# Profit Maximization Methods in Managerial Economics

The profit maximization theory states that firms (companies or corporations) will establish factories where they see the potential to achieve the highest total profit. The company will select a location based upon comparative advantage (where the product can be produced the cheapest). The theory draws from the characteristics of the location site, land price, labor costs, transportation costs and access, environmental restrictions, worker unions, population etc. The company will then elect the best location for the factory to maximize profits. This is anathema to the idea of social responsibility because firms will place their factory to achieve profit maximization. They are nonchalant to environment conservation, fair wage policies and exploit the country. The only objective is to earn more profits. In economics, profit maximization is the process by which a firm determines the price and output level that returns the greatest profit. There are several approaches to profit maximization.

## 1. Total Cost-Total Revenue Method

To obtain the profit maximizing output quantity, we start by recognizing that profit is equal to total revenue (TR) minus total cost (TC). Given a table of costs and revenues at each quantity, we can either compute equations or plot the data directly on a graph. Finding the profit-maximizing output is as simple as finding the output at which profit reaches its maximum. That is represented by output Q in the diagram.

There are two graphical ways of determining that Q is optimal. Firstly, we see that the profit curve is at its maximum at this point (A). Secondly, we see that at the point (B) that the tangent on the total cost curve (TC) is parallel to the total revenue curve (TR), the surplus of revenue net of costs (BC) is the greatest. Because total revenue minus total costs is equal to profit, the line segment CB is equal in length to the line segment AQ.

Computing the price, at which the product should be sold, requires knowledge of the firm’s demand curve. Optimum price to sell the product is the price at which quantity demanded equals profit-maximizing output.

## 2. Marginal Cost-Marginal Revenue Method

An alternative argument says that for each unit sold, marginal profit (MÏ€) equals marginal revenue (MR) minus marginal cost (MC). Then, if marginal revenue is greater than marginal cost, marginal profit is positive, and if marginal revenue is less than marginal cost, marginal profit is negative. When marginal revenue equals marginal cost, marginal profit is zero. Since total profit increases when marginal profit is positive and total profit decreases when marginal profit is negative, it must reach a maximum where marginal profit is zero or marginal cost equals marginal revenue. If there are two points where this occurs, maximum profit is achieved where the producer was collected positive profit up until the intersection of MR and MC (where zero profit is collected), but would not continue to after, as opposed to vice versa, which represents a profit minimum. In calculus terms, the correct intersection of MC and MR will occur when:

dMR/dQ < dMC/dQ

The intersection of MR and MC is shown in the next diagram as point A. If the industry is perfectly competitive (as is assumed in the diagram), the firm faces a demand curve (D) that is identical to its Marginal revenue curve (MR), and this is a horizontal line at a price determined by industry supply and demand. Average total costs are represented by curve ATC. Total economic profit are represented by area P,A,B,C. The optimum quantity (Q) is the same as the optimum quantity (Q) in the first diagram.

If the firm is operating in a non-competitive market, minor changes would have to be made to the diagrams. For example, the Marginal Revenue would have a negative gradient, due to the overall market demand curve. In a non-competitive environment, more complicated profit maximization solutions involve the use of game theory.

## 3. Maximizing Revenue Method

In some cases, a firm’s demand and cost conditions are such that marginal profits are greater than zero for all levels of production. In this case, the MÏ€ = 0 rule has to be modified and the firm should maximize revenue. In other words, the profit maximizing quantity and price can be determined by setting marginal revenue equal to zero. Marginal revenue equals zero when the marginal revenue curve has reached its maximum value. An example would be a scheduled airline flight. The marginal costs of flying the route are negligible. The airline would maximize profits by filling all the seats. The airline would determine the profit maximum conditions by maximizing revenues.

## 4. Changes in Fixed Costs Method

A firm maximizes profit by operating where marginal revenue equals marginal costs. A change in fixed costs has no effect on the profit maximizing output or price. The firm merely treats short term fixed costs as sunk costs and continues to operate as before. This can be confirmed graphically. Using the diagram, illustrating the total cost-total revenue method, the firm maximizes profits at the point where the slope of the total cost line and total revenue line are equal. A change in total cost would cause the total cost curve to shift up by the amount of the change. There would be no effect on the total revenue curve or the shape of the total cost curve. Consequently, the profit maximizing point would remain the same. This point can also be illustrated using the diagram for the marginal revenue-marginal cost method. A change in fixed cost would have no effect on the position or shape of these curves.

## 5. Markup Pricing Method

In addition to using the above methods to determine a firm’s optimal level of output, a firm can also set price to maximize profit. The optimal markup rules are:

(P – MC)/P = 1/ -Ep
or
P = (Ep/(1 + Ep)) MC

Where MC equals marginal costs and Ep equals price elasticity of demand. Ep is a negative number. Therefore, -Ep is a positive number.

The rule here is that the size of the markup is inversely related to the price elasticity of demand for a good.

## 6. Marginal Revenue Product of Labor (MRPL) Method

The general rule is that firm maximizes profit by producing that quantity of output where marginal revenue equals marginal costs. The profit maximization issue can also be approached from the input side. That is, what is the profit maximizing usage of the variable input? To maximize profits, the firm should increase usage “up to the point where the input’s marginal revenue product equals its marginal costs”. So mathematically the profit maximizing rule is MRPL = MCL. The marginal revenue product is the change in total revenue per unit change in the variable input- assuming input as labor. That is, MRPL = Î”TR/Î”L. MRPL is the product of marginal revenue and the marginal product of labour or MRPL = MR x MPL.