Consider an economy with two consumers, A and B and two goods, 1 and 2. The utility function of consumer A is given byU (x¹_a, x²_b)=x¹_a+4x¹_aand its initial allocation is (w¹_a,w²_a) = (127,94).The utility function of consumer B is given by U (x¹_b,x²_b) =x¹_b+16ln(x²_b) and its initial allocation is (w¹_b,w²_b) = (48,26).

a) Set upthe Pareto (or central planner) problem of this economy.

b)Draw the contract curve for this economy inside theEdgeworthbox.Indicate the value of the critical coordinates (extension of theEdgeworthbox axesand the values of anyintersectionof the contract curve with the box axes).

c)Now consider that these consumers operate in a competitive market (ie they are price takers).Find the demand functions for goods 1 and 2 from consumers A and B.

Find the competitive balance and indicate in the balance found:

d)What allocation of good 1 to consumer A (x¹_a)?

e)What allocation of good 2 to consumer A (x²_a)?

f)What allocation of good 1 to consumer B (x¹_b)?

g)What allocation of good 2 to consumer B (x²_b)?

h)What is the relative P1/P2 equilibrium price?