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Suppose the representative firm has a production function Y = 20N and the representative consumer has the utility function u(c, `) = √ c + √ `. Also, let the government spend G = 2 financed by lump sum taxes of size T.
(a) What is the representative firm's demand for labor? What must be the equilibrium wage rate? What is the size of the firm's profit?
(b) What is the optimal allocation of the representative consumer? What is the supply of labor?
(c) Draw the labor market equilibrium in a graph. What is the equilibrium employment?
(d) Given the equilibrium is the labor market, is the final goods market in equilibrium as well? That is, is c + G = Y ?
(e) Use a general equilibrium graph (the one with the PPF and indifference curves) to show the effect of an increase in G on employment.
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