B2) Woolworths has two types of milk packages: 2 litres and 5 litres. There are two types of customers: small families and large families. There are 200 small families and 100 large families. A small family's value is 5 for the 2 litre milk and 6 for the 5 litre milk; a large family's value is 6 for the 2 litre milk and 10 for the 5 litre milk. Woolworths does not know whether a customer has a small family or large family. The marginal cost per litre is 1. Suppose the price for the 2-litre milk is P2, and the price for the 5- litre milk is Ps. If a family does not purchase milk, it gets a value of 0. a) What is the participation constraint for a small family to purchase the 2-litre milk? [1 mark] b) What is the incentive compatibility constraint for a small family to purchase the 2-litre milk? [1 mark] c) To maximize its profit, what prices P2 and Ps should Woolworths choose? [4 marks] d) Given the profit maximizing prices, what is Woolworths's profit? What is the total consumer surplus for the small families? What is the total consumer surplus for the large families? [4 marks] e) Are there other values of P2 and Ps that improve the total surplus (of Woolworths and all families) in part d)? If yes, give an example of such P2 and Ps. If no, explain why. [4 marks]