Perfect Competition: Pricing and Output Decisions

2 years ago

Atiqur Rahman

10 minutes

Objective of a Firm: Profit Maximization

The output determination model of a perfectly competitive firm requires a close understanding of the goals of the firm as well as the information available to it. Any business enterprise has the knowledge of its cost structure, but minimizing the cost is not the predominant objective of the firm. In economic analysis, profit maximization is usually taken to be the objective of a firm.

Profit = Revenue – Cost

Therefore, in addition to the cost structure, the firm needs to make an estimation of the revenue, which is realized by selling different quantities of the output. The quantity sold multiplied by the price charged for each unit by the firm is the revenue earned by the firm.

Revenue = Price × Quantity

Therefore, the cost and demand conditions jointly determine the profits of the firm, which, upon maximizing, gives the equilibrium output level. The question of whether firms actually seek to maximize profit has been controversial. Profit maximization as an objective of the firm is discussed in further subsections with respect to the size of the firm, control of the firm and its structure.

1. Large-sized versus Small-sized firm / Manager controlled versus Owner controlled firm

Small firms are usually owner-managed, and profit maximization appears to be a plausible objective as the profits of any firm are pocketed by the owner. However, in the case of large corporations, there is a separation of ownership and management.

When a manager has the power to take day-to-day decisions of the corporation, then profit maximization may not be the goal as these managers are salaried personnel having no direct effect of profits on their salary (except the case when salaries are in accordance with profits of the firm).

It has been suggested by William Baumol that managers of a large corporations aim at maximizing sales instead of profits. Other goals which could be pursued by the managers of a large firm could be:

Revenue maximization
Revenue growth
Higher payments of dividends to the shareholders
Maximize short-run profits at the expense of long-run profits

The above argument suggests that profit maximization is not the predominant objective of a large manager-controlled firm. But such deviation by managers from the profit-maximizing objective could not continue for long. There are several reasons why such deviation from the goal is limited:

The future job prospects of a manager essentially depend on how profitably the current firm is run by the manager. Therefore, they eventually resort to profit maximization as their goal.
If a large firm deviates from profit maximization, then eventually, its share prices will follow a downward trend. A depressed share price could lead to the replacement of the management team.
Usually, the salaries of managers are tied up with the profits of the firm. In such cases, the managers have a fair incentive to follow the profit maximization principle.

Thus it could be said that in any case, firms that come close to maximizing profits are likely to survive in the long run. Therefore, the working assumption of profit maximization seems quite reasonable.

2. Cooperatives

A Cooperative is an association of people or businesses owned and managed by its members for mutual benefit. For example, a food cooperative is set up to provide food to its members at the lowest possible prices. Such enterprises do not follow profit maximization as their major objective. Its purpose is to provide the best service to its members at the minimum cost.

Profit Maximization: Total Approach

Profit maximization is a common objective of firms belonging to different market forms. The goal of maximizing profits determines the equilibrium quantity supplied by the firm. Profits are defined as the difference between the revenues and costs of the firm. Suppose the firm’s output is denoted by Q, then the total revenue (TR) is defined as:

TR (Q) = P×Q

Where P is the price of the product, and Q is the number of units of output sold. Thus, TR is the product of the price of the good and the number of units sold.TR increases as the quantity sold increases.

However, the quantity is a function of price, and a downward-sloping demand curve suggests that the demand falls as the price of goods increases. Thus, the TR of a firm is a positively sloped curve, as shown in Figure 1 below.

The total cost (TC) is also a function of output. The short-run total cost curve is shown in the figure above. A firm’s profit is the difference between revenue and cost and, therefore, is a function of output.

𝝅(Q) = TR(Q) – TC(Q)

The profit is, therefore, maximized where the difference between the total revenue and total cost is maximum.

In figure 3 above, TR and TC curves are shown, and the corresponding profit curve is derived. From the output level 0 to Q⁰, the profits are negative as the total cost curve is above the total revenue curve. It implies that the revenues are not sufficient to cover the fixed and variable costs of production.

As the quantity sold increases, the total revenue increases more rapidly than the total costs, and the profits become positive. At the output level Q^*, the difference between TR and TC is maximum and it is where the profits are maximized. However, if the firm sells more than Q^*, the profits start to fall and eventually become negative after the output level Q¹.

The bold red curve in Figure 4.3 is the profit function. It is negative at the initial output levels, then starts to increase and reaches the maximum level at Q*, after which it falls off.

Profit Maximization: Marginal Approach

The profit maximization behaviour of the firm can also be understood with the help of marginal curves. Marginal revenue (MR) is the change in revenue resulting from one unit increase in the output level sold. It is per unit change in the total revenue of the firm and is, therefore, the slope of the TR curve.

In Figure 4, the MR at point A would be the slope of the dotted line. Marginal cost (MC) is the per unit change in cost resulting from one unit increase in the output level produced. It can be read as the slope of the TC curve. In Figure 5, MC at point B is the slope of the dotted line.

In Figure 4.3, the equilibrium has been obtained at output level Q* where the distance between TR and TC curves is maximum. At this level, the slope of the TR and the TC curves are the same (the tangents to both curves are parallel). This implies that the marginal revenue and marginal cost are the same at the equilibrium level of output.

The rule for profit maximization for any firm is MR = MC (whether the firm is competitive or not). The marginal revenue curve is derived from the demand curve; therefore, it is downward sloping whenever the demand curve is downward sloping.

However, the MC curve is U-shaped, and it has both a downward and upward curvature. Thus, equality of marginal revenue and marginal cost is not enough to maximize profits. It becomes important to check the consequence of this condition under the following two cases:

Marginal cost is downward sloping.
Marginal cost is upward sloping.

In Figure 6 above, the MR curve is taken to be a straight line (the case when the price is constant for every output level). The MC curve is U-shaped and intersects the MR curve at X and Y.

According to the condition, MR = MC, both points X and Y should qualify to yield the profit-maximizing output level. However, only one of these points is profit maximizing. The firm should not stop production at Q¹ as increasing the output level will add more to the revenues than to the costs, thus increasing profits.

But as the firm reaches output level Q2, it has no further incentive to increase the output. If the output increases further, the firm would add more to the cost than to the revenues, thus reducing the profit level. Hence, the profit-maximizing output level is given by point Y and not by point X.

The profit maximization condition can be summarized as follows:

Total Approach	Marginal Approach
The difference between TR and TC curves is maximum	MR = MC MC curve should be steeper than the MR curve in case the MR curve has a zero slope as under perfect competition. (or the MC curve should cut the MR curve from below).

Using calculus, the profit maximization condition can be derived as follows:

𝝅(Q) = TR(Q) – TC(Q)

d𝝅/dQ = (dTR/dQ) – (dTC/dQ) = 0

i.e. according to the first-order condition, MR = MC, and the second-order condition is

𝑑²𝑇𝑅/𝑑²𝑄 − 𝑑²𝑇𝐶/𝑑²𝑄 < 0

i.e., the slope of the MR curve < slope of the MC curve.

Thus, both conditions for profit maximization are derived algebraically.

Perfect Competition: Pricing and Output Decisions

Objective of a Firm: Profit Maximization