How do prices serve as signals and incentives to producers to enter a particular market? to leave a certain market?

Several factors go into this answer. First. Producers must be cognizant of whether the market place is suitable for their goods and or services by determining the profit margin. Often times there are variable costs (a component required to make the product or service for sale.) For instance, if one is selling laptops and all the components inside are at a low cost but when put together ... you can sell it for a higher price than what it cost make. But if the cost of one component, lets say for example the hard drive goes up in price by 3 times what ot originally cost, then it may not be profitable to sell that laptop and you would exit the market. If that same hard drive dropped in price, theoretically, one would re enter that market.