Question

A company has 600600 employees who work 150150 hours a month each. Each worker earns $18$⁢18 per hour. There is a profitable project the company would like to start, but it would require an additional 27,00027,000 working hours within three months to be completed, and all the employees are fully loaded with other projects. The company does not want to hire new staff; they would like the project to be completed by the current workforce instead.

Given that the wage elasticity of labor supply is 1.051.05, calculate the hourly wage the company should offer its employees to encourage them to work on the new project. Use the midpoint method and round to two decimal places throughout your calculations. Enter your answer in the box below.

Answer 1

Initial labor hours (L1) = 600 x 150 = 90,000

New quantity of labor (L2) = 90,000 + 27,000 = 117,000

Let new wage be W2.

Elasticity of labor supply = [(L2 - L1) / (L2 + L1)] / [(W2 - W1) / (W2 + W1)]

1.05 = [(117,000 - 90,000) / (117,000 + 90,000)] / [(W2 - 18) / (W2 + 18)]

1.05 = (27,000 / 207,000) / [(W2 - 18) / (W2 + 18)]

1.05 = [27,000 x (W2 + 18)] / [(207,000 x (W2 - 18)]

1.05 = (27,000W2 + 486,000) / (207,000W2 - 3,726,000)

217,350W2 - 3,912,300 = 27,000W2 + 486,000

190,350W2 = 4,398,000

W2 = $23.10