5.7 Monopolies
Market Power and Combivir
In June 1981, the CDC reported cases of pneumonia in otherwise healthy gay men in cities like Los Angeles, New York, and Boston. This marked the beginning of the AIDS crisis, caused by HIV, which weakens the immune system and makes individuals vulnerable to life-threatening illnesses like pneumonia. Since then, AIDS has claimed over 36 million lives worldwide. While there’s no cure, antiretroviral therapies, such as Combivir, have significantly reduced mortality. These drugs, which prevent HIV from replicating, helped cut AIDS-related deaths by 50% between 1995 and 1997.
Combivir, however, highlights a critical issue: drug pricing. In the U.S., a single pill costs $12.50, amounting to $9,125 annually for a patient taking two pills daily. For many, this price is unaffordable. The problem isn’t production costs—making one pill costs just 50 cents. The high price stems from market power. GlaxoSmithKline (GSK), the pharmaceutical giant, holds the patent for Combivir, granting it a monopoly. Competitors can’t produce the drug without facing legal consequences, allowing GSK to set prices far above marginal cost.
In India, where the patent isn’t recognized, Combivir sells for 50 cents per pill—the efficient price where P = MC. This stark difference illustrates the deadweight loss caused by monopolies: thousands of patients who could afford the drug at 50 cents are priced out at $12.50.
Pharmaceutical monopolies are uniquely powerful because demand for these drugs is inelastic. When faced with life-threatening illnesses, patients have little choice but to pay high prices. This allows firms like GSK to charge significant markups.
One proposed solution is price controls, which cap how much firms can charge above production costs. While this improves access, it risks stifling innovation. Developing new drugs is costly—often exceeding $1 billion—and most experimental drugs never reach the market. Without the promise of profits, firms lack the incentive to invest in research. This tension between affordability and innovation is central to the debate.
A more promising solution, proposed by Nobel laureate Michael Kremer, is the patent buyout. Under this model, governments purchase patents from pharmaceutical firms, ensuring profits for innovators while allowing generic manufacturers to produce the drug. Generics, which replicate the original drug after its patent expires, increase competition and drive prices down. While patent buyouts cost taxpayers, the cost would be spread across the entire population, minimizing the burden on individuals.
Solving for the Monopolist’s Q Decision
Monopolists restrict quantity supplied in order to drive up prices and maximize their profit. In this section, I’ll show you how to predict how much monopolists will restrict Q.
First, write down the profit function \(\pi = TR - TC\). Next, take its derivative with respect to quantity \(Q\). Then, set the derivative equal to zero. This works because, at the maximum point of a function (such as a downward-facing parabola), the slope of the tangent line is zero.
\[\begin{align} \pi &= TR - TC\\ \frac{d \pi}{dQ} &= 0 = \frac{d TR}{dQ} - \frac{d TC}{dQ}\\ 0 &= MR - MC\\ MR &= MC\\ \end{align}\]
This is the proof you’ve seen before that maximizing profit is the same as setting marginal revenue equal to marginal cost.
For example: if the monopolist faces a demand curve given by \(P = 100 - 2Q\) and the monopolist’s marginal cost is \(MC = 20\),
\[\begin{align} MR &= \frac{d}{dQ} PQ\\ &= \frac{d}{dQ} (100 - 2Q)Q\\ &= \frac{d}{dQ} 100 Q - 2 Q^2\\ &= 100 - 4Q \end{align}\]
When the monopolist faces a linear demand curve, their marginal revenue has the same y-intercept as the demand curve, but twice the slope (so half the x-intercept). Let’s find the monopolist’s profit maximizing \(Q\):
\[\begin{align} MR &= MC\\ 100 - 4Q &= 20\\ 4 Q &= 80\\ Q &= 20 \end{align}\]
The profit-maximizing amount for the monopolist to supply is 20 units. Let’s finish the problem by finding the monopolist’s price (the maximum they can sell those 20 units for), and the monopolist’s profit (assuming zero fixed costs, so \(TC = 20Q\)):
\[\begin{align} P &= 100 - 2Q\\ &= 100 - 2(20)\\ &= 60 \end{align}\]
\[\begin{align} \pi &= TR - TC\\ &= PQ - 20 Q\\ &= 60 (20) - 20^2\\ &= 1200 - 400\\ &= 800 \end{align}\]
So in review: when the monopolist faces the demand curve \(P = 100 - 2Q\) and has a marginal cost of \(20\), they set MR = MC to find their profit maximizing output \(Q = 20\), the maximum price the market can bear is given by the demand curve: \(P = 60\), and the monopolist can make a profit of $800. Here’s what’s happening visually:
Compare the market under the monopolist to the market if there was instead perfect competition and the price was driven down to marginal cost, like we’ve studied before:
\[\begin{align} P &= MC\\ 100 - 2Q &= 20\\ 2Q &= 80\\ Q &= 40\\\\ P &= 100 - 2(40)\\ P &= 100 - 80\\ P &= 20\\\\ \pi &= PQ - 20Q\\ \pi &= 20 (40) - 20 (40)\\ \pi &= 0 \end{align}\]
So under the monopolist, the price is higher, the quantity exchanged is lower, and profit to firms is higher.
Question 1
- If demand is given by \(P = 60 - Q\) and the monopolist’s marginal cost is $20 per unit, find the monopolist’s \(Q\), \(P\), and \(\pi\).
Answer:
\[\begin{align} \end{align}\]
- Continuing from part a, find the \(Q\), \(P\), and \(\pi\) under perfect competition.
Answer: \[\begin{align} \end{align}\]
- Compare: under a monopolist, the price is (higher/lower), the quantity exchanged is (higher/lower), and the profit to firms is (higher/lower).
Answer:
Question 2
- If demand is given by \(P = 50 - 0.5 Q\) and the monopolist’s marginal cost is $40 per unit, find the monopolist’s \(Q\), \(P\), and \(\pi\).
Answer: \[\begin{align} \end{align}\]
- Continuing from part a, find the \(Q\), \(P\), and \(\pi\) under perfect competition.
Answer:
\[\begin{align} \end{align}\]
- Compare: under a monopolist, the price is (higher/lower), the quantity exchanged is (higher/lower), and the profit to firms is (higher/lower).
Answer: