5. Draw an Edgeworth Box for an exchange economy with two consumers, John (J) and Kelly (K) and two goods, Apples (A) and Bananas (B). Put Apples on the horizontal and Bananas on the vertical. Put Kellys origin in the bottom left corner. Both J and K have strictly positive endowments of both goods with e_A^J + e_A^K > e_B^J + e_B^K . Show an endowment point in this economy where e_A^J + e_A^K and e_B^J + e_B^K

6. Using an Edgeworth Box and initial endowment allocation consistent with the previous question, show the set of allocations that are Pareto Improvements when J and K have preferences according to:

(a) U_k(A_k , B_k) = 2A_k + 3B_k

U_J (A_J , B_J ) = 5A_J + 2B_J

(b) U_K(A_K , B_K) = 2A_K + 3B_K

U_J (A_J , B_J ) = min {2A_J , 4B_J}

(c) U_K(A_K , B_K) = 2A_K + 3B_K

U_J (A_J , B_J ) = A_J² B_J³

7. Using an Edgeworth Box consistent with question 5, show the contract curve when J and K have preferences according to:

(a) U_k(A_k , B_k) = 2A_k + 3B_k

U_J (A_J , B_J ) = 5A_J + 2B_J

(b) U_K(A_K , B_K) = 2A_K + 3B_K

U_J (A_J , B_J ) = min {2A_J , 4B_J}

(c) U_K(A_K , B_K) = 2A_K + 3B_K

U_J (A_J , B_J ) = A_J² B_J³