6) In each of the following problems we consider a two good two consumer exchange economy. Consumer i's utility function is given by uz(x,y) and endowments are denoted by 0;=(0;", 0'). In each of the problems below, do the following: i) Find set of pareto efficient allocations. ii) For each of the utility function below plot an indifference curve and find demand functions. iii) Find set of competitive equilibria. iv) Try and plot utility possibility frontier in each of the cases below. (a) U (x,y)= 2x+3y, 07=(10,1) U2(x,y)= 3x+3y, 02=(1,6) (b) U (x,y)= xy, 0;=(10,0) Uz(x,y)= x+y, 0z=(5,10) (c) U.(x,y)= xy, 0;=(8,16) U2(x,y)= xy, 02=(8,16) (d) U (x,y)= V(xy), 0,=(3,16) U2(x,y)= 5xy, 02=(15,8) 6) In each of the following problems we consider a two good two consumer exchange economy. Consumer i's utility function is given by uz(x,y) and endowments are denoted by 0;=(0;", 0'). In each of the problems below, do the following: i) Find set of pareto efficient allocations. ii) For each of the utility function below plot an indifference curve and find demand functions. iii) Find set of competitive equilibria. iv) Try and plot utility possibility frontier in each of the cases below. (a) U (x,y)= 2x+3y, 07=(10,1) U2(x,y)= 3x+3y, 02=(1,6) (b) U (x,y)= xy, 0;=(10,0) Uz(x,y)= x+y, 0z=(5,10) (c) U.(x,y)= xy, 0;=(8,16) U2(x,y)= xy, 02=(8,16) (d) U (x,y)= V(xy), 0,=(3,16) U2(x,y)= 5xy, 02=(15,8)