Consider the following:

(i) Suppose labor and capital are complements in production. Explain why a firm's long-run demand for labor is more elastic than its short-run demand.
(ii) Suppose labor and capital are substitutes in production. Will the firm's long-run demand for labor still be more elastic than its short-run demand? Why or why not?

(i) Consider an increase in the wage rate. The short-run demand curve shows that the amount of labor employed will fall. If labor and capital are substitutes in production, less labor implies that the marginal revenue product of capital falls. Thus, the firm uses less capital, which lowers the marginal revenue product of labor. The amount of labor used is further reduced, and the cycle repeats until a long-run equilibrium is reached.
Therefore, in the long run, the quantity of labor hired falls more than in the short run, making long-run demand the more elastic.
Yes, long-run demand for labor is more elastic than short-run demand in the case where labor and capital are substitutes-the cycle is different but the result is the same. When the wage rate rises and the amount of labor falls, the marginal revenue product of capital (and thus the demand for capital) will rise. The firm will use more capital, and in the substitute case, this reduces the marginal product of labor. The firm responds by using less labor, and the cycle repeats. Less labor and more capital will be employed in the long-run equilibrium than in the short-run equilibrium.