Emilie loves profiteroles. She makes a profiterole by combining one wit of chocolate sauce (say 8 fl az) and two puffs (stuffed with paste). She receives one unit of utility per profiterole. Bertrand just likes to mt. He receives one mat of utility pm puff or per unit of chocolate sauce. Bertrand and Emilie are on a diet that assigns points to food: p„ is the mumbo of points for a puff, and p, 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 pea is less then (or equal to) the point-value of their endowment. (1) Let al E Rs be the amount of chocolate sauce and e fl Its be the quantity of puffs consumed by consumer i (i is Emilie or Bertrand). Write down both agents' utility func.ons. (Note: Suppose any amount of profiteroles in H is possible.) (2) What kind of goods ace chocolate sauce and puffs for Bertrand? Shaw his edit femme curves on a graph. (3) What kind of goods are chocolate sauce and pulls for Emilie? Show her indiffer-ence curves on a graph. (9) 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 pulls (16 puffs). Represent this two-consumer, two-goad exchange economy in an Edgeworth box, remembering to indicate the endowment point. (5) Find the contract curve M this economy. (6) What H the equilibrium point in this Edgeworth box? What is the equilibrium paint ratio }Vol?