Profit Maximization

In economics, profit maximization is the short run or long run process by which a firm may determine the price, input, and output levels that lead to the highest profit. Neoclassical economics, currently the mainstream approach to microeconomics, usually models the firm as maximizing profit.

There are several perspectives one can take on this problem. First, since profit equals revenue minus cost, one can plot graphically each of the variables revenue and cost as functions of the level of output and find the output level that maximizes the difference (or this can be done with a table of values instead of a graph). Second, if specific functional forms are known for revenue and cost in terms of output, one can use calculus to maximize profit with respect to the output level. Third, since the first order condition for the optimization equates marginal revenue and marginal cost, if marginal revenue (mr) and marginal cost(mc) functions in terms of output are directly available one can equate these, using either equations or a graph. Fourth, rather than a function giving the cost of producing each potential output level, the firm may have input cost functions giving the cost of acquiring any amount of each input, along with a production function showing how much output results from using any combination of input quantities. In this case one can use calculus to maximize profit with respect to input usage levels, subject to the input cost functions and the production function. The first order condition for each input equates the marginal revenue product of the input (the increment to revenue from selling the product caused by an increment to the amount of the input used) to the marginal cost of the input.

The principal difference between short-run and long-run profit maximization is that in the long run the quantities of all inputs, including physical capital, are choice variables, while in the short run the amount of capital is predetermined by past investment decisions. In either case there are inputs of labor and raw materials.

Example of Profit Maximization

In the early 1960s and before, airlines typically decided to fly additional routes by asking whether the extra revenue from a flight (the Marginal Revenue) was higher than the per-flight cost of the flight.

In other words, they used the rule Marginal Revenue = Total Cost/quantity

Then Continental Airlines broke from the norm and started running flights even when the added revenues were below average cost. The other airlines thought Continental was crazy – but Continental made huge profits.

Eventually, the other carriers followed suit. The per-flight cost consists of variable costs, including jet fuel and pilot salaries, and those are very relevant to the decision about whether to run another flight.

However, the per-flight cost also includes expenditures like rental of terminal space, general and administrative costs, and so on. These costs do not change with an increase in the number of flights, and therefore are irrelevant to that decision.

Limitations of the Profit Maximization Rule (MC = MR)

1. In the real world, it is not so easy to know exactly your Marginal Revenue and Marginal Cost of the last products sold. For example, it is difficult for firms to know the price elasticity of demand for their good – which determines the MR.
2. The use of the profit maximization rule also depends on how other firms react. If you increase your price, and other firms may follow, demand may be inelastic. But, if you are the only firm to increase the price, demand will be elastic.
3. It is difficult to isolate the effect of changing the price on demand. Demand may change due to many other factors apart from price.
4. Increasing price to maximize profits in the short run could encourage more firms to enter the market. Therefore firms may decide to make less than maximum profits and pursue a higher market share.