The correct answer is option 1: "The interplay of the forces of demand and supply."

In a free-market economy, the price mechanism refers to the way prices are determined through the interaction of supply and demand. The price of a product or service is influenced by both the quantity supplied by producers and the quantity demanded by consumers. When demand for a product is high and supply is low, prices tend to increase. Conversely, when supply is high and demand is low, prices tend to decrease.

The price mechanism plays a crucial role in a free-market economy as it allocates resources efficiently. When prices increase, producers are incentivized to increase supply, leading to a higher quantity of goods or services available in the market. On the other hand, when prices decrease, consumers are encouraged to buy more, leading to higher demand.

By allowing the forces of demand and supply to interact and determine prices, the price mechanism helps in balancing supply and demand, ensuring that resources are allocated efficiently and productively in a free-market economy.