A monopolist considers whether to disclose some information about its product. The information will affect how the consumer values the product but its impossible to predict in advance how the consumer will react. With probability q the consumer will view it as good news and he would be willing to pay a high price V for the product. But with probability 1-q it will be viewed as bad news and the consumer would only be willing to pay a low price v where 0 < v < V.
The consumer’s reaction to the information is subjective and cannot be observed by the monopolist. That is, after disclosing the information, the monopolist can’t tell whether the consumer’s willingness to pay has risen to V or fallen to v.
In the absence of disclosure, the consumer is uncertain whether his the value is V or v and so his willingness to pay is equal to the expected value of the product, i.e. qV + (1-q)v. This is therefore the price the monopolist can earn.
Supposing that the monopolist can costlessly disclose the information, what would its profits be then? It won’t continue to charge the same price. Because with probability (1-q) the consumer’s willingness to pay has dropped to v and he would refuse to buy at a price of qV +(1-q)v. At that price he will buy only with probability q and since that would be true at any price up to V, the monopolist would do better setting a price of V and earning expected profit qV.
Alternatively he could set a price of v. For sure the consumer would agree to that price (whether his willingness to pay is V or v) and so profits will be v. And since this is the highest price that would be agreed to for sure, v and V are the only prices the monopoly would consider. The choice will depend on which is larger qV or v.
But note that both qV and v are smaller than qV +(1-q)v. Disclosing information lowers monopoly profits and so the information will be kept hidden.
This little model can play a role in the debate about mandatory calorie labeling.