Consider an endowment economy with two people, Chris and Jane, who consume only two goods X and Y . Chriss utility is given by U (Xc; Yc) = Xc2Yc while Janes utility is given by U (Xj;Yj) = Xj2Yj2. Chriss endowment is Xc = 20 and Yc = 30 while Janes endowment is Xj =50andYj =20.

(a) Derive expressions for Chris and Janes marginal rate of substitution.

(b) Derive an expression for the Contract Curve in terms of Janes consumption of Xj and Yj.

(c) Is the initial endowment of Chris and Jane on the Contract Curve?

(d) Assuming the price of Y is one, py = 1, and the price of X, px; is unknown, write separate expressions for Chriss and Janes endowment income.

(e) Derive Janes demand for X and Y . You do not need to use a Lagrangian to answer this question.

(f) Using Chris and Janes demands, solve for the equilibrium price of X, px, remembering that both of their incomes are endowment incomes.