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) = y 2 1 and c2(y2) = y 2 2 . Find the demand function for good 1 of each household and the market demand function for good 1, and illustrate each household demand and the market demand curves in a graphic.