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 fresh-made 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: u(v,q,t) = v.q-p:q In which: o Her willingness to pay for quality: v {1,2}. o q: quantity of yogurt she is going to buy o p: the price she has to pay for each unit she buys Seller has cost of production for each customer: c(q) = q2 The profit is given by: p.q- c(q) Seller does not know buyer's willingness to pay but knows the distribution: Prob(v = 1) =>; Prob(v = 2) = Solve for the second degree price discrimination pricing strategy. [Hint: Seller wants the low type to participate and does not want high type to pretend to be low type.] 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 fresh-made 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: u(v,q,t) = v.q-p:q In which: o Her willingness to pay for quality: v {1,2}. o q: quantity of yogurt she is going to buy o p: the price she has to pay for each unit she buys Seller has cost of production for each customer: c(q) = q2 The profit is given by: p.q- c(q) Seller does not know buyer's willingness to pay but knows the distribution: Prob(v = 1) =>; Prob(v = 2) = Solve for the second degree price discrimination pricing strategy. [Hint: Seller wants the low type to participate and does not want high type to pretend to be low type.]