Two consumers, Annie and Belle, live on a desert island and consume cherries x1 and dates x2. Annie has preferences given by UA(x A 1 , xA 2 ) = min{x A 1 , xA 2 }, while Belle has preferences given by UB(x B 1 , xB 2 ) = 2x B 1 + x B 2 . Every year Annie is endowed with 1 cherry and 5 dates, while Belle is endowed with 5 cherries and 1 date.

(a) [5 marks] What is Belle's marginal rate of substitution of cherries for dates? How many dates is she willing to give up to get one more cherry?

(b) [5 marks] Define the concept of a Pareto efficient allocation.

(c) [5 marks] Define concept of the contract curve. Give an equation for the contract curve for this economy.

(d) [5 marks] What is the competitive equilibrium in this economy? Give the equilibrium allocation and prices.

(e) [5 marks] Now suppose that Annie is given an extra cherry before trade. Annie now has 2 cherries and 5 dates and Belle has 5 cherries and 1 date. What happens to the competitive equilibrium? Compare to your answer in part (d).