Consider the decisions of a representative consumer whose preferences are given by u(C, 1) = aC + Blog l, in which C is the quantity of consumption and I is the quantity of leisure. The parameters a and 3 are positive. The consumer faces two constraints. The time constraint is given by 1 + N = 1 with Ns as the time spent working (or the labor supply). Further, consumers take wages as given (outside of their control) and obtain wage income equal to wNs. The budget constraint is C = w(1 1) + T, with as the real dividend income received from the representative firm and T as the real lump- sum taxes paid to the government. Assume for simplicity that T = 0. Assume that there is a representative firm in the economy. This firm takes the wage rate was given 4zNd0.5 -wNd. Nd is the labor demand of the and wants to maximize profits defined by = firm and z is a given productivity parameter. What is the optimal labor demand of the firm? What are the prices of consumption goods and leisure (pc and p, in order) in the competitive equilibrium?