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: (, ,) =
• In which:

1. Her willingness to pay for quality: {1,2}.
2. q: quantity of yogurt she is going to buy
3. p: the price she has to pay for each unit she buys

• Seller has cost of production for each customer: () = 2
• The profit is given by: ()
• Seller does not know buyer's willingness to pay but knows the distribution: ( = 1) = 4/5 ; ( = 2) = 1/5 .

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.]