Suppose the market demand for a good is = 120 0.5. The monopolist (total) cost function is = 20.

Find the single-price monopolist's profit-maximizing output, price, and profit.

Suppose the monopolist identifies two groups of customers that make up its demand. The first group, as a whole, has demand 1 = 60 0.11. The second group, as whole, has demand 2 = 60 0.42. The monopolist is able to charge a separate price to each group but the price of each unit for a group is the same for every unit. (There is also no two-part pricing). Find the price-discriminating monopolist's profit-maximizing outputs, prices, and total monopoly profit.

What rule does the monopolist use to decide which group pays the lower price for the good? Show that this rule is satisfied here.