This exercise is a modication of our housing economy. Consider a world with a set H consisting of n houses held by an agent (the chief) who is interested only in gold and N merchants who own gold but are III 1 interested only in houses. Denote the chief as agent N + 1 and gold as good N+1. Gold is divisible but the houses are not. The initial bundle of the chief is (1,1,...,1,0) containing 0 units of gold and 1 unit of each house. His consumption set contains all bundles of the form (0,0,...,0,m). Each merchant i owns an initial amount m,> 0 of gold (suppose my > m > ... > m > 0), can consume only one house, and has a strict ordering over the houses a. Define the competitive equilibrium for this economy first in words and then formally. b. Find a competitive equilibria for this economy, if it exists. c. Check if First Welfare Theorem holds for this economy, i.e. whether each competitive equilibrium allocation is Pareto efficient or not.