Q.What is the marginal product of an input?
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Start your 14-day free trial to unlock the full solution →The marginal product of an input is the additional output generated by employing one more unit of that input, while keeping all other inputs constant.
In economics, particularly when studying the theory of production, we are interested in how output changes as we vary the amount of inputs used. The concept of "product" refers to the total quantity of goods or services produced. When we talk about the marginal product of an input, we are focusing on the change in this total output.
Imagine a firm that uses various inputs like labour, capital, and raw materials to produce a good. If the firm decides to increase the use of one specific input, say labour, while keeping all other inputs (like the number of machines or the factory size) fixed, how much additional output will it get? This "additional output" is precisely what the marginal product measures. It helps firms understand the productivity of each additional unit of an input and make decisions about optimal resource allocation.
The marginal product of an input is defined as the change in total product (or total output) resulting from a one-unit change in the quantity of that specific input, assuming all other inputs remain unchanged. For example, if a factory adds one more worker to its existing team, and the total number of units produced increases, the increase in output is the marginal product of that additional worker.
The marginal product of an input (e.g., labour, ) is calculated as:
where is the marginal product of labour, is the change in total product, and is the change in the quantity of labour.
Alternatively, if we consider discrete units, the marginal product of the -th unit of an input is:
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