Profit maximization In each of the above market categories, there is an underlying assumption that suppliers are aware of their cost and revenue functions. Profit maximization occurs at the point at which marginal cost = marginal revenue, and the selling price which will optimize sales volume and thus maximize profits can be calculated by finding the value of the demand or total revenue curve at this optimal level. This is illustrated graphically in Figure. • Total Costs and Revenues • Profit Curve • Marginal cost and revenue If, for the purpose of analysis, we accept the assumption of known cost and demand functions inherent in the microeconomic model, the optimal selling price can be determined mathematically with relative ease, as in Example 1. Example 1 A supplier has calculated his demand and total cost functions as follows: Demand function x = 50,000 - 20p Total cost function TC = £100,000 + 40x By solving the demand function in respect of p, we can find the price function P: Price function 20p = 50,000-x p = 2,500 - 0.05x We can now determine the total revenue function simply by multiplying the price function, p, by the sales volume, x. Total revenue function TR = 2500x - 0.05x From this stage, we can calculate the optimal sales volume in two different ways. We can either proceed via the derivation of marginal cost and marginal revenue (a), or develop and solve an equation for total profits (b): Setting marginal cost = marginal revenue, to determine optimum sales volume, we have: (b) Total profits = total revenues - total costs: TP = 2,500x - 0.05x°- £100,000 - 40x Taking the first derivative of this equation, we have: and setting this derivative to equal zero, we have: 0=2,500 - 0.1x-40 as above, x= 24,600 We now substitute this optimal sales volume figure (however calculated) in the price function derived earlier, in order to calculate the selling price at this volume: p = 2,500 - 0.05 (24,600) optimum selling price p = 1,270 Note that when alternative (b) is employed, it will be necessary to go to the second derivation of the profit function in order to confirm that the slope is negative: If this second derivative had been positive rather than negative, we would have calculated the sales volume that maximized the loss for the supplier rather than the profit. However theoretically attractive such a strict micro-economic approach to the pricing decision might be, the reader would doubtless wish to argue that the assumptions are so restrictive as to make it of very limited practical value as a prescriptive model (see Dorward 1987] for a full critique). As Nagle (1984) put it, '(Marketeers) are soon disillusioned if they look to economics for practical solutions to pricing problems' (p. S4). In the real world, the variables which can influence both cost and demand are of such magnitude and quantity that the information required by the analysis is unlikely to be forthcoming at a reasonable price, if at all. Fur-thermore, as we saw in the section on monopoly, profit maximization will often not be achievable in practice even by those suppliers in the best position to realize it, and indeed it might not be the only objective pursued by the firm in any event, although as stated earlier, profitability - whether maximising or satisficing - must invariably remain the principal focus if other aims are to be met. In practice, in the absence of perfect information, the vast majority of suppliers, in any market category, will have no option but to set out to achieve a target profit rather than a maximum profit, and most pricing decisions will use formulae based on cost and desired profitability levels rather than the direct application of an economic model. However, familiarity with the academic theory behind the pricing decision, and the significance of the different types of market on the flexibility inherent in that choice, will enable the manager to gain a better appreciation of the forces at work, and thus improve the quality of the decision itself.