1. Labor Market
Consider an economy with production function given by Y = AK0.5L0.5 where A is the total factor productivity (TFP), K is the capital stock and L is the labor input. For simplicity assume capital is fixed and equal to 1. Assume A=150.
Write the firm’s problem of choosing labor demand. Derive the demand for labor as a function of the real wage.
Assume labor supply is inelastic and fixed at L̄ = 100. Find the equilibrium values of the wage and the employment level for this economy. Display graphically the labor supply and the labor demand curves. Carefully label your graph.
Suppose the economy faces a positive productivity shock and TFP is now A=200. Display graphically the new labor demand function. What are the equilibrium values of employment and the real wage?
Compute the total output when A=150 and when A=200. What is the output’s growth rate? Compare that growth rate with the growth rate in A. How does the growth rate of output per capita compares to the growth rate in A? Explain carefully.
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