The shaded region is the profits of the firm. The price line is also the marginal revenue and the average revenue for the firm. So, the company earns profit only when marginal cost is less than the marginal revenue (the area denoted by the shaded portion). When marginal cost increases more than the marginal revenue, the firm incurs loss and so production must be reduced. Also, at the point of profit maximizing quantity, the marginal revenue and marginal cost are equal. This concept helps the firm to decide at what point the production must be increased or decreased. This also brings out the relationship between supply and demand. When the supply (the quantity produced) is less than the quantity demanded, the firm incurs profit and when the supply is more than demand, the firm incurs a loss. Based on this, the firm can also decide the right amount of supply that has to be made to the market to get maximum profits.

Criticism

Despite the usefulness of this theory, there is also a lot of shortcomings associated with it. First and foremost, this theory assumes that firms operate in perfect competition. In reality, this is far from truth. The firms operate in anything but a perfect environment and in that case, these concepts may fail. In a non-perfect world, profit maximization is computed using game theory and this includes lot more factors like competition, pricing, demand and supply.

A firm can increase or decrease its price and production to keep pace with the competition. When the firm decides to alter its production based on the market share of the firm and its competitors, profit maximization will not be marginal revenue minus marginal cost. For example, a monopolistic company will look to control its supply to ensure that it gets maximum profit whereas in an oligopoly environment, the companies with the maximum market share tend to control the supply and the smaller firms may not be able to alter its production levels to attain maximum profitability.

Another fundamental drawback of this theory is its assumption that, "Firms maximize profits because...

Owner-managers may utilize the firm for both consumption and production. "Owner-managers will consume within the firm when the consumption possibilities offered there are not available elsewhere (e.g., utility gained from work autonomy or leading an organization) or when the cost of the utility received is lower than if consumption took place in the household (e.g., if tax policy allows certain expenses to be deducted from business but not personal income)." McCann & Vroom (2009;p.2).
The third aspect is the entry and exit of firms from a market. When a company is earning a lot of profit (maximum profits), the entry will be attractive to other firms. As more and more companies enter the market, it will result in intense competition and fragmentation of market share. As a result, the profits of the company will reduce and it will be difficult for a single firm to earn maximum levels of profit. The stronger firms will earn more than the weaker ones, irrespective of the cost of production and the quantity produced.

Conclusion

In short, the profit maximization theory in economics is a sound theory to understand the levels of production or supply required to attain maximum profits. It gives the fundamentals on which a firm can build its profit maximizing ability. but, its applicability in a real world is limited because of the above mentioned reasons.