Screening:

Problem 2. Screening: In class, we considered price discrimination via quality. The same model also works for price discrimination via lump sum discount (buy more at a lower price per unit). Consider a small yogurt shop that sells freshmade yogurt to customers. The shop owner is facing two types of customers and is currently designing a price menu and want to max. expected revenue by giving a larger discount to the customers who buy more. Buyer's utility function is given by: 11(1), q, t) = v - q p - q In which: 0 Her willingness to pay for quality: 1; E {1,2}. 0 q: quantity of yogurt she is going to buy 0 p: the price she has to pay for each unit she buys Seller has cost of production for each customer: C(q) = q2 The prot is given by: p - q C(q) Seller does not know buyer's willingness to pay but knows the distribution: Prob(v = 1) = g; Prob(v = 2) =% _ Solve for the second degree price discrimination pricing strategy. mint: Seller wants the low type to participate and does not want high type to pretend to be low type]