Please answer all subquestions with detailed steps thank you! Given a firm producing output using a typical production function we discussed in course, and 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.

Then, assume the firm uses a Cobb-Douglas production function = ^()^(1). In this case, the marginal product of labor is given by (1 )^()^().

The parameter is 2/3, and the firm uses one unit of capital.

1. Calculate (show your steps) how the firm's labor input changes if the wage increases by 1%.
2. Calculate how the firm's labor input changes if the wage is unchanged, but the firm decides to double its capital stock.