Question

Suppose that two firms are producers of spring water, which can be obtained at zero cost. The marginal revenue for their combined output is MR =10-2Q where MR is marginal revenue and Q is the number of litres of spring water sold by both firms per hour. If the 2 producers act according to the oligopoly model, how much will their combined output be? How much is the market price of water per litre?

Answer 1

profit maximize condition will be achieved

at MR = MC

$10-2a = 0$

$2a = 10$

$a = 5$

total revenue = price $\times$ quantity

TR = PQ

TR = $\int$ MR $d\theta$

TR $= \int$$(10-2a)d\theta$

TR = $10a-a^2$

$p= \frac{TR}{a}$

$= \frac{(10-a^2)}{a}$

$= 10-a$

$p= 10-5$

$=5$

market price of water per liter = $5