Question: Consider an economy with a production function given by = 0.5 0.5 , where A is the total factor productivity (TFP), K is the capital

Consider an economy with a production function given by = 0.5 0.5 , 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 also that A=100. a) Write the firm's problem of choosing labor demand. Express the firm's demand for labor as a function of the real wage. b) Assume labor supply is perfectly inelastic and fixed at = 25. 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. c) Suppose the economy faces a positive productivity shock and TFP is now A=125. Display graphically the new labor demand function. What are now the equilibrium values of employment and the real wage? d) Compute the total output when A=100 and when A=125. What is the output's growth rate? Compare that growth rate with the growth rate of A. How does the growth rate of output per capita compare to the growth rate of A? Explain carefully

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