Focus On Profit Maximisation Models For Firms

In both perfectly competitive market and the one that can influence price, profit-maximising output make decision for any firm, which because profit is difference between (total) revenue and (total) cost, to find out the firm’s profit-maximising output level means analysing its revenue. Suppose that the firm’s output is q, and revenue is R. This revenue is equal to the price of the product P times the number of units sold: R = P*q. The cost of production C also depends on the level of output. The firm’s profit is °, thus (Robert & Daniel, 2005):

°(q) = R (q) – C (q)

To maximise profit, the firm selects the output for which the difference between revenue and cost is the greatest. This principle is illustrated in figure below.

(Robert & Daniel, 2005)

Objectives of Firm

Firms have two kinds of objective: maximising goals and non-maximising goals. The marginal analysis is particularly important for maximising goals. However, the marginal analysis cannot find out how firms maximise profits or revenue. It simply show that what the output and price must be if they do succeed in maximising these items, whether by luck or by judgment (Alan & Stuart, 2007, p47).

Maximising goals

Profit maximisation

The traditional theory of the firm assumes that firms aim simply to maximise profit, the assumption is from two directions:

First, owners are in control of the day-to-day management of the firm.

Second, the main desire of owners is for higher profit (Alan & Stuart, 2007, p47).

Both of these assumptions are questionable, for example: some of very large firms such as Shell, M&S and Ford are run by managers. There may be thousands of shareholders of each firm, but each shareholder will typically own only a few shares, which means that the typical owner has little or no power (Brain & Robin, 1998).

Profit is maximised where marginal revenue (MR) equal to marginal cost (MC), i.e. where the revenue raised from selling an extra unit is equal to the cost of producing that extra unit. To assume that it is the owners who control the firm neglects the fact that the dominant form of industrial organisation is the public limited company, which is usually run by managers rather than by owners. This may lead to conflict between the owners (shareholders) and the managers, which because the ways of managers reach to their goals are differ from the owners. This conflict is referred to as a type of principle-agent problem and emerges when the shareholders (principles) contract a second party, the managers (agents), to perform some tasks on their benefit. This has led to a number of managerial theories of firm behavior, such as sales revenue maximisation and growth maximisation (Alan & Stuart, 2007, p48).

Sales revenue maximisation

On a day-to-day basis most firms likely seek goals rather than profit maximisation. In terms of Sales Maximisation: many firms make decisions designed to increase or maximise production and the amount of output sold. More sales means more revenue, but not necessarily more profit.

Henry and William (2007) pointed out that William J. Baumol is a polyhistor who has contributions to the field of industrial organisation. Baumol (1958) explored the implications of sales revenue maximisation as an objective function, different from that which is usually assumed (profit or value maximisation, depending on whether one works with a static or a dynamic model) for firms in imperfectly competitive markets. Analysis of the strategic implications of such alternative objective functions, sales maximisation has become a standard element in the analysis of imperfect competition. Baumol also takes the view that economics is indicating what a firm’s objective function ought to be, it analyze the implications of alternative objective functions for firm and/or market performance (Henry and William, 2007).

Baumol (1959) has suggested that the manager-controlled firm is likely to have sales revenue maximisation as its main goal rather than the profit maximisation favoured by shareholders. His argument is that the salaries of top management are more closely correlated with sales revenue than profits (Alan & Stuart, 2007, p48).

Baumol’s Sales Revenue Maximising Model

In Baumol’s Sales Revenue Maximising Model, managers’ rewards are more linked to quantity of sales than to profit, thus firms aim to maximise sales revenue, but subject to a profit constraint.

In figure the firm will choose to produce level of output A, giving total revenue B and profit C. This implies a higher level of output, and therefore a lower price, than the equivalent profit-maximiser, who would produce output D and earn revenue E (Howard & Lam, 2001).

Williamson’s Managerial Utility Maximising Model

Williamson’s (1963) managerial theory of the firm is similar to Baumol’s maximising sales revenue as a major firm objective. However, Williamson’s is more broadly, managers seeking to increase satisfaction through the greater expenditure on both staff levels and higher sales revenue. Capital can come from profits, external finance and sales revenue. In Williamson’s opinion, increased sales revenue is the easiest means of providing additional funds, since higher profits have in part to be distributed to shareholders, and new finance requires greater accountability. Baumol and Williamson are describing the same phenomenon, but in different terms.

