Consider a firm that produces output using a typical production function as discussed in the course, and that hires workers in a competitive labor market. 1. Explain what determines the firm's choice of its labor input. Use a suitable figure. Discuss how changes in the capital stock and in the wage affect the firm's choice of its labor input. Suppose that the firm uses a Cobb-Douglas production function Y KaN1-a In this case, the marginal product of labor is given by (1 a)K"N-a. The parameter a is 2/3, and the firm uses one unit of capital. 2. Calculate (show your steps) how the firm's labor input changes if the wage increases by 1%. 3. Calculate how the firm's labor input changes if the wage is unchanged, but the firm decides to double its capital stock