2. Consider a static economy with a representative consumer and a representative firm. The representative firm produces according to y = zn, where z > 0 is total factor productivity, and n is labor employment. Production generates pollution p as a side effect outside of the control of the firm, according to p = vy for 0 0. Carefully explain your result. Suppose now a government which taxes production at the proportional rate 7, with the proceeds T redistributed to the consumer in a lump-sum fashion. Carefully define a competitive equilibrium. Still under the assumption that u(c,,p) = + 6 log p, compute the socially-optimal level of . Carefully explain your reasoning, and interpret your result. Are there alter- native policies which achieve the same goal? Explain. Answer the previous question, now assuming that u(c, , p) = log c+6 p. Explain how the policy induces the consumer to change behavior in this setting, in contrast to the one in the previous