# Profit Maximization

| Updated May 13, 2018

In economics it is often assumed that companies try to maximize profit. That is, they try to maximize revenue while at the same time minimizing costs. In order to do that, firms need to look “at the margin”. That means, they have to keep an eye on changes in revenue (i.e. marginal revenue) and changes in costs (i.e. marginal costs) for every additional unit sold.
To introduce the principle of profit maximization, it seems reasonable to focus on firms in a competitive market first. However, as we will see later on, this principle can be applied to most firms in various market situations (monopoly, oligopoly, etc.).

As mentioned above, to maximize profits, a firm needs to examine changes in revenue and costs for every additional unit sold. As long as the resulting increase in revenue is larger than the increase in costs, total profit can still be raised by producing more. This will hold true until marginal revenue (MR) equals marginal cost (MC). In other words, a profit maximizing firm will produce until MR=MC.

This can be illustrated by looking at a simple diagram that shows the relations between output and costs or revenue respectively. Though, before we can do this, we need to find out what the relevant marginal cost and marginal revenue curves look like.

## Marginal Revenue

Computing marginal revenue in a competitive market is actually pretty simple. In fact, it is always equal to the price of the good or service sold (for more information see how to calculate marginal revenue) To explain this, let’s look at a characteristic of competitive firms. They are said to be price takers. That is, they do not have enough power to influence market prices (unlike for example a monopolist), since they only control a small share of the market. So no matter how much a competitive firm produces, price  will not change and revenue for each additional unit sold will be equal to the given market price. As a result, the marginal revenue curve will be a horizontal line at the level of the market price.

## Marginal Cost

Most firms face increasing marginal cost as output increases. This is a result of diminishing marginal products (for more information see how to calculate marginal cost).To give an example, think of a car factory that is currently producing at a low capacity. There are only few workers employed and the machines are barely used. If the factory increases production, idle capacities can easily be put to use and additional workers can add a lot of value. In other words, marginal costs are low and marginal product is high. However, if the factory is already running at full capacity, increasing production will be more expensive (e.g. because machines are overused) and additional workers will not add much value (e.g. because they have to wait to use equipment). Therefore, when output increases, marginal product diminishes and marginal cost increases. As a result, the marginal cost curve will slope upwards.

## Illustration

As mentioned above, we can visualize the principle of profit maximization in a simple diagram (see below). The x-axis represents output quantity (Q), while the y-axis stands for costs and revenue respectively (C and R). Illustration 1: Profit Maximization
The Marginal revenue curve (MR) is a horizontal line at the level of the market price (p*). The marginal cost curve on the other hand (MC) is upward sloping, as described above. The intersection of the two lines (O*) is located at the profit maximizing level of output (q*) for the given price level. It becomes apparent that shifting MR will affect the output quantity, but not the price level. Thus, profit maximization for competitive firms means, finding the optimal level of output for a given price.

## In a Nutshell

Firms in a competitive market can maximize profits if they produce up to the point where marginal revenue equals marginal cost (MR=MC). Marginal revenue for competitive firms is constant and equal to the price of the good or service sold. Marginal costs on the other hand are usually increasing as output increases, due to the diminishing marginal product.
It is important to note that even though marginal revenue and marginal cost curves may look differently for firms in other market situations (e.g. monopoly, oligopoly, etc.), the profit maximizing level of output will still be located at the intersection of the two.

## One comment

1. roberto says:

it’s good that you help people.