Monopoly Profit Maximization

Profit Maximization Perfect Competition vs Monopoly

Profit maximization as a monopoly versus profit maximization in perfect competition requires additional work and analysis.

In perfect competition, firms are price-takers. They can not influence prices, therefore their marginal revenue is always the same. Their marginal revenue is always just the existing market price.

As a monopoly though, you get to decide where along the market demand curve you want to position your product or service in terms of price and quantity produced.

Sounds great, but be careful. There are more things to consider. Imagine the demand curve for light bulbs looks like Figure 1 below.

Fig 1. Monopoly demand curve

As a monopolist, any time you change the price of your product or service, it changes the price of all other units sold as well.

This is why the monopolist's marginal revenue curve slopes downward as opposed to being perfectly horizontal like for firms in perfect competition. This is also why, as a monopolist, you have to be very precise in terms of how you approach this.

As it turns out, monopolists also find their average revenue curves interesting.

Unlike firms in perfect competition whose marginal revenue equals average revenue, both of which equal the market price, monopolists also have a downward sloping average revenue curve. Why is that interesting?

Well, consider the definition of average revenue:

$AR=\frac{TotalRevenue}{TotalQuantitySold}=\frac{P\times Q}{Q}$

Let's use Figure 2 to help explain why the monopolist's average revenue curve is interesting.

Fig 2. - Marginal and average revenue for a monopolist

First, let's break the graph down. We know that marginal revenue for a monopolist is downward sloping because the only way to increase quantities sold is by lowering the price of all units sold.

However, you might have noticed that Figure 2 also labels average revenue (AR) as equal to D. If you're thinking that the D in the graph stands for demand, you would be correct! But why?

Well, it's simple math for a monopolist. You see, since the monopolist faces the entire demand curve, it will receive whatever quantity is demanded at the corresponding price associated with the demand curve. Therefore, at each point on the demand curve, the monopolists' AR will be the price it sets multiplied by the quantity demanded at that price, divided by the quantity demanded.

Monopoly Profit Maximization Graph

We wouldn't be very good economists if we didn't have a monopoly profit maximization graph.

Now, we know that a monopolist's Marginal Revenue curve slopes downward, that its Average Revenue curve also slopes downwards, and that it's actually exactly equal to the market demand curve.

However, before we create the profit maximization graph for your monopoly, let's consider your Marginal Cost (MC) curve.

As it turns out, your MC is like most MC curves regardless of the type of market a firm is in. Therefore, your MC curve initially curves downward before curving upward, as a direct result of the Law of Diminishing Returns.

The interaction of the monopolist's MR, AR and MC curves is illustrated in Figure 3 below.

Fig 3. Monopoly profit maximization graph

As you can see, when the MC curve rises up to the point where it meets the MR curve, that's precisely where the monopolist will set its level of production, and maximize its profits!

Profit Maximizing Price Monopoly

What is the profit maximizing price for a monopoly?

As a seasoned economics student, you know that the golden rule of profit maximization is universal in the sense that it applies across all markets. Therefore, in order to maximize profits for your light bulb monopoly, all you need to do is set production levels at the point where your Marginal Revenue equals your Marginal Cost.

We also know that a monopolist's Marginal Revenue curve slopes downward, that its Average Revenue curve slopes downwards and is exactly equal to the market demand curve, and that its MC curve curves downward before curving upward as a direct result of the Law of Diminishing Returns, all of which are captured nicely in the graph in Figure 4 below.

Fig 4. - Profit maximizing price

Here's the really neat thing. The profit-maximizing price is actually above the Marginal Revenue curve, unlike firms in perfect competition, and therefore by definition, also above the Marginal Cost curve at the profit-maximizing output level.

Monopoly Profit Maximization Example

Let's look at a numerical monopoly profit maximization example.

Assume that Table 1 is representative of your light bulb monopoly.

Table 1. Monopoly Profit Maximization Numerical Example, StudySmarter Originals

Can you identify at what output profit is maximized? Can you do it by using what you've learned about Marginal Cost and Marginal Revenue?

Do you see anything that surprised you? If not, our job is done here.