posted by jennifer .
Suppose a monopolist faces an inverse demand function P=100-1/2Q, and the monopolist has a fixed marginal cost of $20. How much more would the monopolist make from perfect price discrimination compared to simply producing where marginal revenue equals marginal cost?
Drawing a picture would help.
A normal monopolist would set MC=MR. Under this example, optimal Q=80, thus P=60. Total revenue is 80*60=4800. Total cost (represented by the area under MC between 0 and 80) is 80*20=1600. So, profit = 3200.
For the perfect price discriminator, total profit would be the area under demand, and above MC. In this example it is a simple triangle. Height=100-20=80, width =160. So area=profit=.5*80*160 = 6400