Consider an economy with two consumers, "A" and "B" and two goods, "1" and "2". The consumer utility function "A" is given by U(₁^A,₂^A) = ₁^A + ₂^A and its initial endowment is (₁^A,₂^A) = (120,90). The utility function of consumer B is given by U(₁^B,₂^B) = {18₁^B, ₂^B} and its initial endowment is (₁^B,₂^B)=(60,42). a) Assemble the Pareto (or central planner) problem of this economy. b) Draw the contract curve of this economy inside the Edgeworth box. Indicate the value of the critical coordinates (extension of the axes of the Edgeworth box and the values of any intersections of the contract curve with the axes of the box). c) Now consider that these consumers operate in a competitive market (i.e. they are price takers). Find the demand functions for goods "1" and "2" of consumers "A" and "B".