Presumably, the student's question -- what factors determine "how much a firm will make in the product market -- is intended to elicit information regarding profits that can be made, as opposed to volume of product manufactured. That, then, means the answer is a product primarily of the size of the market and of the amount of competition the company in question must confront. A company that enjoys a monopoly over a particular product -- and monopolies are illegal when they occur as a result of one company's efforts at depriving other companies from the opportunity to compete -- will reap tremendous profits if the market is large and the cost of manufacturing is contained. The absence of competition in the marketplace generally results in the customer or consumer being forced to pay more than would be the case if that customer or consumer had alternative sources of the item or service in question. The more competition, the lower the costs, as consumers have options and manufacturers must minimize their profit margin in order to win market share.
Profitability in the absence of competition can be constrained if the product is a luxury item that consumers may want but can easily go without. Such items may have a very limited market because of their cost, but still be profitable because that limited market wants the product and is willing to pay the price, no matter how exorbitant. Rolls Royce is an enormously expensive line of automobiles that remains profitable because the small percentage of car buyers that can afford it want it and are willing to pay hundreds of thousands of dollars for that particular automobile.
In short, market size and level of competition are the key indicators in determining profitability. They are not, however, the sole indicators when the item or service being marketed appeals to niche categories of consumers who are able to ignore cost for the appeal of owning an expensive product. In such cases, the costs associated with producing the item may not be particularly relevant to wealthy consumers. For most items, however, the costs of manufacturing, including labor and materials, and the level of competition are the most important factors.