Consider the one-period model we discussed in class. Suppose the representative consumer has preferences over consumption (c) and leisure (l), represented by the following utility function: u(c, l) = 2 ln(c) + ln(l). Her time endowment is h = 1. Suppose the lump-sum tax and government expenditure are both zero, G = T = 0. The production function of the representative firm is given by Y = zK 1 2 N 1 2 where the total factor productivity and capital are given by z = 2 and K = 9. (a) What is the Pareto Optimum allocation of consumption, leisure, working time, and aggregate output in this economy? (b) What is the wage rate in the competitive equilibrium to support the Pareto Optimum allocation (in other words, what should be the wage rate so that the competitive equi- librium achieves the same allocation as the Pareto Optimum allocation)? (c) Continuing from the previous part: what is the dividend income from the representative firm (i.e., the profit of the representative firm)