6. Why does a profit-maximizing firm hire workers up to the point where the wage equals the value of marginal product? Show that this condition is identical to the one that requires a profit-maximizing firm to produce the level of output where the price of the output equals the marginal cost of production. 7. Why is the short-run demand curve for labor downward sloping? 8. What mix of inputs should be used to produce a given level of output? 9. Suppose the firm is hiring labor and capital and that the ratio of marginal products of the two inputs equals the ratio of input prices. Does this imply that the firm is maximizing profits? Why or why not? 10. Suppose the wage increases. Show that in the long run the firm will hire fewer workers.