In central problem three questions arises : 1) why the central problems arises ?Ans. Because people have problem of choice.
2) why the problem of choice arises ?Ans. Because of scarcity of resources.
3) why the scarcity of resources arises?Ans the scarcity of resources arises because;1. Human wants are unlimited.2. Resources are limited.
Now in market economy:There are three problems1) what to produce2) how to produce3) for whom to produce
If you know that, what to produce, how to produce and for whom to produce than the first problem, problem of scarcity of resources will solve and if scarcity of resources will solve then the problem of choice will never arises

Overview:
In a market economy, the central problem of an economy is solved through the interaction of buyers and sellers in the marketplace. This economic system allows individuals and businesses to make decisions based on their own self-interests, leading to the allocation of resources in the most efficient way possible. The market economy is characterized by the presence of competition, private ownership of resources, and the freedom to engage in voluntary exchange.

Allocation of Resources:
One of the central problems of an economy is the allocation of scarce resources to satisfy unlimited wants and needs. In a market economy, this problem is addressed through the price mechanism. The interaction of buyers and sellers in the marketplace determines the prices of goods and services. The price serves as a signal to both producers and consumers about the scarcity and desirability of a particular product. When the demand for a product increases, its price rises, signaling producers to increase production to meet the demand. On the other hand, when the demand decreases, the price falls, indicating producers to reduce production. This price mechanism ensures that resources are allocated efficiently to the production of goods and services that are in high demand.

Competition:
Competition is a vital aspect of a market economy. It encourages producers to improve the quality of their products, reduce costs, and innovate in order to attract more customers. Competition ensures that resources are used efficiently and that goods and services are produced at the lowest possible cost. It also provides consumers with a wider variety of choices and better prices. In a competitive market, inefficient producers are driven out as they are unable to compete effectively, leading to the survival of the most efficient firms.

Private Ownership:
Private ownership of resources is another key feature of a market economy. Individuals and businesses have the right to own and control resources, such as land, capital, and labor. This ownership provides individuals with the incentive to use their resources in the most productive manner. It allows them to make decisions based on their own self-interests, leading to the efficient allocation of resources. Private ownership also encourages individuals to invest in productive assets and take risks, as they can reap the rewards of their efforts.

Voluntary Exchange:
In a market economy, individuals and businesses engage in voluntary exchange. This means that transactions take place only when both parties agree to the terms. Voluntary exchange allows individuals to specialize in the production of goods and services in which they have a comparative advantage. It promotes specialization and division of labor, which leads to increased productivity and efficiency. Through voluntary exchange, individuals and businesses are able to meet their own needs and wants by trading with others, resulting in a mutually beneficial outcome.

Conclusion:
A market economy solves the central problem of an economy by utilizing the price mechanism, competition, private ownership, and voluntary exchange. These elements work together to allocate resources efficiently, encourage innovation and growth, and provide individuals with the freedom to make choices based on their own self-interests. By allowing the forces of supply and demand to interact freely, a market economy promotes economic efficiency and maximizes the welfare of society as a whole.