1. Consider the following representative agent model. The representative consumer has preferences given by u(c, l) = c + Bl where c is consumption, is leisure, and > 0. The consumer has an endowment of one unit of time and ko units of capital. The representative firm has a technology for producing consumption goods, given by Y = 2K L-a where Y is output, z is total factor productivity, K is the capital input, L is the labor input, and 0 < a < 1. The market real wage is w and r denotes the rental rate on capital. Solve for all prices and quantities in a competitive equilibrium (there are two cases to consider).