An analyst pays to discover something that everyone else hopes to read from the price. She studies the business, forms a judgment about its future receipts, and buys when the quoted terms make that judgment valuable. Her purchase helps move the price. Other buyers can then learn something from the movement without having paid for her investigation. The price’s capacity to carry knowledge gives rise to the difficulty: if it carried the whole useful result, the observer could obtain the same information as the investigator and save the expense. The earlier inquiry into The Efficient Market reached this tension at its boundary. Sanford Grossman and Joseph Stiglitz made it the center of a model. The information entering a price has to come from somewhere, and acquiring it must remain attractive to those expected to do the acquiring.1
A simple comparison shows why the gross advantage and the cost of acquiring it must be kept together. Suppose a claim will pay either 80 or 120, each with probability one half, and a risk-neutral buyer can purchase at most one unit for a fixed price of 100. There is no short selling or interest, and the alternative is to keep the money. Without additional information, buying has expected profit zero. A perfect report received before the decision lets the buyer purchase only when the payoff will be 120. The expected gross profit is 10; a report costing 3 leaves an expected net gain of 7. Now let a publicly observed quote reveal the payoff by being 80 in the low state and 120 in the high state. Buying at either quote yields zero profit, and paying 3 for the same information makes the buyer worse off by 3. These are two stipulated decision problems, not a market equilibrium. They isolate the source of the incentive: an informative report is worth paying for when it improves a decision beyond what the freely observed quote already permits.2
Grossman and Stiglitz make that price emerge from the trading of informed and uninformed investors. Their economy contains a safe asset and a risky asset whose payoff combines a signal that can be purchased with a further unpredictable component. Informed investors observe the signal and the price. Uninformed investors observe the price and understand its statistical relationship to the eventual return. An unobserved fluctuation in the supply of the risky asset introduces noise: the same price movement can reflect the informed traders’ news or a change in the amount the market must absorb. The price therefore transmits some of the signal while leaving a reason to acquire it directly. Traders in the specified model have constant absolute risk aversion, and its random variables are jointly normal. Within that setting, market clearing and rational inference determine how much an observer can learn from the number on the screen.3
The number of people buying information then adjusts to the advantage left after its cost. At an interior equilibrium, becoming informed and remaining uninformed offer the same expected utility once the information charge is included. A price that revealed the signal completely would let each informed price-taker stop buying the report while continuing to learn from the market. If nobody acquired it, however, a trader would want to start whenever the private benefit exceeded the cost. Under that condition, positive information cost and complete revelation cannot jointly sustain the proposed equilibrium. The paper’s no-noise limit makes the conflict exact: positive informed participation invites withdrawal, while zero participation invites entry. The condition matters. Information too costly to be worth acquiring when nobody has it can support a different outcome, with everyone uninformed. The paradox concerns the attempted combination of useful privately financed discovery and a price that gives away its entire informational advantage.4
Partial revelation allows the investigation to earn its cost while still making the price useful to people who never investigate. The compensation is an ex ante advantage in the model’s portfolio decision, with risk, information quality and expense included. A realized profit on one trade can reflect favorable news after the purchase; a realized loss can occur despite an informative report. Neither observation alone measures the report’s value. The model also makes the amount of research responsive to the market around it. More supply noise, holding the informed share fixed, makes the price less revealing. In the particular interior equilibrium, the resulting entry into research exactly offsets that loss of informativeness. The number of researchers changes even when the final informational quality of the price does not. Market activity and market knowledge are separate quantities, joined by incentives whose effects must be traced through the adjustment.
The contradiction has a boundary, and that boundary distinguishes the informational result from a judgment about social value. If the report is free, reading it no longer creates the expense that made an equally informed nonbuyer better off. If knowledge is produced for another purpose or financed outside the trading opportunity, its continued production requires a different incentive account. These changes alter the question the model answers. Even within the model, incomplete revelation supplies no general reason to preserve wasteful obscurity or to subsidize every investigation. Grossman and Stiglitz expressly leave the social benefits of information and the welfare properties of their allocation for further work. Prices can coordinate decisions, research can consume resources, and a private advantage can partly concern which trader receives a gain. The welfare inquiry must count those consequences separately from how accurately the price reflects a signal.5
The price can spare an observer the work of learning because someone else has done work whose result the price conveys. Its success in spreading that result changes the reward for producing the next one. The paradox keeps both movements in view: discovery alters the price, and the price alters the incentive to discover. A market can be highly informative while leaving a remaining advantage to informed participants; its useful imperfection has to be understood through the conditions that sustain it. The question is who pays for the knowledge, who can use it, and how much of its value the producer can retain. The final plate follows that question out of the trading room and into the sale of information itself. In The Secret, showing a prospective buyer what makes the knowledge valuable can give away the very thing its owner hoped to sell.