Consider an economy with 3 goods and 30 agents. There are 10 agents each with the utility function u (x1; x2; x3) = ln x1 + 2 ln x2 + 3 ln x3 and endowments e1 = (3; 2; 1).

Also, the other 20 agents each have the utility function u (z1; z2; z3) = 3 ln z1 + 2 ln z2 + ln z3 and endowments e2 = (1; 2; 3).

Normalize p3 = 1.

1) Derive all 3 market-clearing conditions. 2) Calculate the Walrasian equilibrium prices p1 and p2.