Maximizing Profit Under Monopoly

Monopoly. It's not just a game. In this video we'll talk about how a firm uses market power to maximize profit. We'll begin with a controversial example.

This is the AIDS virus. Worldwide, it has killed more than 36 million people. In the United States, however, AIDS is no longer the death sentence that it once was. Beginning in the mid-1990s, death rates from AIDS began to fall dramatically with the introduction of new drugs such as Combivir. These new drugs are great, but they're expensive, and they're expensive not because it costs a lot to manufacture these drugs. The per-pill costs of production are actually quite low. Instead, these drugs are expensive because they're the subject matter of this chapter -- Monopoly.

GlaxoSmithKline, or GSK, owns the patent on Combivir and that means that it has the right to exclude competitors. Only GSK can legally sell Combivir. The patent gives GSK a monopoly, or more generally we say it gives them market power. Market power is the power to raise price above marginal cost without fear that other firms will enter the market. Now how do we know the price is above marginal cost? Here's a simple test -- in the United States, Combivir costs around $12 to $13 per pill. India, however, does not recognize the patent on Combivir. So in India, there are many producers of Combivir who sell in a competitive market. As we know, in a competitive market, price will fall to marginal cost and in India the price of Combivir is about 50 cents per pill. Thus, in the United States, the price of Combivir is about 25 times higher than the marginal cost.

Let's say a few words about the sources of market power. The basic idea is that a firm has market power when it's selling a unique good and there are barriers to entry, forces which prevent competitors from entering the market. Barriers to entry could include patents, as we've already discussed. There may also be other government regulations creating barriers to entry, such as exclusive licenses. Economies of scale can mean that a single big firm can sell at lower cost than any of many small firms, making it difficult to establish a competitive market even with free entry. Exclusive access to an important input.

Diamonds, for example, are found in only a few places in the world. If you control a number of these diamond mines, you can monopolize the market for diamonds, where you will have market power in the market for diamonds. Technological innovations can give a firm temporary market power. A firm with knowledge or abilities that other firms don't yet have will have some market power, for example. Now we'll say a little bit more about these later. What we want to do now is to focus on how a firm with market power chooses to set its price. What is the profit maximizing price?

So how does a monopolist maximize profit? By producing at the level of output where marginal revenue is equal to marginal cost. Great! That's the same rule as for a competitive firm -- choose a level of output where marginal revenue is equal to marginal cost. The only difference is that for a competitive firm, marginal revenue was the same as price, and that's not true for a monopolist. A monopolist is not a small share of the market. Since it's selling a unique good, the monopolist faces the entire downward sloping market demand curve. As a result, marginal revenue is going to be less than price. Let's show how to calculate marginal revenue for a monopolist.

Let's start with the demand curve, and suppose that we're initially selling two units. We can sell those two units for $16 a piece. Total revenue therefore is $16 times 2 units, or $32. Now, remember that marginal revenue is the change in total revenue from selling an additional unit. So suppose that we sell an additional unit -- three units in total. We can sell three units for $14 -- $14 is the maximum per unit price we can get when selling three units. So when the quantity sold is three, total revenue is 14 times three, or $42. That means marginal revenue, the change in revenue from selling that additional unit, is $10. Now we can actually arrive at the same conclusion in another revealing way.

Marginal revenue can be broken down into two parts. First is the revenue gain from selling an additional unit. That's just this area right here. We can sell an additional unit, the third unit for $14. That's the revenue gain. But, in order to sell that additional unit, we had to lower the price on the previous units that we were selling, so there's also a revenue loss. We were receiving $16 per unit when we sold just two units. When we sell three units, we have to lower the price to $14, so we lose $2 per unit on these previous units or a total loss of $4. So marginal revenue is just the revenue gained -- $14, minus the revenue loss, $4, or $10 just as before. Notice also that the revenue gain is just the price of the third unit, so since it's the revenue gain minus the revenue loss, we can also see right away that for a monopolist, marginal revenue must be less than the price.

Okay, let's remember where we're going. We want to find the profit maximizing price, which is the level of output where marginal revenue is equal to marginal cost. But do we need to go through this tedious process to find marginal revenue for each unit? No. There's a shortcut, and that's what I'm going to show you next.

Here's the shortcut for finding marginal revenue, and this will work for any linear demand curve, and those are the only ones we're really going to be working with in this class, so it'll work just fine for us. Take a linear demand curve, then the marginal revenue curve begins at the same point on the vertical axis as the demand curve, and it has twice the slope. So if we were to write the demand curve in inverse form, as P is equal to A minus B times Q, then the marginal revenue curve is equal to A minus 2B times Q. That's it. Pretty simple.

Let's give a few more examples. Let's use our shortcut on these two different demand curves. In the first case, the marginal revenue curve begins at the same point on the vertical axis. It has twice the slope. So notice what that means is that if the demand curve hits the horizontal axis at 500, the marginal revenue curve must hit the horizontal axis at 250. More generally, since it has twice the slope, the marginal revenue curve splits the distance between the vertical axis and the demand curve in half. So the distance from the vertical axis to the marginal revenue curve is half the total distance to the demand curve, throughout the length of the marginal revenue curve.

Okay, what about our second demand curve? Notice that it hits the horizontal axis at 200, therefore the marginal revenue curve must hit the horizontal axis at 100. Pretty simple, and again, this will work for any linear demand curve, any demand curve which we're going to see in this course. Great. We're now ready for the big payoff -- how a firm uses market power to maximize profit. So here is our demand curve and our marginal revenue curve with twice the slope. Let's introduce the marginal cost curve.

We're going to make it flat at 50 cents per pill. How does the firm maximize profit? Well it compares for each unit the revenue for selling that additional unit compared to the cost of selling that unit. If the marginal revenue is bigger than the marginal cost, then that's a profitable unit to sell, so the firm keeps producing so long as marginal revenue is bigger than marginal cost. That is, it produces until marginal revenue is equal to marginal cost. That point tells us the profit maximizing quantity of output, in this case, 80 million pills.

Now what is the maximum amount per pill that we can sell these 80 million pills for? Where do we find that? We find that by looking up to the demand curve. Remember the demand curve tells us the maximum willingness to pay. So the maximum willingness to pay for a pill is $12.50. Eighty million units -- that's the profit maximizing quantity, $12.50 -- that's that profit maximizing price per unit. One more curve -- let's remember our average cost curve. If we introduce this curve we can now show profits on the diagram, just as we did with a competitive firm. The profit is the price minus the average cost -- in this case that's $10 per pill -- times the quantity -- in this case 80 million units -- so profit is the shaded area given right here.

So now we've got everything. Whenever we have a monopoly question, we have a demand curve, we draw the marginal revenue curve, we draw a marginal cost curve if it's not given. We can then find the profit maximizing output quantity -- that's given when marginal revenue is equal to marginal cost. We go up to the demand curve to find the profit maximizing price. The difference between the price and average cost gives us the profit per unit, times the total number of units gives us total profit.

Okay. That's our big lesson for today. What we're going to do next time is look at -- how does the difference between price and marginal cost -- how does the mark-up vary? And what we're going to show is the mark-up varies with the elasticity of demand. Remember, I told you elasticity of demand would come back. Well, here we're going to use it again in our next lecture.