Marginal physical product: Meaning, Criticisms & Real-World Uses

Marginal Physical Product: Definition, Formula, Example, and FAQs

The marginal physical product (MPP), also known as marginal product, is a fundamental concept in microeconomics that measures the additional output produced by adding one more unit of a specific input while keeping all other inputs constant³⁸, ³⁹. It quantifies the change in total product resulting from an incremental increase in a variable factor of production, such as labor or capital. Understanding the marginal physical product is crucial for businesses aiming for profit maximization and efficient resource allocation.

History and Origin

The concept of marginal physical product is deeply rooted in the broader marginal productivity theory, which gained prominence in the late 19th century³⁶, ³⁷. Economists like John Bates Clark and Philip Henry Wicksteed significantly developed this theory, building on earlier observations by thinkers such as Johann Heinrich von Thünen in the 1820s.³⁴, ³⁵ The idea that wages and other factor payments are linked to their contribution to output was not entirely new, with Adam Smith noting a relationship between wage rates and labor productivity.³³

The law of diminishing returns, a core principle that dictates the behavior of marginal physical product, has an even earlier history. It can be traced back to the mid-1700s, with Jacques Turgot being credited as one of the first economists to articulate this concept, particularly in agriculture.³¹, ³² David Ricardo and Thomas Malthus further applied and popularized the law of diminishing returns in the early 19th century, observing its implications for land rent and population growth.³⁰ These developments laid the groundwork for understanding how additional inputs affect production, forming the bedrock of modern production theory.

Key Takeaways

Marginal physical product (MPP) measures the additional physical output gained from adding one more unit of a variable input, holding other inputs constant.
MPP is a critical component of marginal analysis in microeconomics, helping businesses optimize resource use.
The law of diminishing returns states that beyond a certain point, the marginal physical product will eventually decrease as more units of a variable input are added to a fixed input.
Businesses use MPP to make informed decisions about hiring, investment, and production levels to minimize costs and maximize profits.
When MPP becomes negative, adding more of that input actually reduces total output.

Formula and Calculation

The marginal physical product (MPP) is calculated as the change in total output divided by the change in the quantity of the variable input.

For a variable input such as labor ((L)) and total output ((Q)):

MPP_L = \frac{\Delta Q}{\Delta L}

Where:

(\Delta Q) = Change in total output
(\Delta L) = Change in the quantity of labor (or other variable input)

For example, if a company increases its labor from 5 to 6 workers, and its total output increases from 100 units to 110 units, the marginal physical product of that additional worker is (110 - 100 = 10) units. This calculation helps a firm understand the productivity contribution of each additional unit of input.²⁹

Interpreting the Marginal Physical Product

Interpreting the marginal physical product involves understanding its relationship with total output and the implications of the law of diminishing returns. Initially, as more units of a variable input are added, the MPP may increase due to factors like specialization and better utilization of fixed resources.²⁷, ²⁸ This is a phase of increasing marginal returns.

However, beyond a certain point, the marginal physical product will begin to decline.²⁶ This signifies the onset of the law of diminishing returns, where each additional unit of input contributes less to the total output than the previous one.²⁵ For instance, if adding a fifth worker to a small bakery with limited ovens leads to less additional output than the fourth worker, the marginal physical product is diminishing. It is crucial to note that diminishing returns do not imply a decrease in total output, only that the rate of increase in total output is slowing.

Eventually, adding too much of a variable input to fixed inputs can lead to a negative marginal physical product, meaning that total output actually decreases. This occurs when additional inputs hinder production, perhaps by causing congestion or inefficiencies.²³, ²⁴ Businesses typically aim to operate in the region of diminishing but positive marginal physical product to optimize their production function.

Hypothetical Example

Consider a small T-shirt printing business with a fixed number of printing machines. The owner wants to determine the optimal number of employees to hire.

0 employees: 0 T-shirts
1 employee: 10 T-shirts
2 employees: 25 T-shirts ((\Delta Q = 15); MPP = 15)
3 employees: 45 T-shirts ((\Delta Q = 20); MPP = 20)
4 employees: 60 T-shirts ((\Delta Q = 15); MPP = 15)
5 employees: 70 T-shirts ((\Delta Q = 10); MPP = 10)
6 employees: 75 T-shirts ((\Delta Q = 5); MPP = 5)
7 employees: 73 T-shirts ((\Delta Q = -2); MPP = -2)

In this scenario:

Adding the second and third employees leads to increasing marginal physical product (15 and 20, respectively), possibly due to improved workflow and specialization.
Adding the fourth, fifth, and sixth employees shows diminishing marginal physical product (15, 10, and 5). The workers are still contributing to total output, but at a decreasing rate, perhaps because they start sharing machines or getting in each other's way.
Adding the seventh employee results in a negative marginal physical product (-2), meaning total output declines. This indicates severe overcrowding or coordination issues, making the additional worker counterproductive.

