Question: The Bergen Company and the Gutenberg Company are the only two firms that produce and sell a particular kind of machinery. The demand curve for their product is

P = 580 – 3Q

where P is the price (in dollars) of the product, and Q is the total amount demanded.

The total cost function of the Bergen Company is

TC_B = 410Q_B

where TC_B is its total cost (in dollars) and Q_B is its output. The total cost function of the Gutenberg Company is

TC_G = 460Q_G

where TC_G is its total cost (in dollars) and Q_G is its output.

a. If these two firms collude and they want to maximize their combined profits, how much will the Bergen Company produce?

b. How much will the Gutenberg Company produce?

c. Will the Gutenberg Company agree to such an arrangement? Why or why not?