Consider a firm with the production function y(L) = L and assume p = 1. (a)...

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Consider a firm with the production function y(L) = √L and assume p = 1. (a) Find labor demand of a firm that is competitive on both labor and commodity market. Draw the labor demand curve. (b) Suppose that the inverse labor supply curve is w(L) = 2L. Find a competitive equilibrium employ- ment and wage rate. Mark the equilibrium in the graph. Consider the case of Monopsony: (c) Find a total labor cost of a monopsony that recognizes its impact on wage rate C₁ (L) = w(L)L and calculate marginal labor cost MCL (L). (d) Explain why marginal cost of labor MCL (L) is above wage w(L) for any L. Draw MCL (L) and CL(L) curves. (e) Set up a profit function of a monopsony and derive the optimality condition. Explain why the optimality condition holds. (f) Find optimal level of labor L and wage w. Mark them in a graph and compare with the competitive outcome from b). Is the result intuitive? Explain. Consider a firm with the production function y(L) = √L and assume p = 1. (a) Find labor demand of a firm that is competitive on both labor and commodity market. Draw the labor demand curve. (b) Suppose that the inverse labor supply curve is w(L) = 2L. Find a competitive equilibrium employ- ment and wage rate. Mark the equilibrium in the graph. Consider the case of Monopsony: (c) Find a total labor cost of a monopsony that recognizes its impact on wage rate C₁ (L) = w(L)L and calculate marginal labor cost MCL (L). (d) Explain why marginal cost of labor MCL (L) is above wage w(L) for any L. Draw MCL (L) and CL(L) curves. (e) Set up a profit function of a monopsony and derive the optimality condition. Explain why the optimality condition holds. (f) Find optimal level of labor L and wage w. Mark them in a graph and compare with the competitive outcome from b). Is the result intuitive? Explain.