Two firms in a grimy Ohio town produce the same product in a competitive industry. Each has an old factory using an old technology. It still pays to operate these factories but it would not pay to expand them. The only variable factor used by either firm is labor. Each firm pollutes the other and thus reduces the output of the other firm. The production functions of firms A and B respectively are Q a = L .5 a ( )Q b and Q b = L .5 b ( )Q a, where L .5 a and L .5 b are the square roots respectively of the amount of labor used by firms A and B. The wage rate of labor is $1 and the price of the firms output is $12.
a. If the two firms each maximize profits independently, what is their total output and how much quasi-rents do their factories earn?
b. If someone buys them both and maximizes joint profits, how much quasi-rent is earned in total?

Question

Two firms in a grimy Ohio town produce the same product in a competitive industry. Each has an old factory using an old technology. It still pays to operate these factories but it would not pay to expand them. The only variable factor used by either firm is labor. Each firm pollutes the other and thus reduces the output of the other firm. The production functions of firms A and B respectively are Q a = L .5 a (  )Q b and Q b = L .5 b (  )Q a, where L .5 a and L .5 b are the square roots respectively of the amount of labor used by firms A and B. The wage rate of labor is $1 and the price of the firms output is $12. 
a. If the two firms each maximize profits independently, what is their total output and how much quasi-rents do their factories earn?
b. If someone buys them both and maximizes joint profits, how much quasi-rent is earned in total?

Quizplus · Accepted Answer

The Answer of Two firms in a grimy Ohio town produce the same product in a competitive industry. Each has an old factory using an old technology. It still pays to operate these factories but it would not pay to expand them. The only variable factor used by either firm is labor. Each firm pollutes the other and thus reduces the output of the other firm. The production functions of firms A and B respectively are Q a = L .5 a (  )Q b and Q b = L .5 b (  )Q a, where L .5 a and L .5 b are the square roots respectively of the amount of labor used by firms A and B. The wage rate of labor is $1 and the price of the firms output is $12. 
a. If the two firms each maximize profits independently, what is their total output and how much quasi-rents do their factories earn?
b. If someone buys them both and maximizes joint profits, how much quasi-rent is earned in total?

Two Firms in a Grimy Ohio Town Produce the Same