Question: Consider an economy with one representative consumer and one representative firm. There is no government (no taxes). The consumer's utility function is U =

Consider an economy with one representative consumer and one representative firm. There 

Consider an economy with one representative consumer and one representative firm. There is no government (no taxes). The consumer's utility function is U = log(c)-N where c is consumption and N is labor supply. The consumer's budget constraint is c = wN + t in real terms. The representative firm has a standard Cobb-Douglas production function F(z,K,N) = zK N-4. Suppose z-1 and K=1 so that the production function is simplified to F(N) = N-4. Set up the labor market clearing condition and derive an equation that implicitly determines the equilibrium wage. %3D %3! %3D

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