For the closed-economy, one-period model, suppose that U (C, l) = min (C, β × l), and F (K, N) = αK + δN, where β > 0, α > 0, and δ > 0.
Determine consumption, employment, output, leisure, and the real wage in a competitive equilibrium, and explain your solutions. Also draw a diagram with the consumer’s preferences and the production possibilities frontier, and show the competitive equilibrium in this diagram.