Baumol’s Sales Revenue Maximization Model

Introduction

Baumol’s Sales Revenue Maximization Model was developed by an American Economist W. J. Baumol. He propounded a model of sales maximization in his book “Business Behaviour, Value and Growth”. This model, like other managerial theories, is an alternative to the profit maximization model.

In a dominated corporate world where management is divorced from ownership, Baumol challenges the profit maximization assumption regarding business behaviour. He laid emphasis on how sales maximization is a more valid and realistic assumption of business behaviour in the dominated world.

According to him, the sales maximization model is one of the managerial theories of the firm. In this model, more emphasis was given to the manager’s role and their interest in deciding price, output and advertising policies.

The objective of this model is not to maximize the physical volumes of sales but to maximize the total revenue from sales. Thus, this theory is also known as the revenue maximization model.

Baumol does not reject the profit motive altogether. But according to him, there is a minimum acceptable level of profits which must be earned by the managers so as to finance the growth of the firm in the future through retained profits.

This can be explained as the managers in oligopolistic firms seeking to maximize sales subject to a minimum profit constraint. In other words, managers seek to maximize total revenue subject to a minimum profit constraint.

To quote Baumol, “My hypothesis then is that oligopolistic firm typically seeks to maximize their sales subject to a minimum profit constraint. The determination of the minimum just acceptable profit level is a major analytical problem and I shall only suggest here that it is determined by long-run considerations. Profits must be high enough to provide the retained earnings needed to finance current expansion plans and dividends sufficient to make future issues of stocks attractive to potential purchasers. In other words, the firm will aim for that stream of profits which allows for the financing of maximum long-run sales. The business jargon for this is that management seeks to retain earnings insufficient magnitude to take advantage of all reasonably safe opportunities for growth and to provide a fair return to shareholders”.

Baumol Sales Revenue Maximization Theory: Price and Output Determination

Assumptions of Baumol’s Sales Revenue Maximization Model

i. There is a single period time horizon of the oligopolistic firm.

ii. The firm aims at maximizing its total sales revenue in the long run subject to a minimum profit constraint.

iii. The firm’s minimum profit constraint is set competitively in terms of the current market value of its shares.

iv. The oligopolistic firm is facing cost curves which are normally U-shaped, and the demand curve is downward sloping possessing a negative relationship between price and output. Its total cost and revenue curves are also of the conventional type.

In the Baumol sales maximisation model, let us determine the price and output under an oligopolistic firm graphically. It is shown in figure1. In the figure, Total revenue, total cost and total profits are measured on Y-axis, and output is measured on X-axis.

TC is the total cost curve in the long run as it starts from the origin. TR is the total revenue curve faced by the oligopolistic firm. OP is the total profit curve which starts from the origin, reaches a maximum and then falls thereafter as the level of output increases. Total profit is defined as the difference between total revenue and total cost at various levels of profit.

Thus, the total profit curve measures the vertical distance between the total cost and total revenue curve at various levels of output. Profit is maximum when the firm is producing OB level of output. So, if an oligopolistic firm wants to maximize profit, it should produce OB units of output.

But we have seen above that an oligopolistic firm under the Baumol sales maximization model seeks to maximize sales subject to a minimum profit constraint. If the firm wants to maximize sales, then it would produce OD level of output, which is greater than the profit-maximizing level of output OB. It is clear from the figure that sales-maximizing output is greater than profit-maximizing output.

At OD level of output, total revenue is maximum as shown by point TR2. At this level of output, the firms are earning a total profit equal to HD, which is less than the maximum total profit BF. Suppose the minimum profit constraint is denoted by line TL which indicates the minimum total profits that a firm wants to obtain. This minimum profit line TL cuts the total profit curve at point G.

According to Baumol, if the firm seeks to maximize sales subject to a minimum profit constraint OT then it would produce and sell OC units of output. The total revenue at output level OC is CTR1. The total revenue that is earned at output level OC is less than the maximum total revenue TR2. But the total revenue that is earned at output level OC is the maximum obtainable revenue with respect to the minimum profit constraint as shown by minimum profit line TL.

