Difficult# Price Discrimination: Splitting Hairs and Prices

MICRO-@U6$4Z

Brian is the only hair salon in town. He has monopoly power over haircuts in the city.

Brian faces two different demand curves. Men have a demand curve for haircuts of $P_M = 20 - Q_M$ where $P_M$ is the price that men pay and $Q_M$ is the number of haircuts that men buy. Women have a demand curve of $P_W = 30-\frac{1}{2}Q_W$, where $P_W$ is the price that women pay and $Q_W$ is the number of haircuts that women buy. Every haircut costs him $10$ to perform, and the fixed cost of running the shop is $100$.

Right now, Brian charges the same price for men and women, such that $P_M=P_W$, and maximizes profits as best as he can with a single price. However, next week, he will start charging men and women different prices, and maximizes profits as best he can with two prices.

How much will his profits **increase** next week?