All agents in the economy have preferences described by the following CES utility function: N U(c1,02, ...cN) E 20? = 019+ 03 + + 0% i=1 Where 0; denotes consumption of good i, for i = 1, ...N. N is the total number of goods available in the economy (and the total number of rms present in the economy), and 19 6 (0,1) is a parameter expressing substitutability across goods: \"high\" 19 denotes high substitutabilityj while \"low\" 19 denotes 10w substitutability, or high differentiation. Consumers in the economy maximize utility subject to the budget constraint: N Zing-cz- = I i=1 where pi denotes the price of good i, and I denotes income. The country is populated by L agents, and in equilibrium total consumption of a good must be equal to total production of that good: xi = Lci.Ci 9-1 Pi (1) where A is the Lagrange multiplier associated to the budget constraint. Plot the residual demand function (1) en the (ci, pi) plane. (b) Does the residual demand function depend on the number of firms? And on the prices charged by other firms? To answer this question, you can solve for A by plugging (1) into the budget constraint