Question

A delivery service company hires messengers to deliver expensive goods around a wealthy city. Each messenger has a vehicle that he or she brings to the job. Therefore, the only input the company needs to choose is the number of messengers to hire per day. Because the items are expensive and often heavy, it may take several messengers (a team of messengers) to make a single delivery. The market for delivery services in the city is competitive, so the company charges a flat-rate competitive price per delivery (let P stand for that price). The market for messengers is also competitive, so the company pays its messengers a competitive daily wage (let wstand for the wage). The number of deliveries per day depends on the number of messengers. Specifically, the number of deliveries (y) depends on the number of messengers (2), according to the following function: y = 24/5 1st attempt Part 1 (1 point) Feedback See Hint Suppose the price for each delivery is $340 and the daily wage paid to each messenger is $68. If the firm wants to maximize profits, it will hire Ⓡ 12 messengers per day.

Answer 1

Answer

Part 1)

In order to maximize profit a firm hires that amount of labor such that Marginal revenue product = wage rate.

Wage rate = 68,

Marginal Revenue product is the additional revenue a firm earns when he hire one additional unit of labor.

Marginal revenue Product(MRP) = MP*P

where MP = Marginal Product of labor = dy/dx = (4/5)x^-1/5 and P = Price of output = 340

Hence, MRP = wage rate

=> 340(4/5)x^-1/5 = 68

=> x^1/5 = 4

=> x = 1024

Hence, he should hire 1024 messengers per day.