The firm can earn minimum profit OT as shown by the minimum profit line TL even by producing OA units of output, but the total revenue earned at output level OA is less than at output level OC.

If the objective of the oligopolistic firm is to maximize sales subject to minimum profit constraint, then it would not produce OA units of output. The output associated with maximum sales is larger than profit-maximizing output OB but less than total revenue-maximizing output OD.

The oligopolistic firm under the Baumol sales maximization model would be in equilibrium at output level OC. At this output, firms are earning total profits equal to GC. In Baumol’s sales maximization model, firms maximizing sales subject to minimum profit constraints will lead to lower prices and greater output in comparison to profit maximization. The price would be lower in the sales maximization model because the output is greater, and the demand curve and average revenue faced by an oligopolistic firm are negatively sloped.

The price that is charged at output level OC is calculated by dividing total revenue by units of output produced. The total revenue earned by producing OC units of output is CTR1. The price that is charged for output level OC is CTR1/OC.

Baumol’s Sales Revenue Maximization Theory: Non-Price Competition

Under the sales maximization model, another important feature of the firm is non-price competition. We have seen under oligopoly that oligopolistic firms are reluctant to change prices as it can give the wrong signal to their competitors. Firms rather than engaging in price competition indulge themselves in maximizing sales by promoting their products with the help of advertisements, banners, posters, giving free samples, product modification, the introduction of special services for the customer etc.

It has been widely observed by many economists that oligopolistic firm is often very much reluctant to use price-cutting to promote their sales. The greater the intensity with which oligopolistic firms indulge in non-price competition can be better explained with a sales-maximization objective rather than with the profit-maximization objective. This increase in non-price competition expenditure increases the volume of sales and thus increases the total revenue earned by the oligopolistic firms.

On the other hand, the effect of changes in price on total revenue is doubtful. This happens because of the nature of demand, whether it is elastic or not elastic. Any reduction in price increases the total revenue in that it usually adds to the number of units which can be sold; simultaneously, it also works in the opposite direction by reducing the revenue on each unit sold.

The effect of reduced prices on profits is more uncertain because if it fails to raise total revenue, it will most probably reduce profits because the increase in output as a result of a reduction in price will increase total costs. On the other hand, while the profitability of advertising and product modification improved service is doubtful, their favourable effect on sales is quite certain.

Let us now explain how much optimal advertising expenditure a firm will undertake under the Baumol sales maximization model.

Optimal Advertising Outlay under Baumol Sales Maximization Model:

We have seen that under the Baumol sales maximization model, firms seek to maximize sales subject to a minimum profit constraint. The important question is how much optimal advertising expenditure would be incurred by a firm so as to achieve this objective. This is shown in Figure 2.

In the figure, Total revenue, total cost and total profits are measured on Y-axis, and advertisement outlay is measured on X-axis. TC is the total cost curve faced by the firm. TR is the total revenue curve faced by the oligopolistic firm, which shows the change in total revenue as the advertising outlay is raised, given the price of the product.

OP is the total profit curve which starts from the origin, reaches a maximum and then falls thereafter as the level of output increases. The curve OD is the advertisement cost incurred by the firm, and it is drawn so as to make 450 angles with X-axis.

Baumol, based on his empirical evidence, assumed that an increase in advertising outlay by a firm will always raise the physical volume of sales up to a point. After reaching this point, sales are increasing at a diminishing rate.

Given the price of the product, as a result of an increase in advertising outlay, the total revenue will increase in proportion to the increase in the physical value of sales. Thus, this increase in advertising outlay will cause the total revenue to increase up to a certain point and beyond this point, diminishing returns are likely to sets in. The cost that a firm is incurring on fixed and variable costs is taken to be independent of the advertisement outlay.