If management seeks to maximise sales revenues without any thought to profit at all (pure sales revenue maximisation) then this would lead to output unit is neither raising nor lowing total revenue, i.e. its marginal revenue is zero (Alan & Stuart, 2007, p48).

Manager’s utility is constrained by the relationship between profits and staff expenditure. Up to the level of maximum profit, staff expenditures and discretionary profits expand together, but if output continues to increase, profits decline as staff expenditures increase (Kenneth & Caroline & E.L, 1992).

Constrained sales revenue maximisation

Both Baumol and Williamson pointed that shareholders can exercise some constraint on managers. Maximum sales revenue is usually occur well than the level of output of maximum profits. The shareholders may demand at least a certain level of distributed profit, so that sales revenue can only be maximised subject to this constraint.

Marris’s Model of Growth maximisation

The opinion that goals of owners (profit) have been in conflict with the goals of management (sales revenue) has been assumed. However, Marris (1964) believes that owners and managers have a common goal – maximum growth of the firm.

Marris (1964) supports that the growth is the primary goal that both managers and owners have. Managers seeking a growth in demand for the firm’s products or services to raise power or status, while owners seeking a growth in the capital value of the firm to increase personal wealth.

The ‘retention ratio’, which is the ratio of retained to distribute most of the profits created by Marris. If managers distributed most of the profit (low retention ration), then the retained profit can be used for investment, stimulating the growth of the firm. In this case shareholders may be less content, and the share price lower, thus increasing the risk of a takeover bid (Alan & Stuart, 2007, p49).

The major objective of the firm that both managers and shareholders are in accord is then seen by Marris as maximizing the rate of growth of the firm’s demand and the firm’s capital (balanced growth), subject to an acceptable retention ratio.

Profit maximisation is usually based on the assumption that firms are owner-controlled, whereas sales and growth maximisation usually assume that there is a separation between ownership and control. (Alan & Stuart, 2007, p51)

Penrose’s Effect Theory

In the review of Penrose’s the Theory of the Growth of the Firm for the Economic Journal, Marris (1961) predicted that the book would prove to be one of the most influential books of the decade. In his entry to the New Palgrave, he added that ‘this proved an understatement’ (Marris, 1987, p.831). It is interesting to note that Marris based this last view on the then available literature. This was primarily limited to ‘managerial theories of the firm’ (Marris, 1996) and in particular to the so called ‘Penrose effect’ (that administrative, especially managerial, limits to the rate of growth exits), as well as to the potential impact of this effect on macroeconomic growth (Uzawa, 1969).

Penrose and the neo-classical theory

Richardson (1999) said that Mrs. Penrose’s theory of the growth of the firm is widely known and accepted. In the foreword of the third edition of her book, she states quite explicitly, in relation to neoclassical theory, in her opinion ‘useful to attempt to’ integrate ‘the two approaches’.

An important focus of managerial theories was on the extent to which managerially run firms could pursue objectives different to short-term profit maximisation, for example the maximisation of sales revenue (Baumol, 1959, 1962), discretionary expenditures (Williamson, 1964) of growth maximisation (Marris 1964), and what are the implications of such behaviour for ‘managerial capitalism’ (Edith & Christos, 2002, p.30).

Penrose’s own role in this context was seen in terms of her providing justification for the motivation for growth and the ‘Penrose effect’. Concerning the former, and following a critique by Marris (1961) that her treatment of profits and growth was ‘woolly’, as well as Slater’s (1980) work, Penrose admitted that profits and growth could not be treated as ‘equivalent criteria for the selection of investment programmes’ (Penrose, 1985, p.8). Nevertheless, she maintained that she found the assumption that managers of firms try in general to make as much money as seems practical to be not only the most useful, but in fact the only general assumption from which reasonably general conclusions can be drawn (Penrose, 1985, p.12)

The total effect of Edith Penrose’s work was that of destruction of the neoclassical model of the firm, followed by reconstruction. In the following years, and despite the wide recognition the work received, classroom microeconomic theory, and also classroom industrial organisation, often seemed to continue as if nothing had happened (Marris, 1987, p.831)