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## Monopoly Profit Maximization

Monopoly profit maximization is an interesting, albeit somewhat complex exercise.

Let's say you wake up the one day and your magic money vending machine is no longer a magic machine because instead of giving you money, it gives you ready-to-sell light bulbs. In every other sense, however, it behaves exactly the same as the magic machine in that as you put more and more dollars in, the machine gives you increasing and then decreasing quantities of light bulbs. The other difference, of course, is that now you also have to sell the light bulbs in exchange for receiving money back.

So how exactly do you determine how many light bulbs to make?

In economics there are some "golden rules" and one of them is the **profit maximization golden rule**. Are you ready to hear it?

**The profit maximization golden rule is**: in order to maximize profits, regardless of the market structure, a firm must produce goods and services up to the point where their marginal revenue is equal to their marginal cost.

A golden rule wouldn't be worth much if it wasn't universally applicable. As such, monopoly profit maximization is achieved at the level of production where a firm's marginal revenue is equal to its marginal cost.

Now as a monopolist, you know that you're the only one with this magic machine. In other words, other people can't use your machine to manufacture light bulbs because you have the ultimate barrier to entry! There is only one machine that can produce them, and you have it. In fact, it's **barriers to entry** that make monopolies possible.

Interestingly, barriers to entry can take many forms, including technological innovation, patents, government policies, start-up costs, and licensing requirements.

Regardless of your particular barrier to entry, you get to decide exactly where your optimal production level and price is because you are not competing with anyone.

This wonderful situation comes with a greater degree of rigor and scrutiny, however.

## 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.

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.

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.

In a monopoly, a firm's average revenue curve equals the firm's demand curve.

## 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 law of diminishing returns** states that the output generated by adding units of factors of production to a fixed amount of capital (machinery) will eventually begin producing diminishing output.

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

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.

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.

Input Type | Input Count | Cost per Input | Output | Total Cost | Marginal Cost | Price | Average Revenue | Marginal Revenue | Total Revenue | Profit |

Machine | 1 | $1.00 | 0 | $1.00 | -$1.00 | |||||

Employee | 2 | $0.50 | 1 | $2.00 | $1.00 | $10.00 | $10.00 | $10.00 | $10.00 | $8.00 |

Employee | 4 | $0.50 | 2 | $3.00 | $1.00 | $9.00 | $9.00 | $8.00 | $18.00 | $15.00 |

Employee | 6 | $0.50 | 3 | $4.00 | $1.00 | $8.00 | $8.00 | $6.00 | $24.00 | $20.00 |

Employee | 7 | $0.50 | 4 | $4.50 | $0.50 | $7.00 | $7.00 | $4.00 | $28.00 | $23.50 |

Employee | 8 | $0.50 | 5 | $5.00 | $0.50 | $6.00 | $6.00 | $2.00 | $30.00 | $25.00 |

Employee | 9 | $0.50 | 6 | $5.50 | $0.50 | $5.00 | $5.00 | $0.00 | $30.00 | $24.50 |

Employee | 10 | $0.50 | 7 | $6.00 | $0.50 | $4.00 | $4.00 | -$2.00 | $28.00 | $22.00 |

Employee | 12 | $0.50 | 8 | $7.00 | $1.00 | $3.00 | $3.00 | -$4.00 | $24.00 | $17.00 |

Employee | 15 | $0.50 | 9 | $8.50 | $1.50 | $2.00 | $2.00 | -$6.00 | $18.00 | $9.50 |

Employee | 18 | $0.50 | 10 | $10.00 | $1.50 | $1.00 | $1.00 | -$8.00 | $10.00 | $0.00 |

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.

To learn everything you need to know on the topic of monopolies check our explanation - Monopoly!

**Economies and Diseconomies of Scale**

Since a monopoly can determine the price it sets, and therefore the quantity of output it will produce, it is able to use the long-run average total cost curve, or LRATC, as it's Average Total Cost curve.

Since the LRATC is the relationship between output and average total cost when fixed costs have been chosen to minimize the average total cost for each level of output, there are many possible choices of fixed cost.

For a monopolist, its ATC, or LRATC curve looks like a smooth U shape as follows:

What determines the shape of the long-run average total cost curve is the influence of the monopolist's output on its long-run average total cost of production. Monopolists that can leverage scale effects in production find that their long-run average total cost changes substantially depending on the quantity of output they produce. As a result, a monopolist can realize increasing returns to scale when its output increases more quickly than corresponding increases in inputs.

As you can see in Figure 5, the monopolist's optimal LRATC level of output is at point A where it has exhausted the Economies of Scale portion of the curve without stepping into the Diseconomies of Scale portion of its LRATC curve.

Learn more on this topic in our articles:

- Returns to Scale

- Increasing Returns to Scale

- Decreasing Returns to Scale

- Constant Returns to Scale

## Monopoly Profit Maximization - Key Takeaways

- The profit maximization golden rule is: in order to maximize profits, regardless of the market structure, a firm must produce goods and services up to the point where their marginal revenue is equal to their marginal cost.
- In a monopoly, a firm's average revenue curve equals the firm's demand curve.
**The law of diminishing returns**states that the output generated by adding units of factors of production to a fixed amount of capital (machinery) will eventually begin producing diminishing output.- A monopolist enjoys each point on its Long-Run Average Total Cost curve for each point of production on its demand curve.

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##### Frequently Asked Questions about Monopoly Profit Maximization

How to maximize profit in Monopoly?

In order to maximize profits regardless of the market structure a firm must produce goods and services up to the point where their Marginal Revenue is equal to their Marginal Cost.

How a profit-maximizing monopoly chooses output and price?

It chooses profit-maximizing output where MC=MR and reads the price off the demand curve

What is the profit-maximizing condition for a monopoly firm?

The profit-maximizing condition for a monopoly firm is: MC=MR

How to calculate profit-maximizing price and quantity for monopoly?

Choose profit-maximizing output where MC=MR and read the price by plugging the values in the demand curve equation

Does a monopoly always maximize profit?

As monopoly is a single seller in the market and is also a price setter it will always aim to profit maximize.

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