Consider an economy with 2 goods and 2 identical agents, each of whom has the following utility function, 11(31, 3:2) = In 3:; + 2111332. The...

1. Consider an economy with 2 goods and 2 identical agents, each of whom has the following utility function, u (x1; x2) = ln x1 + 2 ln x2. The aggregate endowments of the 2 goods are given by (1; 2). Suppose there is a social planner who cares about agents equally.(a) [10 points] Set up the plannerís problem.

(b) [20 points] Calculate the first-best outcome (i.e., the social planner's solution).

2. Consider an economy with 2 goods and 2 identical agents, each of whom has thefollowing utility function, 11(31, 3:2) = In 3:; + 2111332. The aggregate endowments ofthe 2 goods are given by (1, 2). Suppose there is a. social planner who cares aboutagents equally. (a) [10 points] Set up the planner’s problem.(b) [20 points] Calculate the first-best outcome (11.6., the social planner’s solution).