For the closed-economy, one-period model, suppose that U (C, l) = ln (C) + β × l, and F (K, N) = zKαN 1−α , where β > 0, and 0 < α < 1.
Determine consumption, employment, output, leisure, and the real wage in a competitive equilibrium, and explain your solutions. Also, in this problem, show that the competitive equilibrium allocation is Pareto optimal.