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# 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?