In the price system, prices are used to determine what goods and services are produced and who gets them.
There are at least two major advantages to this. First, it allows consumers to decide which things they want to buy. They choose to buy or not to buy a given product at a given price. This gives them the greatest control over their economic lives. Second, it allocates resources efficiently. Prices send strong signals about what is wanted and what is not. Suppliers respond to these prices automatically. This is much more efficient than a system in which a government tries to determine what is and is not needed and adjusts production accordingly.
The major disadvantage of the price system is that it prevents poor people from getting the things they need. Prices essentially ration goods on the basis of ability to pay. When people cannot afford to buy necessities, they are denied access to those goods. This can be seen as inequitable.
The price system and I assume you mean the free price system, is very important in an economy. There are advantages and disadvantages to it.
In a free price system, the forces of supply and demand determine prices. The most efficient use of resources is when supply matches demand. Supply and demand are equal when the market determines the price at which a number of goods supplied equals a number of goods demanded. The price system also allows us to buy many products. Manufacturers are willing to make products when they can make money. When supply equals demand, businesses are maximizing the profit potential at the given price level.
One disadvantage of the price system is that for certain products, the costs of setting up the industry are so high, there is only one seller of the product. In cases like these, such as with the electric and the natural gas companies, or with the water companies, without government regulation, prices could be very expensive since they are the only provider of the product. In these cases, the government needs to regulate these industries because the price system would lead to very high prices for water, electricity, and natural gas. Since the setup costs for these industries are so high, there is no competition for these companies. This could cause consumers to make some very difficult choices if the prices are regulated by the government.
The price system is the price mechanism in a free market economy. Profit is the main motivation for businesses, and consumers are free to buy any good or service they choose. Equilibrium is achieved when supply equals demand for a product. Besides the two advantages of the price system described by pohnpei, another advantage is that the price system encourages competition. Technically, a free market economy is essentially one without government intervention, although a strict example of this would be hard to find in the world today.
Going back to competition, we see that when companies have to compete with other companies for market share, it is more likely that these companies will try to produce better products and sell those products at optimum prices to potential and current customers. Companies allocate financial resources toward more research and development (R&D) hoping to gain advantage in terms of an increased customer base and optimal price. Customers benefit because more variety and better quality products at optimal prices may increase their quality of life. For example, in the medical field, competition has fueled great medical breakthroughs and advantages for patients.
A disadvantage of the price system is the possibility of large scale unemployment in different market sectors due to automation. As more and more companies automate in order to increase production efficiency, workers are disenfranchised. Job losses may contribute to financial insolvency and this can affect the overall health of the economy. Another disadvantage of the price system is that both good and harmful products can be sold side by side: for example, consumers can purchase as many harmful cigarettes as they desire at the same store where they buy good organic meats and vegetables.