Consider a representative firm that produces using capital (K) and labor (N), but that owns no capital. The firm can hire workers in the labor market at a wage w and can rent capital market at a rental rate r (that is, the firm can rent K units of capital for which it would have to pay rK). The production function of the firm is given by zF (K, N) where: F (K, N) = KαN β and α + β < 1. a) (2 points) Does the technology exhibit constant returns to scale? If not does it exhibit increasing returns, decreasing returns, or neither? b) (2 points) Pose the profit maximization problem of the firm. c) (2 points) Find the firm’s optimal capital and labor demand. Hint: You can combine the firm’s FOC taking their ratio (diving one by the other) to get the labor demand as a function of the capital. Then you can use this to replace in the FOC to get the capital demand as a function of prices and parameters. d) (2 points) Find the firm’s optimal profits. Hint: Use the firm’s FOC to replace for the prices (r and w), then replace for labor as a function of capital (that you found above) and finally replace for the optimal capital demand.