The correct answer is A.
A perfect monopoly exists when there is only one seller of a good or service in a market. The monopolist has the ability to control the price of the good or service, and there are no close substitutes available. This means that the monopolist can charge a higher price than would be possible in a competitive market, and consumers have no choice but to pay that price.
Option B is not correct because a monopoly does not need to have an absolute franchise of the product. A monopoly can exist even if there are other sellers of the product, as long as the monopolist is the only one who can control the price.
Option C is not correct because a monopoly does not need to be the only one who has the permit to sell the product. A monopoly can exist even if there are other sellers of the product, as long as the monopolist is the only one who can control the price.
Option D is not correct because a monopoly does not need to be the only one who has the knowledge of the product. A monopoly can exist even if there are other sellers of the product, as long as the monopolist is the only one who can control the price.
In conclusion, a perfect monopoly exists only if the single vendor can prevent the entry of all other vendors in the market.