The premise

I’ve written an exam for a class of 70 students. Some might call that a test of learning; I call it a product.
If I’ve invested effort in creating it, why not recover some of that investment?

Here’s the demand curve:

• 5 students would each pay $100 for a copy.

• 30 students would pay $25.

• The remaining 35 would pay nothing (due to ethics or overconfidence).

At first glance, this looks like a simple pricing problem.

• At $25, I sell to 35 students for $875 total.

• At $100, I sell to 5 students for $500.

Economically, I should set the lower price.
But there’s a catch: this isn’t a normal product market — it’s an information market.

The information paradox

An exam is a non-rivalrous good: once one person has it, everyone can have it at zero cost.
It’s also infinitely replicable, and unless I embed self-destructing ink and invent some new technology that precludes taking a picture or scan of it, there’s no way to prevent resale.

That means the first buyer instantly becomes my competitor.
This is a classic case of information arbitrage: a market failure caused by the inability to enforce property rights on knowledge.

This is the same problem faced by:

• software developers before digital rights management (DRM),

• concert promoters battling ticket resellers,

• and even governments trying to contain insider information leaks.

From retail to wholesale

To handle resale, I have two choices:

1. Sell to everyone at once at a price that maximizes direct revenue, or

2. Sell exclusive distribution rights to one student who will then act as the monopolist reseller.

Let’s explore option 2 — the wholesale exam license model.

Suppose one entrepreneurial student sees the resale opportunity:

They can sell:

• 4 copies at $100 = $400

• 30 copies at $25 = $750
  for total revenue of $1,150.

If they want a $150 profit, they’d pay me up to $1,000 for the exclusive rights. This converts me from a teacher into a licensor, not unlike a software publisher or franchise owner.

Auctioning off the monopoly

Of course, I can’t know which student values this monopoly most.
An auction reveals it.

In a second-price (Vickrey) auction, each bidder reveals their true valuation.
If the top bidder values the monopoly at $1,000 and the next bidder at $600, the winner pays slightly more than $600 -- my expected revenue exceeds any fixed price sale.

This is essentially mechanism design in action: structuring rules to extract maximum surplus from participants with private information.

Comparison to real-world markets

This “exam market” echoes several advanced economic phenomena:

• Ticket scalping: Early buyers exploit fixed prices by reselling to those with higher willingness to pay.

• Software licensing: Publishers sell rights to distribute digital goods rather than the goods themselves.

• Insider trading: Information asymmetry creates outsized value for those who act first.

• Patent licensing: Exclusive rights to knowledge are auctioned, not the knowledge itself.

• Cryptographic zero-knowledge proofs: Ironically, these exist precisely to verify knowledge without revealing it — the anti-exam-sale mechanism.

Even the optimal pricing problem here resembles the Myerson auction model (1981 Nobel-winning work): when buyers’ valuations differ and resale is possible, the seller should design mechanisms that extract maximum expected utility from the highest bidder — effectively turning private information into public revenue.

Risk discounting

Our monopolist student faces risk:

• Probability of being caught: \(p\)

• Penalty (grade or fine): \(F\)

Expected profit is:

\[E[\pi] = (1 - p) \cdot R - pF - C\]

where \(R\) is resale revenue and \(C\) is the cost of acquiring the exam.
For the market to exist, \(E[\pi] > 0\).
Once \(pF \ge R\), rational actors exit -- just as strong copyright laws suppress piracy.

Lessons in applied economics

1. Information goods break standard pricing models because marginal cost ≈ 0.

2. Resale converts a competitive market into a single-buyer monopoly.

3. Auctions reveal the true valuation under asymmetric information.

4. Risk and enforcement restore equilibrium by raising expected cost.

5. Ethics remain the simplest (and cheapest) enforcement mechanism.

Mathematical Appendix

Let’s formalize this tragicomic economy.

1. Direct sale (no resale)

If I sell directly to \(n\) students at price \(P\), my revenue is:

\[R_d = P \cdot n(P)\]

where \(n(P)\) is the number of students willing to pay at least \(P\).

From our data:

• \(n(25) = 35\)

• \(n(100) = 5\)

So:

\[R_d(25) = 25 \times 35 = 875 \\ R_d(100) = 100 \times 5 = 500\]

Optimal direct price is \(P = 25\).

2. Monopoly resale

Let \(V_i\) be each student’s valuation, sorted \(V_1 > V_2 > \ldots > V_N\).
If one buyer purchases exclusive rights, their resale revenue is:

\[R_m = \sum_{i=2}^{k} V_i\]

where \(k\) is the number of buyers they can reach.
The monopolist’s maximum bid is therefore:

\[B^* = R_m - \pi_m\]

where \(\pi_m\) is their desired profit.

If \(R_m = 1{,}150\) and \(\pi_m = 150\), then \(B^* = 1{,}000\).
Thus my profit from selling the license exceeds any direct retail scheme.

3. Auction revenue

In an optimal auction, expected revenue approaches the second-highest valuation (by revenue equivalence theorem).
If two capable resellers exist with valuations \(V_1 = 1{,}000\) and \(V_2 = 600\), my expected revenue is roughly:

\[E[R_a] \approx V_2 = 600\]

This is below the monopoly valuation but above direct sale revenue — demonstrating why auctions dominate fixed pricing in markets with asymmetric information.

4. Expected profit under risk

With enforcement risk, the monopolist’s expected profit is:

\[E[\pi] = (1 - p)R_m - C - pF\]

Setting \(E[\pi] = 0\) gives the break-even enforcement condition:

\[p = \frac{R_m - C}{R_m + F}\]

If the detection probability exceeds this threshold, the illicit market collapses.

Final note

This entire exercise, of course, violates every principle of ethics and education. But it demonstrates something economics teaches better than morality ever could: Markets appear wherever incentives exist — even in the classroom.

Disclaimer: Not everything you read on the web is accurate or even true. Always do your own research before treating something as fact — real research, not just a few YouTube videos or quick searches. Trust reputable sources, check the evidence, and read critically.