Question

"According to the marginal productivity theory, the \(V M P_{L}=M R P_{L}\) is the firm's demand curve for labour, when labour is the single variable factor'. Comment.

Short answer

Based on the Marginal Productivity Theory and understanding the concepts of Value of Marginal Product of Labor (VMPL) and Marginal Revenue Product of Labor (MRPL), we can write a short answer as follows: The statement "According to the marginal productivity theory, the VMPL = MRPL is the firm's demand curve for labor, when labor is the single variable factor" is accurate in the context of a perfectly competitive market. In such a market structure, the price of the output (P) remains constant, and firms maximize profit by hiring workers until VMPL equals MRPL. In this scenario, the VMPL curve represents a firm's demand curve for labor. However, it is crucial to consider the specific market structure and other factors influencing output prices, as they may affect the relationship between VMPL and MRPL and, consequently, the demand curve for labor.

Step-by-step solution

Define Marginal Productivity Theory

The Marginal Productivity Theory states that a firm will hire workers until the value of the marginal product of labor (the additional output generated by hiring one more worker) is equal to the cost of hiring that worker. In other words, the firm will continue to hire workers as long as the additional revenue generated by hiring the worker is greater than the wage paid to that worker.

Understanding Value of Marginal Product of Labor (VMPL)

The Value of Marginal Product of Labor (VMPL) is the additional revenue a firm receives by employing one more unit of labor, holding all other factors of production constant. It is calculated by multiplying the marginal product of labor (MPL) by the price of the output (P). The formula for VMPL is: VMPL = MPL × P

Understanding Marginal Revenue Product of Labor (MRPL)

The Marginal Revenue Product of Labor (MRPL) is the additional revenue a firm receives by employing one more unit of labor, holding all other factors of production constant, and considering the changes in the price due to the additional production. Unlike VMPL, MRPL takes into account the diminishing marginal returns which can cause the price of output to decrease as production increases. The formula for MRPL is: MRPL = ΔTR / ΔL where ΔTR represents the change in total revenue, and ΔL represents the change in the quantity of labor.

Relationship between VMPL and MRPL in Perfect Competition

In a perfectly competitive market, the price of the output (P) remains constant, no matter the quantity produced. This is because individual firms are price takers and cannot influence the market price. Therefore, in perfect competition, firms will maximize profit by hiring workers until VMPL = MRPL. Under these conditions, a firm's demand curve for labor is determined by the VMPL curve, as it shows the additional value generated by each unit of labor.

Comments on Statement

In conclusion, the statement "According to the marginal productivity theory, the \( VMPL = MRPL \) is the firm's demand curve for labor, when labor is the single variable factor" is accurate in the context of a perfectly competitive market. In this market structure, VMPL and MRPL are equal due to constant output prices, and the VMPL curve illustrates a firm's demand for labor. However, it is essential to consider the specific market structure and any other factors influencing output price, which may affect the relationship between VMPL and MRPL and therefore the demand curve for labor.