The marginal product of labor (MP_L) measures the additional output a firm produces by hiring one more worker, assuming other inputs remain constant. The MP_L indicates how much extra output the firm gains from employing an additional unit of labor.

However, firms are generally more concerned with the additional revenue generated by employing an extra worker. This is where the Value of the Marginal Product of Labor (VMP_L) becomes important.

The Value of the Marginal Product of Labor is defined as the monetary value of the additional output produced by an additional unit of labor. It is calculated by taking the marginal product of labor, measured in units of output, and multiplying it by the market price of the product to find the revenue. The result is expressed in terms of monetary units, reflecting the worker's contribution to the firm's total revenue.

In a perfectly competitive market, the firm is a price taker, meaning it sells its product at a fixed price, regardless of the quantity produced. The price remains constant, unaffected by changes in output. So, VMP_L is calculated by multiplying the marginal product of labor by the constant market price of the product being produced.

While the price remains fixed as output increases, the marginal product of labor declines continuously. As a result, the value of the marginal product of labor also decreases continuously, resulting in a downward-sloping VMP_L curve for labor.

The value-of-marginal-product curve represents the labor demand curve for a competitive, profit-maximizing firm.