Emilie loves profiteroles. She makes a profiterole by combining one unit of choc

Question

Emilie loves profiteroles. She makes a profiterole by combining one unit of chocolate sauce (say 8 fl oz) and two puffs (stuffed with paste). She receives one unit of utility per profiterole. Bertrand just likes to eat. He receives one unit of utility per puff 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 pc 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 point-value of their endowment. Let x_i^c R_+ be the amount of chocolate sauce and x_i^D R_+ be the quantity of puffs consumed by consumer i (i is Emilie or Bertrand). Write down both agents utility functions. What kind of goods are chocolate sauce and puffs for Bertrand? Show his indifference curves on a graph. What kind of goods are chocolate sauce and puffs for Emilie? Show her indifference curves on a graph. 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 two-consumer, two-good exchange economy in an Edgeworth box, remembering to indicate the endowment point. Find the contract curve in this economy. What is the equilibrium point in this Edgeworth box? What is the equilibrium point ratio p_p/p_c?

Explanation / Answer

1.Let us denote profiterole by P, chocolate sauce by C, puff by T, utilities of Bertrand and Emilie by U1 and U2

Thus, U1=min(1C,2T) as they are consumed proportionally and from 1unit P 1unit U1 is derived.

U2=C+T as he receives utility from per puff and per chocholate.Thus, they are substitute unlike the complement as previous.

2. For Bertrand it is chocholate sauce and puffs are complements. Hence, the shape of his indifference curve is L shaped.

3. For Emilie the goods are substitutes. Hence, the shape of the indifference curve will be downwards sloping straight line.

4. ICs of Bertrand will be downwards sloping straight line and for Emilie it is L shaped. Lower left corner represents the origin of Bertrand and upper right corner is the origin of Emilie. Equilibrium points are those where L shaped ICs are tangent to downwards sloping straight line.

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