1. Suppose 50% of all agents in an economy have U=ln x + ln y, and the other 50% have U=2 ln x + ln y. All agents start with one unit of x and one unit of y. Find the general equilibrium relative prices and allocations.
The budget constraint for each agent is:
\(\omega_X P_X+\omega_Y P_Y \leqslant X P_X+Y P_Y\)
Where \(\omega_X=\omega_Y=1\)