Marginal revenue product

What Is Marginal Revenue Product?

Marginal revenue product (MRP) is the additional revenue generated by employing one more unit of a specific factor of production, typically labor or capital, while keeping all other inputs constant. It is a fundamental concept in microeconomics, falling under the broader financial category of factor pricing and resource allocation. Companies use marginal revenue product to determine the optimal quantity of inputs to maximize their profit maximization. It helps businesses understand how changes in their inputs affect their overall revenue and production.

History and Origin

The concept of marginal productivity, from which marginal revenue product derives, emerged in the late 19th century as a cornerstone of neoclassical economic theory. Economists such as John Bates Clark and Philip Henry Wicksteed were instrumental in its development. Clark, an American economist, notably contributed to the theory of marginal productivity, seeking to explain the distribution of income among factors of production like labor and capital from national output.⁸,⁷ His seminal work, "The Distribution of Wealth" (1899), elaborated on this theory within a theoretical model of perfect, static competitive equilibrium.⁶ This framework suggested that, under ideal conditions, each factor would be compensated according to its marginal contribution to the total product.

Key Takeaways

• Marginal revenue product (MRP) measures the revenue increase from adding one more unit of an input.
• Firms use MRP to make hiring and resource allocation decisions to maximize profits.
• It is calculated by multiplying the marginal physical product of an input by the marginal revenue generated from selling the additional output.
• The law of diminishing returns often means that MRP will eventually decrease as more units of an input are added.
• MRP helps explain the demand for factors of production in a competitive labor market.

Formula and Calculation

The marginal revenue product (MRP) is calculated by multiplying the marginal physical product (MPP) of a factor of production by the marginal revenue (MR) generated from the sale of one additional unit of output.

Where:

• (\text{MRP}) = Marginal Revenue Product
• (\text{MPP}) = Marginal Physical Product (the additional output produced by one more unit of input)
• (\text{MR}) = Marginal Revenue (the additional revenue earned from selling one more unit of output)

In a scenario of perfect competition, where a firm is a price taker, the marginal revenue (MR) is equal to the market price (P) of the output. In this specific case, the formula can also be expressed as:

Interpreting the Marginal Revenue Product

Interpreting the marginal revenue product involves comparing it to the cost of employing that additional unit of input. A firm will continue to hire or utilize a factor of production as long as its MRP is greater than or equal to its marginal factor cost (MFC). The marginal factor cost is the additional cost incurred by employing one more unit of a factor. For example, in the case of labor, the marginal factor cost is typically the wage rate.

If the marginal revenue product of an additional worker is $100, and their wage rate (MFC) is $80, the firm gains $20 by hiring that worker. Conversely, if the MRP is $70 and the wage is $80, the firm would lose $10 and would not hire that worker. The optimal point for a firm, leading to economic efficiency, is when MRP equals MFC. This principle underpins a firm's demand curve for labor or other inputs.

Hypothetical Example

Consider "EcoSolutions Inc.," a company that manufactures biodegradable packaging. The company currently employs 10 workers, and with these workers, they produce 1,000 units of packaging per day, selling each unit for $2.

EcoSolutions Inc. is considering hiring an 11th worker.

1. Current Output and Revenue: With 10 workers, output is 1,000 units, and total revenue is (1,000 \text{ units} \times $2/\text{unit} = $2,000).
2. Hiring the 11th Worker: After hiring the 11th worker, the total output increases to 1,080 units.
3. Calculate Marginal Physical Product (MPP): The additional output from the 11th worker is (1,080 - 1,000 = 80 \text{ units}). So, MPP = 80 units.
4. Calculate Marginal Revenue (MR): Since EcoSolutions sells each unit for $2, and we assume the price remains constant (as is often the case for a firm in a competitive market), MR = $2.
5. Calculate Marginal Revenue Product (MRP): Using the formula, MRP = MPP (\times) MR = 80 units (\times) $2/unit = $160.

If the daily wage for the 11th worker is, say, $150, then EcoSolutions Inc. would hire this worker because the marginal revenue product ($160) exceeds the wage ($150). If the wage were $170, the company would not hire the 11th worker as the cost outweighs the revenue generated. This example illustrates how the concept guides employment decisions based on the productivity of additional labor.

Practical Applications

Marginal revenue product is a cornerstone in various real-world economic and business decisions, particularly within the realm of supply and demand for inputs.

