Question

Explain the relationship between marginal product and average product. Why can we expect marginal product to equal average product at average product’s maximum point?

Short answer

Marginal Product (MP) influences the Average Product (AP), causing it to increase when MP is greater and to decrease when MP is lesser. At the maximum point of AP, MP must equal AP; otherwise, the AP would either continue to increase (if MP was greater) or decrease (if MP was lower).

Step-by-step solution

Understanding the Concepts

The Marginal Product (MP) is the additional output that is produced by using one more unit of a particular input, while keeping other inputs constant. The Average Product (AP) is the output per unit of input, calculated by dividing the total output by the number of units of input used. Initially, as inputs increase, both MP and AP increase because of more efficient use of resources.

Relationship Between MP and AP

The relationship between Marginal Product and Average Product is such that when MP is greater than AP, the AP is increasing. Conversely, when MP is less than AP, AP is decreasing. This is because the additional output from the marginal unit is boosting the overall average or dragging it down, respectively.

Equalizing of MP and AP

When AP reaches its maximum, the additional output from the next unit of input (MP) will be exactly the same as the AP. This is the point where MP intersects AP. If MP were higher, AP would still be increasing. Likewise, if MP were lower, AP would start to decrease. Therefore, the point at which MP equals AP corresponds to the peak of the AP curve.

Key concepts

Marginal Product

Imagine a farmer working on the fields. When the farmer hires the first helper, the work gets done significantly faster due to better use of resources – this speed-up is what we refer to as the Marginal Product (MP). It represents the additional quantity of the output that results from using one more unit of an input, like labor or capital, while other inputs remain constant. MP can give insights into the efficiency of production. If the MP is rising, the last unit of input added is producing more output than the units before it, indicating improved production efficiency.

However, there’s a twist: as the farmer adds more helpers, they may start getting in each other's way. This is when the Law of Diminishing Returns kicks in, and the MP starts decreasing because each additional unit of input contributes less to the overall output. It is a crucial concept to understand when making decisions about scaling production.

Average Product

The Average Product (AP) tells the farmer how much each helper, on average, contributes to the total output. It's calculated by dividing the total output by the total number of units of input used. When the farm starts its operations, the AP increases with each new worker since they’re effectively using tools and resources together. However, this only continues up to a point.

As more workers flood the fields, they start stepping on each other's toes, and the average contribution each makes begins to drop. The AP is a fundamental measure that helps in evaluating the overall efficiency of all the inputs used during the production process. Knowing the point at which the AP reaches its peak can inform the farmer of the optimal number of workers to hire before efficiency begins to decline.

Production Function

Now, let's take the farmer's knowledge and apply it to a broader concept: the production function. A production function is a mathematical equation that tells us how much output we can expect from different amounts of various inputs. It maps out the relationship between inputs used in production and the resulting output.

Think of it like a recipe: if you know the amounts of flour, sugar, and butter you have, the production function is the recipe that tells you how many cookies you can bake. In a similar way, the production function enables economists and managers to predict output levels based on different combinations and amounts of inputs. Understanding the production function is vital for making strategic decisions in resource allocation and scaling production efficiently.

Managerial Economics

Managerial economics is where all these concepts – Marginal Product, Average Product, and Production Function – come into play in real-life decision-making. It is the application of economic theory to business management. It provides a toolbox for managers to make informed decisions to maximize profits and improve the efficiency of their organizations.

In our agricultural example, the farmer uses managerial economics when deciding how many workers to hire. By understanding the interplay between MP and AP, and knowing the production function of his farm, the farmer can optimize production to ensure that resources are not wasted, costs are minimized, and outputs are maximized. Managerial economics also involves analyzing market conditions, making pricing decisions, and assessing the risks and uncertainties of business operations, making it integral to successful business strategy.