For example, when there are 3 stylists, the total revenue is 225 x 60 = $13,500.

To find the marginal revenue product (MRP) of the stylists, we need to calculate the additional revenue that each additional stylist brings in:

MRP = ΔTR / ΔInput

For example, when going from 2 to 3 stylists, the MRP is ($12,000 - $9,000) / (3 - 2) = $3,000.

Using this method, we can fill in the entire MRP column in Table 30.2, which ranges from $3,000 to $600 as the number of stylists increases.

To find the profit-maximizing number of hairstylists, we want to hire until the marginal revenue product equals the wage rate ($600):

MRP = Wage

For example, when there are 3 stylists, the MRP is $1,800. Since this is greater than the wage rate of $600, the salon should continue to hire more stylists. However, when there are 4 stylists, the MRP drops to $600, which is equal to the wage rate. Therefore, the profit-maximizing number of hairstylists is 3.

Table 302 Shows How Many Hairstyling Appointments a Hair Salon Can