The total cost TC is obtained by adding a fixed amount of other costs (OM) to the advertising cost curve OD. Total profit is defined as the difference between total revenue and total cost at various levels of profit. Thus, the total profit curve measures the vertical distance between the total cost and total revenue curve at various levels of output.

If the firm seeks to maximize its profit, then to earn GA1 units of profit, it would have to incur advertising expenditure equal to OA1. If the firm seeks to maximize sales subject to a minimum profit constraint TL, then it should spend OA2 advertisement expenditure. This sales maximization advertisement expenditure OA2 is more than the profit-maximizing expenditure OA1. It can be seen here that the objective of sales maximization subject to a constraint leads to a greater level of advertisement expenditure than the profit maximization objective.

Baumol’s Sales Revenue Maximization Theory: Change in Overhead Cost

The important aspect of the Baumol sales maximization model is the effect of changes in overhead cost on the prices of the product. Under profit maximization theory, if the overhead cost does not vary with output, then changes in overhead cost do not affect the prices of the product and nor even the output produced of the products.

But in general, changes in overhead costs do affect the price of the product and the output. To quote Baumol, “This piece of received doctrine is certainly at variance with the business practice where an increase in fixed costs is usually the occasion for serious consideration of a price increase”.

We have seen under Baumol that firms seek to maximize sales subject to minimum profit constraints. Under the Baumol sales maximization model, we can rationalize the change in the price of the product as a result of a change in overhead costs.

Suppose oligopolistic firms are in equilibrium; that is they are maximizing sales subject to a minimum profit constraint. Any increase in overhead costs would result in an increase in the total cost of production. This increase in the total cost of production would result in a fall in the profit level below the minimum acceptable profit level.

In order to prevent this fall in the profit level below the minimum acceptable profit level and to be in equilibrium, oligopolistic sales maximization firms would reduce the production of the product so as to raise the price of the product. It is shown in Figure 3.

In the figure, total profits are measured on Y-axis, and output is measured on X-axis. OP is the total profit curve which starts from the origin, reaches a maximum and then falls after that as the level of output increases.

Now suppose for certain revenue and cost functions, the total profits curve PP is shown as in the figure. Suppose the minimum profit constraint is denoted by line TM which indicates the minimum total profits that a firm wants to obtain. The oligopolistic firm that seeks to maximize sales subject to a minimum profit constraint TM is in equilibrium at OA level of output.

Now suppose there is an increase in overhead cost by the amount PP1. With any increase in overhead cost, there is an increase in the total cost of production and, thus, a reduction in the profit earned by the firm. This increase in overhead cost would shift the total profit curve uniformly downward by the amount PP1.

After an increase in overhead cost, the new profit curve is PP1. This increase in the overhead cost does not affect the profit-maximizing level OM. This is so because any increase in overhead cost reduces the height of the profit curve uniformly downward with no change in the location of its peak.

But the sale maximizing output with TM minimum profit constraint will reduce output from OA to OB. This reduction in profit would induce firms to raise the price of the product. So, under the Baumol sales maximization model, any increase in overhead cost would result in an increase in the price of the product.

Baumol Sales Revenue Maximization Theory: Corporation Income Tax

Under the sales maximization model of Baumol, we can easily explain the impact of corporation tax on product price and output. Corporate income tax is defined as a tax on the profits of public limited companies. The same can be explained as changes in overhead cost. It is shown in Figure 3.

Let us suppose that the corporation income tax of amount PP1 has been imposed. The profit-maximizing firm cannot do anything to shift any part of the corporate income tax to the consumer. Profit maximizing firm cannot even gain anything by raising the price of the product or changing its output as a result of the imposition of corporate income tax.

Hence, the price of the product and the output remain unaltered due to the imposition of the corporate income tax. The corporation income tax reduces the height of the total product curve from PP to PP1, but it does not make the peak of the curve move either left or right. For the sales maximization firm with minimum profit constraint, the price of the product will be raised, and output would decline as a result of corporate income tax.

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