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How would i solve, Macro Economics (Williamson 5e), Chapter 5: Mathematical Appendix, Problem #1
For the closed-economy, one-period model, suppose that
U (C, l) = ln (C) + β × l, and
F (K, N) = zK^αN^ (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.