QUESTION 2: Consider an exchange economy with N agents and N goods called 1,...,N. Agent i has an endowment of e>0 units of good i. All agents derive utility from the consumption of each good and their utilities are continuously differentiable, strictly convex and symmetric. In particular, each agents utility function is U(x!,...,x")=A)*x! +.+*x".,A>0.

(a) Find the Walrasian equilibrium prices and consumption of each good by each agent. [10 marks]

(b) END Suppose there is a dictator who demands y units of each good with y=e/N.

(i) Define and explain k-disloyalty and consequently disloyalty. [10 marks]

(ii) Find conditions on e and N such that there is a Nash equilibrium where every agent is loyal to the dictator [20 marks]

(iii) Comment on the sustenance of this dictatorship as a function of the population size N and the per-capita initial endowment e. [10 marks]