Consider a 2-agent, 2-good pure exchange economy, where agents are denoted by superscripts and goods by subscripts. The endowments for the economy are 1 = 1 1 + 1 2 and 2 = 2 1 + 2 2 for goods 1 and 2, respectively, where is the endowment of good {1,2} for agent {1,2}. Consumption of goods 1 and 2 are denoted by 1 and 2, respectively, where the Edgeworth box for the economy is drawn with 2 on the vertical axis. Let 1 and 2 denote the allocations of goods 1 and 2, respectively, for agent 1, implying the corresponding allocations for agent 2 are 1 1 and 2 2. The utility functions are 1 = 1 2 1 for agent 1 and 2 = 1 2 1 for agent 2, where , (0,1).

2. {16 marks] Consider a 2-agent, Z-good pure exchange economy, where agents are denoted by superscripts and goods by subscripts- The endowments for the economy are E1 = e} + 912 and E2 = e; + eff for goods 1 and 2, respectively, where oil, is the endowment of good m 6 {1,2} for agent it 6 {1,2}. {Ionsurnption ofgoods 1 and 2 are denoted by x1 and 12, respectively, where the Edgeworth box for the economy is drawn with x; on the vertical axis. Let f1 and :2; denote the allocations of goods 1 and 2, respectively, for agent 1, implying the corresponding allocations for agent 2 are E1 f1 and E; 2. The utility functions are u1 = xfx'\" for agent 1 and u.2 = :tfxg' for agent 2, where 11,3 E (0,1). a. Show that the contract curve is given by the function: _ _ _ o was '2'\") ' (1 me + 03 am Verify that the contract curve connects the lower left and upper right corners of the Edgeworth box