A monopolist sells bottles of mineral water to two customers: the high demand customer's demand is described by q_h= 3802p_h, and the low demand customer's demand is described by q_l=150p_l. The total willingness to pay of a consumer forzunits is the area under their inverse demand curve tillzunits. The marginal cost of production is 0. Suppose the monopolist cannot distinguish between the two consumers.

(a)The monopolist is thinking about offering each of the customers two options:

(1) buyQ_x= 380bottles for a total payment of$x, or

(2) buyQ_y= 150bottles for a total payment of$y.

Whatxandyshould the monopolist set? Show your work.

(b)Suppose the monopolist hadmany customers, of which, a fractionnwere the high demand type, and1 - nwere the low demand type. What is the smallestnfor which the monopolist would only offer a 380-bottle package (at a suitably chosen price, not necessarilyx)? Show your work.