Consider a partial equilibrium model with two households with preferences given by u1(x1, m1) = 2 ln(x1 + 1/6) + m1 and u2(x2, m2) = 3 ln (x2+1/3)+m2, and two firms with cost functions for the production of good 1 given by c1(y1) = y1^2 and c2(y2) = y2^2 . Find the competitive equilibrium price for good 1, as well as the equilibrium demand of each household, the equilibrium supply for each firm, the households' utility in equilibrium, the firms' equilibrium profits, the consumer surplus, the producer surplus, and the total surplus.