Consider a simple static macroeconomic competitive equilibrium model, a representative consumer's preference isU(c, l) = (1) log (c) +log (1N), where0< <1.and a representative firm's production function isY=zK^()N^(1),where0< <1.Suppose government collectsnotaxes in this economy.

(a) Show the competitive equilibriumN=(1+)/(1+ )

(b) Calculate the equilibrium consumption and wage for this economy.