M is a monopolist selling goods G. M's cost function is c(y)=4y where y is the total production of G. Some of M's potential customers are members and get a member magazine with coupons. Member demand curve: X1(p, C)=42-(p-C) where X1(p, C) is member demand, p-C is the price they actually pay, p the official price, and C is price reduction with coupon.
Customers' without membership (and therefore no coupons) demand curve: X2(p, C)=32-(p/2)
With price discrimination, what will be the profit maximizing official price, p and what will C be?
Without price discrimination, what p and quantity will maximize profit?
How much would M be willing to pay for the coupon advertising if that is their only way to price discriminate?
The condition for profit maximizing monopolist in case of price discrimination is exhibited in this posting.