The business owner would likely aim to operate with 6 employees to maximize total output, as adding a seventh worker would reduce production. This example illustrates how the marginal physical product informs decisions about scaling operations.

Practical Applications

Marginal physical product analysis is a vital tool for decision-making across various economic and business contexts:

Production Planning: Businesses use MPP to determine the optimal level of inputs, such as labor or raw materials, to achieve desired output levels without incurring excessive costs. By analyzing the MPP of different factors, firms can identify inefficiencies and adjust their production processes.²¹, ²²
Hiring Decisions: A company evaluates the marginal physical product of an additional worker against the marginal cost of hiring that worker (e.g., wages) to ensure that the worker's contribution to output justifies their expense.¹⁹, ²⁰ This directly influences labor market dynamics and optimal employment levels.
Investment Strategy: Understanding the marginal physical product of capital (MPPK) helps firms decide on investments in machinery, technology, and infrastructure. For instance, research indicates that the marginal product of capital can vary significantly across countries, with implications for global capital flows and economic development.¹⁸
Resource Allocation: Governments and organizations can use marginal product concepts in broader economic planning to allocate scarce resources efficiently across different sectors or projects, aiming to maximize overall societal output or specific development goals. This applies to sectors like agriculture, where diminishing returns to land or labor are critical considerations.¹⁷

Limitations and Criticisms

Despite its wide application, the marginal physical product theory and the broader marginal productivity theory face several limitations and criticisms:

Unrealistic Assumptions: A primary criticism is that the theory often relies on assumptions that do not hold true in the real world, such as perfect competition, homogeneous factors of production, and constant technology.¹⁵, ¹⁶ For instance, laborers are rarely homogeneous or perfectly interchangeable, and market conditions are frequently imperfect.¹⁴
Measurement Challenges: In complex, large-scale production environments, it can be extremely difficult to isolate and measure the exact marginal physical product of a single additional unit of input, especially when multiple factors are used jointly.¹², ¹³ The productivity of one factor often depends on the quality and quantity of other factors, making precise attribution challenging.¹¹
Short-Run Concept: The law of diminishing returns, which underpins the behavior of MPP, is primarily a short-run concept where at least one factor of production is fixed.¹⁰ In the long run, all factors can be varied, allowing firms to adjust their scale and potentially avoid sustained diminishing returns.
Ignores Externalities and Market Imperfections: The theory may not fully account for external factors, such as government regulations, labor unions, or market power, which can significantly influence wages and factor prices independently of marginal product.⁸, ⁹
Ethical Concerns: Some critics question whether marginal physical product can serve as a just basis for income distribution, arguing that it does not necessarily reflect the "true" contribution of an individual or factor, especially in situations with non-constant returns to scale.⁶, ⁷

Marginal Physical Product vs. Law of Diminishing Returns

While closely related, marginal physical product and the Law of Diminishing Returns are distinct concepts. Marginal physical product is a measure—the actual additional output from one more unit of input. The law of diminishing returns, conversely, is a principle or observation that describes the behavior of the marginal physical product. It states that, eventually, as more units of a variable input are added to a fixed input, the marginal physical product will decline. In essence, the law of diminishing returns explains why the marginal physical product curve typically slopes downward after a certain point. A decreasing marginal physical product is the direct manifestation of the law of diminishing returns taking effect within a production process.

FAQs

Q1: What is the difference between marginal physical product and average physical product?
A1: Marginal physical product (MPP) measures the additional output from one more unit of a variable input. Average physical product (APP), on the other hand, is the total output divided by the total quantity of the variable input used. MPP focuses on the increment, while APP focuses on the overall per-unit productivity.

⁵Q2: Can marginal physical product ever be negative?
A2: Yes, marginal physical product can be negative. This occurs when adding an additional unit of a variable input actually causes total output to decrease. This usually happens when the fixed inputs become severely overcrowded or over-utilized, leading to inefficiencies and disruptions in the production process.

³, ⁴Q3: How does marginal physical product relate to firm decisions?
A3: Firms use marginal physical product to make crucial decisions regarding production levels and input utilization. By comparing the marginal physical product of an input to its cost and the revenue it generates, firms can determine the optimal quantity of that input to employ to maximize profitability and achieve economic efficiency.¹, ²