1. Consider a two-good quasilinear economy with the following specifications. The two goods are good l and the numeraire good. There are I = 2 consumers, each of which has the same utility function: u(xi,m;)=ln(1+x;)+mi, where i is consumer i's consumption of good I, and m; is his consumption of the numeraire good. There are J=8 firms, each of which has the same cost function: c(q;)=4 Suppose that the initial endowment of the numeraire good is w;=1 for each consumer, so that the total endowment w=2. (There is no initial endowment of good l.) (a) Derive the demand function of good l for each consumer and the supply function of good I for each firm. (b) Derive the aggregate demand function and the aggregate supply function of good l. Also, derive the inverse aggregate demand function and the inverse aggregate supply function. () Find the competitive equilibrium, and compute the Marshallian aggregate surplus in this equilibrium. (d) Suppose that the government impose a tax of $ per unit on the firm. What is the competitive equilibrium under this tax? What is the Marshallian aggregate surplus now? (e) Is Marshallian aggregate surplus in (d) greater or less than your answer in (c)? (You should use a calculator to answer this question) 12 1. Consider a two-good quasilinear economy with the following specifications. The two goods are good l and the numeraire good. There are I = 2 consumers, each of which has the same utility function: u(xi,m;)=ln(1+x;)+mi, where i is consumer i's consumption of good I, and m; is his consumption of the numeraire good. There are J=8 firms, each of which has the same cost function: c(q;)=4 Suppose that the initial endowment of the numeraire good is w;=1 for each consumer, so that the total endowment w=2. (There is no initial endowment of good l.) (a) Derive the demand function of good l for each consumer and the supply function of good I for each firm. (b) Derive the aggregate demand function and the aggregate supply function of good l. Also, derive the inverse aggregate demand function and the inverse aggregate supply function. () Find the competitive equilibrium, and compute the Marshallian aggregate surplus in this equilibrium. (d) Suppose that the government impose a tax of $ per unit on the firm. What is the competitive equilibrium under this tax? What is the Marshallian aggregate surplus now? (e) Is Marshallian aggregate surplus in (d) greater or less than your answer in (c)? (You should use a calculator to answer this question) 12