EXERCISE 5 Emilie loves proteroles. She makes a proterole by combining one unit of chocolate sauce (say 8 oz) and two puffs (stuffed with paste). She receives one unit of utility per proterole. Bertrand just likes to eat. He receives one unit of utility per pull or per unit of chocolate sauce. Bertrand and Emilie are on a diet that assigns points to food: pp is the number of points for a puff, and 33C is the number of points for a unit of chocolate sauce. They would simply like to maintain their current weight, so the diet rules are as follows: They can consume any combination of chocolate sauce and puffs as long as the total number of points is less than (or equal to) the pointvalue of their endowment. (1) Let w: E R+ be the amount of chocolate sauce and :05 e R+ be the quantity of puffs consumed by consumer i (2' is Emilie or Bertrand). Write down both agents' utility functions. (Note: Suppose any amount of proteroles in R+ is possible.) (2) What kind of goods are chocolate sauce and puffs for Bertrand? Show his indif ference curves on a graph. (3) What kind of goods are chocolate sauce and puffs for Emilie? Show her indiffer ence curves on a graph. (4) Suppose that Emilie and Bertrand decide to have a private party. Bertrand brings one bottle of chocolate sauce (8 units) and Emilie brings one box of puffs (16 puffs). Represent this twoconsumer, twogood exchange economy in an Edgeworth box, remembering to indicate the endowment point. (5) Find the contract curve in this economy. (6) What is the equilibrium point in this Edgeworth box? What is the equilibrium point ratio pit/pg