3. (20 points) [VD] Suppose there are two kids in an endowment economy (ie. their parents are the ones who give them stuff), Ann and Jan, with utility functions: [1,: VS; X If UA=4XSA+4XtA where S is the number of stickers and t is the number of toys. Suppose Ann's parents give her 8; = 12 stickers and e; = 8 toys, while Ian's parents give her a} = 6 stickers and e} = 12 toys. (a) (5 points) [VD] Provide a rough sketch of the edgeworth box, be sure to include the endowment and a rough approximiation of the utility functions- (b) (5 points) [VD] What is the contract curve here (note: be careful, there is a discontinuity here)? Add it to your sketch and be sure to label it. (c) (4 points) [VD] Given their inital endowments, what would the outcome be if the girls were allowed to trade in a competitive market equilibrium (hint: do not over think this, if you nd a simple solution, you are likely to be correct. Also, make sure to indicate both prices and the quantities). (d) (2 points) [VD] Suppose their teacher felt it would be better if each person was given the exact same (i.e. $1 = 9 and 3;, = t; = 10). Explain why the girls would never remain at this outcome if allowed to trade. (e) (4 points) [VD] What does it mean for an outcome to be Pareto efficient? Why do economists focus so much on the idea of Pareto efficiency (explain in your own words and if using someone else's words, remember to give citation/ attribution)