This is my question. Thank you.

(2) (Screening Problem) A monopolist decides both the price p and the quality q of the product he sells. Each buyer buys exactly one unit, but buyers vary in terms of their preferences for quality. There are two types of buyers: high-type with utility functions UH (q, t) = 2J5 p and lowtype with utility function UL (q,t) = p. Let the probability of drawing a hightype buyer is 0.2. The cost of production for quality level q is just q (i.e., C(q) = q). The monopolist attempts to maximize his revenue by offering a menu of contracts {(qL, pL) , ((1H, pH)}. Find the optimal screening contract for the monopolist