You own a small business that repairs furnaces and air conditioners. The market
ID: 1206213 • Letter: Y
Question
You own a small business that repairs furnaces and air conditioners. The market is competitive so youmust charge the same price as all other firms - $50 per house visit. You can take on as many customersas you would like when you charge this price.
Your daily production function is given below, where K = the number of vans you have and L = thenumber of employees you have each day:
Q = F(K,L) = 10K2L1/2
(round down if you find a fractional unit of Q. For example, if you pick K and L such that Q=3.12 thenround down to Q=3 in this case)
You currently lease 2 vans and cannot change this in the short run. The daily wage for one of yourworkers is w=$250, and since there is a competitive market for labor you cannot change this either. The daily rental rate on one van is r=$100.
How many employees should you hire? (Please show and explain the math used)
Explanation / Answer
Q = 10K2L1/2
Given, K = 2
Q = 10 x 4 x L1/2
MPL = dQ / dL = 40 x (1/2) / L1/2 = 20 / L1/2
Optimal number of employees is found out when
Price x MPL = Wage rate
$50 x 20 / L1/2 = $250
L1/2 = 1,000 / 250 = 4
L = 16
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