For this and a and b problems, 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. a.  Find the supply function for good 1 of each firm and the market supply function for good 1, and illustrate each firm supply

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For this and a and b problems, 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.


a.  Find the supply function for good 1 of each firm and the market supply function for good 1, and illustrate each firm supply and the market supply curves in a graphic.

b.  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.

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