Problem
Consider an exchange economy with two consumers (A and B) and two goods, X and Y. Suppose each consumer has 100 units of each good. Each consumer has Cobb-Douglas preferences given by: U(X, Y) = XY.
i. Derive the equation of the contract curve.
ii. Find the competitive equilibrium price ratio. Determine whether a pareto-improving trade exists.
iii. Suppose consumer A's utility function is now U(X,Y) = X+2Y. Determine the competitive equilibrium price and allocations.