the average of weighted black market price and weighted official/normal market price is close to the real market price

The average of weighted black market price and weighted official/normal market price is close to the real market price. In some incomplete or restricted markets, people cannot have free access to goods or services, and the goods and services are almost necessities to some people; therefore, they will seek for these goods and services in some black markets. Supply in the official market is usually undersupplied and the price is usually set by the authority, which means it is not determined by the market supply and demand law. In addition, the price is generally lower than that when there is a free market system. When people enter the black market, they will be charged with higher prices. The supply does not meet all the demand; however, usually, people are able to pay the goods and services they need if they are willing to offer high prices. The sum of the black market supply and the official market supply will be still more limited than the supply under a free market system.

In a black market, the cost is higher than the cost under a free market. Because a black market is forbidden by the government, the cost of production is not the only cost, the price also has to consider the risk of suppliers in the black market. A black market is illegal, once the suppliers are caught by the government, their profits will become zero; therefore, if suppliers are more likely to be caught by the government or the government spends more resources on catching these black market traders, the prices in the black market will be higher.

Therefore, because the total supply in the official market, as well as the black market, is lower than the supply in a free market, suppliers in a black market faces much higher risk than those in a free market, it is clear that the weight average price of the prices in official markets and black markets should be higher than the price in a free market. This means a black market will not allow the total supply to be at a free market level. This concept is important as the government does not need to worry too much that a black market existence will let restrictions to products with negative externalities ineffective.