• Hiring Decisions: Businesses extensively use the concept of marginal revenue product to determine how many employees to hire. A firm will continue to add workers as long as the MRP of the last worker added is greater than or equal to the wage rate (marginal factor cost). This analysis helps ensure optimal staffing levels to achieve profit maximization.
• Resource Allocation: Beyond labor, MRP applies to other factors of production, such as machinery or raw materials. Companies assess the MRP of investing in new equipment or acquiring additional resources to ensure these investments yield sufficient returns.
• Wage Determination: In competitive markets, the theory suggests that the wage rate for a particular type of labor tends to align with its marginal revenue product. This connection is vital for understanding how wages are influenced by worker productivity. Recent data from the Federal Reserve, for instance, highlights how strong labor productivity gains can offset wage growth to temper inflationary pressures, indicating the crucial link between productivity and wages in the broader economy.⁵
• Economic Policy and Growth: Policymakers and international organizations like the International Monetary Fund (IMF) monitor productivity trends, including labor productivity, to gauge economic health and potential growth. Structural reforms aimed at improving productivity in areas like labor markets and education are often recommended to boost potential growth and job creation.⁴

Limitations and Criticisms

While a foundational concept, marginal revenue product theory faces several limitations and criticisms, primarily rooted in its underlying assumptions.

One major criticism is the assumption of perfect competition in both product and factor markets. In reality, many markets exhibit imperfections, such as monopolies, oligopolies, or monopsonies, where firms have significant market power. These conditions can distort the relationship between MRP and factor prices, leading to wages or other factor payments that do not precisely equal their marginal revenue product.³

Another critique revolves around the assumption of homogeneous units of labor or capital. In practice, workers possess diverse skills, experience levels, and productivity levels, making it challenging to precisely measure the marginal contribution of an "average" worker. Furthermore, the theory often assumes that factors of production are perfectly mobile and divisible, which is rarely the case in the real world. For example, it's difficult to divide a large piece of machinery into smaller, incremental units.

The "disentanglement problem" also poses a challenge: how does one precisely separate the unique contribution of a single additional unit of a factor when production is a result of the combined efforts of multiple interdependent inputs?² Attributing specific output solely to the "marginal" unit can be complex.

Moreover, real-world factors beyond marginal productivity influence hiring and wage decisions. Surveys, such as those conducted by the Federal Reserve Bank of Dallas, indicate that firms face various impediments to hiring, including a "lack of applicants," "lack of hard skills," and applicants "looking for more pay than offered."¹ These factors suggest that a firm's ability to hire is not solely based on a worker's calculated MRP, but also on market frictions and prevailing market equilibrium conditions. Critics argue that the theory, in its purest form, may oversimplify the complexities of modern labor markets and income distribution.

Marginal Revenue Product vs. Marginal Physical Product

Marginal revenue product (MRP) and marginal physical product (MPP) are closely related but distinct concepts in economics. The key difference lies in what they measure:

MPP focuses purely on the tangible increase in production volume. For example, if adding one more worker increases the number of widgets produced by 10, then the MPP of that worker is 10 widgets. Marginal revenue product takes this a step further by converting that physical output into its monetary value, considering the additional revenue earned from selling those 10 widgets. Therefore, MRP is the financial measure that directly informs a firm's decision-making regarding hiring and investment, as it directly ties to the firm's bottom line, whereas MPP focuses solely on production efficiency.

FAQs

What is the primary purpose of calculating marginal revenue product?

The primary purpose of calculating marginal revenue product is to help businesses make optimal decisions regarding the employment of factors of production, such as labor and capital. By comparing the MRP to the cost of an input (marginal factor cost), a firm can determine whether adding more units of that input will increase its overall profitability.

How does the law of diminishing returns relate to marginal revenue product?

The law of diminishing returns states that as more units of a variable input are added to a fixed input, the marginal physical product of the variable input will eventually decline. Since marginal revenue product is calculated by multiplying marginal physical product by marginal revenue, a declining MPP will lead to a declining MRP, assuming marginal revenue remains constant or also declines. This means that successive units of an input contribute less and less to total revenue.

Can marginal revenue product be negative?

Yes, marginal revenue product can theoretically be negative. If adding an additional unit of a factor of production leads to a decrease in total output (meaning a negative marginal physical product), and assuming marginal revenue is positive, then the marginal revenue product would be negative. This indicates that adding that unit of input would actually reduce total revenue, representing a significant opportunity cost and a clear signal for a firm not to hire or utilize that input.

Is marginal revenue product always equal to the wage rate?

In a theoretical model of perfect competition where firms are wage takers, the wage rate (marginal factor cost) will tend to equal the marginal revenue product in market equilibrium. However, in real-world scenarios, market imperfections, minimum wage laws, unionization, or other factors can cause the wage rate to deviate from the marginal revenue product. Firms will hire up to the point where MRP equals marginal cost of the input to maximize profits.