answer with work shown.

Suppose that you know that a rm's production technology is described by the production function q = aI{Ll where the bar denotes the fact that the capital input is xed (i.e., the rm's decision horizon is short run), the parameter a > 0 and the parameter ['3 lies strictly between zero and one. The rm pays a xed price 7" for each unit of capital and a xed price w for each unit of labor. Given this information: 1. Find the marginal product of labor. 2. Find the average product of labor. 3. Find the short-run cost function. Show all your working. 4. Find the short-run average cost function. 5. Find the short-run marginal cost function. 6. Show that the marginal cost function, in terms of C], can be obtained by using the result that MC(q)=w/ M PL