Profit maximization and Equilibrium of a Firm

Profit maximization and Equilibrium of a firm

In economics, profit may be defined as the net income of the business or the organization after all the costs like rent, wages, and interest, etc. have been deducted from the total income. Generally, the normal rate of profit is incorporated in the cost items of the firm.

Profit is the difference between total revenue and total cost of the business. 'Π' denotes the profit in the economics. Mathematically, Π = TR -TC. The maximum profit of the firm can be easily seen graphically in two ways:

1. Total revenue - Total cost (TR - TC) approach
2. Marginal revenue - Marginal cost (MR - MC) approach

1. Total cost - Total revenue approach

A firm is in equilibrium when it is earning maximum profit. Simply, if the difference between total revenue and total cost is maximum when the output is produced. This state is said to be the firm is in equilibrium maximizing profit. Total revenue refers to a number of total receipts that a firm receives from the sale of products, i.e. gross revenue. It is obtained by multiplying total sales quantity (or output) with the per unit price. Thus, TR = Q × P. Under perfect competition, the price of the product remains constant at any level of output. Hence, total revenue varies positively and proportionately with the level of output. The TR curve slopes upwards to the right at 45⁰. Total cost in the short run is the sum of total fixed cost and total variable cost. Since total fixed cost remains constant and positive at any level of output, total cost follows the trend of total variable cost.

In the figure, total revenue and total cost are measured in Y-axis and output is measured in X-axis respectively. This figure clearly shows the total revenue (TR) and total cost (TC) curves of a firm under perfectly competitive market. The total revenue (TR) curve is a straight line (slopes upwards to the right at 45⁰) through the origin. This clearly shows that the price remains unchanged or constant at all levels of output. The firm is a price taker and can sell any amount of output at the going market price, with its TR increasing proportionately with its sales. The slope of the TR curve is the marginal revenue. It is constant and equal to the prevailing market price since all units are sold at the same price. Thus in pure competition MR = AR = P.

The shape of the total-cost curve reflects the U shape of the average cost curve, that is, the law of variable proportions. The firm maximizes its profit at the output Xe, where the distance between the TR and TC curves is the greatest. At lower and higher levels of output total profit is not maximized at levels smaller than XA and larger than XB the firm has losses.

The total-revenue-total-cost approach is awkward to use when firms are combined together in the study of the industry. The alternative approach, which is based on marginal cost and marginal revenue, uses price as an explicit variable.

2. Marginal revenue - Marginal cost approach

The total revenue - total cost approach is awkward to use when firms are combined together in the study of the industry. The alternative approach, based on marginal cost and marginal revenue, uses price as an explicit variable and it shows clearly the behavioral rule that leads to profit maximization.
Marginal Revenue is defined as the addition made to the total revenue by selling one more unit of the output. In other words, it is the ratio of change in the total revenue with a change in the total sales quantity (by selling one more unit of output). It reflects the rate of change in total revenue. Thus,
MR = ΔTR / ΔQ or MR = TR(n) – TR(n-1)

Marginal cost is the addition made to the total cost by producing one more unit of output. But, the marginal cost in the short run is connected with the variable factor. Thus, the short-run marginal cost is the ratio of the change in the total variable cost of the change in the total quantity produced. It is expressed as MC = ΔTVC / ΔQ

In the figure, revenue and cost are measures in Y-axis and output in X-axis. The marginal curve (MC) is U-shaped, the law of variable proportions which is operating in the short-run during which the size of the plant is constant. The firm maximizes its profit at the level of output defined by the intersection of the marginal cost curve (MC) and marginal revenue (MR) curve (point B). To the left of M1 has not reached its maximum level because each unit output left of M1 brings to the firm a revenue which is greater than its marginal cost. To the right of M1 each unit output cost is more than the revenue earned by its sale, therefore it creates a loss and total profit is reduced. In summary:

• If MC < MR, total profit has not maximized and it pays the firm to expand its output.
• If MC > MR, the level of total profit is being reduced and it pays the firm to cut its production.
• If MC = MR, the short run profits are maximized.

Thus, the first condition for the equilibrium of the firm is that marginal cost is equal to marginal revenue (i.e. MR = MC). However, this condition is not sufficient, since it may be fulfilled and yet the firm may not be in equilibrium. In the figure, that the condition MC = MR is satisfied at point A, yet clearly the firm is not in equilibrium since profit is maximized at M1 > M. The second condition for equilibrium requires that the MC is rising at the point of its intersection with the MR curve. This means that the MC must cut the MR curve from below, i.e. the slope of the MC must be greater than the slope of MR curve. In the figure, the slope of MC is positive at B while the slope of the MR is zero (or negative) at all levels of output.

Reference

Koutosoyianis, A (1979), Modern Microeconomics, London Macmillan