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3. PROFIT MAXIMIZATION (10 POINTS) You are operating a firm that uses labor (L) to produce widgets in a perfectly competitive market. The price of widgets is p = 3. It costs w = 2 to employ each unit of labor. Your firm's production function is y = 2In (L) where y is the number of widgets produced. (a) (3 POINTS) If the firm is maximizing profits, how many units of labor will your firm employ and how many widgets will your firm produce? (b) (2 POINTS) What is your firm's maximized level of profit? (c) (3 POINTS) Now say that the government has decided to impose a tax of 0.10 on each unit of labor that your firm hires. If the firm is maximizing profits, how many units of labor will your firm employ and how many widgets will your firm produce? Assume that the price of widgets is p = 3 and the pre-tax cost to hire labor is w = 2 per unit. How did the imposition of the tax influence your firm's demand for labor and widget output? (d) (2 POINTS) What is your firm's maximized level of profit after the imposition of the tax on labor? How did the tax on labor influence the profitability of your firm? Activate V