There are I consumers in a pure exchange economy. Each consumer i has a utility function ui(xi,yi)=lnxi+lnyi(i=1,,I), where (xi,yi) is the consumption bundle consumed by consumer i. Let a denote the aggregate endowment of good x and b the aggregate endowment of goody in the economy. (a) Show that Pareto optimality requires that yi=(ab)xi for i= 1,I (b) Show that Walrasian equilibrium prices in this economy depend only on the aggregate endowment (a,b) and not on the distribution of the endowment among consumers. There are I consumers in a pure exchange economy. Each consumer i has a utility function ui(xi,yi)=lnxi+lnyi(i=1,,I), where (xi,yi) is the consumption bundle consumed by consumer i. Let a denote the aggregate endowment of good x and b the aggregate endowment of goody in the economy. (a) Show that Pareto optimality requires that yi=(ab)xi for i= 1,I (b) Show that Walrasian equilibrium prices in this economy depend only on the aggregate endowment (a,b) and not on the distribution of the endowment among consumers