How to Find Marginal Revenue on a Graph

Marginal revenue represents the additional income a business earns from selling one more unit of its product. This concept is fundamental for businesses making informed decisions about production levels and pricing strategies. Understanding how selling an extra unit impacts overall revenue helps companies determine the most profitable quantity of goods to produce and optimize their output.

Understanding Key Revenue Curves

To understand marginal revenue visually, it’s helpful to first understand the foundational curves displayed on a graph. The Total Revenue (TR) curve illustrates the entire income a business generates from selling a given quantity of goods. This total revenue is calculated by multiplying the price of each unit by the total number of units sold. For a typical firm that must lower its price to sell more units, the total revenue curve usually begins at zero, increases to a maximum point, and then declines as sales continue to expand beyond that optimal level.

The Demand Curve, often labeled as the Average Revenue (AR) curve, shows the relationship between the price of a product and the quantity consumers are willing to purchase. This curve slopes downwards, reflecting the economic principle that as the price of a good decreases, the quantity demanded by consumers increases. Each point on this curve indicates the price per unit that consumers are willing to pay for a specific quantity. On these graphs, the quantity of goods sold is plotted on the horizontal X-axis, while the price or revenue is represented on the vertical Y-axis.

Locating Marginal Revenue on a Graph

On a graph, the Marginal Revenue (MR) curve has a distinct relationship to the Demand (Average Revenue) curve, especially when the demand curve is depicted as a straight line. For such a linear demand curve, the marginal revenue curve will also be a straight line. Both the demand curve and the marginal revenue curve will originate from the exact same point on the vertical price or revenue axis.

However, as the quantity of goods increases, the marginal revenue curve descends at a rate twice as steep as that of the demand curve. This means that for every unit increase in quantity, the marginal revenue drops by a greater amount compared to the price on the demand curve. A direct consequence of this steeper decline is that the marginal revenue curve will intercept the horizontal quantity axis at precisely half the quantity where the demand curve intersects it. This visual characteristic provides a clear method for plotting the marginal revenue curve once the demand curve is known.

Interpreting Marginal Revenue Visually

Interpreting the marginal revenue curve visually provides significant insights into a firm’s revenue dynamics. The marginal revenue curve lies below the demand curve, with the only exception being the very first unit sold where both curves coincide. This position below the demand curve occurs because to sell an additional unit, a firm needs to lower the price, not just for that new unit, but for all previous units sold as well. The revenue lost on the prior units due to the price reduction causes marginal revenue to be less than the price of the additional unit.

The specific points on the marginal revenue curve carry implications for total revenue. When the marginal revenue curve is positive, it indicates that selling more units will continue to increase the firm’s total revenue. Conversely, when the marginal revenue curve reaches zero, total revenue is at its maximum point, signifying that no further increase in total revenue can be achieved by selling additional units. Finally, if the marginal revenue curve becomes negative, selling more units beyond this point would actually lead to a decrease in the firm’s overall total revenue.