Consider a Monopoly with Inverse Demand Function P = 24

Essay

Consider a monopoly with inverse demand function p = 24 - y and cost function c(y)= 5y² + 4:
i)Find the profit maximizing output and price, and calculate the monopolist's profits.
ii)Now consider the case in which the monopolist has now another plant with the cost structure c₂(y₂)= 10y₂. How much will the monopolist produce in each plant, what is the price, and the total profits of the monopoly?
iii)Now suppose there is a technological change in the first plant and it has the following cost function: c₁ (y₁)
= 2y₁. How much will the monopolist produce in each plant and what is the price?