In the theory of production, which law states that if we keep increasing the employment of one input while holding all other inputs fixed, a point will eventually be reached after which the marginal product of that input will start falling?

Introduction / Context:
This question focuses on a fundamental concept in production theory that explains how output responds when a firm changes the quantity of one input while keeping other inputs constant. Understanding this law is essential for analysing short run production functions, cost curves, and optimal use of factors of production. The law is frequently examined in introductory microeconomics and is closely related to the idea of diminishing returns.

Given Data / Assumptions:

• We are considering a production process with multiple inputs.
• Only one input is increased, while all other inputs remain fixed.
• The statement describes that eventually the marginal product of the variable input begins to decline.
• The options include two named laws and two general terms about time periods.

Concept / Approach:
The law described states that when additional units of a variable input are employed, with other inputs held constant, the additional output produced by each extra unit of that input will at some stage begin to decline. This is the law of diminishing marginal product, also known in some texts as diminishing marginal returns. The law of variable proportions is a broader concept that describes three phases of output behaviour as the variable input increases, including an initial phase of increasing returns and a later phase of diminishing returns. The Short Run and The Long Run refer to time periods in which some or all inputs can vary and are not themselves economic laws.

Step-by-Step Solution:
Step 1: Focus on the key phrase: marginal product of the input will start falling.Step 2: Recall that marginal product means the extra output from employing one more unit of the input.Step 3: The law that directly states this effect is the law of diminishing marginal product.Step 4: The law of variable proportions includes this idea but also covers earlier stages where marginal product may be rising, so it is more general.Step 5: The Short Run and The Long Run describe whether at least one input is fixed or all inputs are variable; they do not specify a law about declining marginal product.Step 6: Therefore, the most precise answer that matches the description in the stem is the law of diminishing marginal product.

Verification / Alternative check:
Standard microeconomics texts define the law of diminishing marginal product as stating that beyond some level of utilisation of a variable factor, with other factors fixed, the marginal product of that variable factor will diminish. They often illustrate this with an example of adding more workers to a fixed amount of land or machinery. Initially, output increases rapidly, but after a point, each additional worker adds less extra output than the previous one. This exactly matches the statement given in the question and confirms that the correct law is the law of diminishing marginal product.

Why Other Options Are Wrong:
Law of variable proportions: While related, this law is a broader framework and does not directly name the specific effect described as its main focus.

The Short Run: This refers to a time period in which at least one input is fixed, but it is not a law and does not guarantee diminishing marginal product.

The Long Run: This is a period during which all inputs can vary, and again, it is a time horizon concept, not the law described.

Common Pitfalls:
Many students confuse the law of diminishing marginal product with the general phrase law of variable proportions because both are taught together. A useful way to avoid confusion is to remember that the question here is focusing narrowly on the falling marginal product, which directly points to diminishing marginal product. The law of variable proportions encompasses the entire pattern of changes in total and marginal product as the variable input increases, so when a question is this specific, diminishing marginal product is the safer choice.

Final Answer:
The law described is the law of diminishing marginal product.