Economists have considered the output y of a manufacturing process as a function of the size of the labor force n using the function
                                       y = kn^p,
where 0 < p < 1. The marginal product of labor, defined as dy/dn, measures the rate that output increases with the size of the labor force, and is a measure of labor productivity.

(a) Show that

(b) How can you tell from your answer to part (a) that as the size of the labor force increases, the marginal product of labor gets smaller? This is a phenomenon known as the law of diminishing returns, discussed more in the next chapter.

Transcribed Image Text:

dy dn kp n' -P n¹-p