MANAGERIAL AND DECISION ECONOMICS, VOL.

9, 77-82 (1 988)

Profit Maximization and Marketing Strategies: Demand Rotation and Social Influences ~

~

C.J. AISLABIE and C.A. TISDELL Department of Economics, University of Newcastle, NSW, Australia

Microeconomic texts discuss alterations in industry demand curves as movements to higher or lower levels. Consider, instead, the implications for a monopolist’s profit of rotating its (linear) demand curve. Where this can be done without cost by pivoting at the current price it will be profitable to continue to pivot the curve until it is horizontal or vertical. The possibility of rotating the demand curve of a ‘new’ product on an arbitrarily selected price allows us to consider the optimality of different advertising strategies (‘bandwagon’ or ‘snob’).

INTRODUCTION Metwally (1981) points out that the Dorfman-Steiner (Dorfman and Steiner, 1954; Hay and Morris, 1979; Reekie, 1975, Ch. 3; Schrimper, 1977; Tisdell, 1976) condition assumes that a firm’s pricing policy is independent of its advertising outlays. Unfortunately, amending the model to remove this limitation reveals that maximum profit is a function of total revenue, profit margin, the advertising elasticity of demand, the price elasticity of demand and the advertising elasticity of price (Metwally, 1981, expression 11). This technically correct solution is not one cast in operational terms. To obtain useful results the analysis needs to incorporate additional simplifying assumptions. Precedent suggests that a difficult problem be stripped to its bare essentials. In these terms the problem becomes one of asking how a profit maximizing firm can determine the most appropriate costless changes to make in the slope of the (linear) demand curve it is assumed to be facing. This turns out to be a somewhat more difficult problem than might appear at first sight. Nevertheless, it is worthwhile exploring, because it reveals a number of findings that are not intuitively obvious. In the next section of the paper we spell out the assumptions underlying our model and briefly discuss the value of assuming that costless changes can be made in the slope of the (linear) demand curve at the current price-output combination. Where costless changes can be made in the slope of the demand curve we show that it will be profitable to continue to pivot the demand curve until it is, in the limit, horizontal or vertical. This reveals an unrecognized implicit assumption underlying the demand curve assumed in the conventional two-dimensional analysis. It also suggests assumptions that need to be incorporated to improve the analysis.

0 143-6570/88/010077-06$05.00 FJ1988 by John Wiley & Sons, Ltd.

In the third section of the paper we analyse the effect of changing the slope of the demand curve (of a product whose final price, output and demand curve slope has not yet been determined) while pivoting the curve on an arbitrarily selected price. This approach is shown to be more rewarding that than adopted in the second section of the paper. However, the value of the analysis in the second section of the paper is brought out in the comparative discussion of the fourth section. The fifth section of the paper builds on the analysis of the third section by dropping the requirement that alternative demand curves have to meet at a common intersection point. Little or no attention has been given in the economic literature to the consequences for a monopolist’s profit of rotating its demand curve, say by suitable advertising or promotion effort. As a rule, standard microeconomic texts only discuss alterations in industry demand curves as movements to higher or lower levels (e.g., Hirshleifer, 1976,p. 25; Leftwich and Eckert, 1982, p. 5 1; Mansfield, 1982, pp. 24- 5). One managerial economics text which gives considerable attention to advertising and promotional decisions, models these as causing shifis in relevant demand curves (Douglas, 1979, Ch. 14). However, there appears to be no reason (especially taking account of social factors as explored by Leibenstein, 1950) why promotional effort cannot rotate a demand curve without changing its essential position, for example at current prices and production levels. At least, thc consequences of this possibility deserve to be explored, and this paper makes a contribution to this task. Furthermore, none of the econometric studies of the relationship between consumer demand and advertising as reviewed by Koutsoyiannis ( 1 982, pp. 137-44) appear to allow for rotation of the demand curve expressed as a function of price. For example, Schoenberg’s (1933, p. 28) estimated equation for

78

C. J . AlSLABlE AND C. A. TISDELL

cigarettes Q, = 1258 - 80.4 P ,

+ 7.9 A, + 47.1 I

(where Q, is the per capita consumption ofcigarettes, P, a price indicator for cigarettes, A, a measure of advertising expenditure and t is time measured in years) does not allow for possible rotation with the level or nature of A, because both the constant term in this equation and the coefficient of P , are independent of A,. In fact, the possibility that different advertising strategies may have different consequences for demand is not discussed. It is clear that we need to cxtend our analysis. Koutsoyiannis (1982, p. 144) after reviewing the rclevant literature, concludes 'that the effects of advertising on buyers have not been theoretically or empirically cstablishcd in a satisfactory way'.

CHANGING THE SLOPE AT THE CURRENT PRICE The basic model is very simple. A monopolist with a linear, constant marginal cost curve is assumed to face a linear demand curve. It is able to make a costless change in the slope of that demand curve. The monopolist, in contemplating making such a change to its demand curves, assumes, in the first instance, that the relevant curves meet at a common intersection point. The naive question that is asked is this: does profit maximization imply that the firm would pivot the slope of its demand curve so that it is more or less steep? The basic situation is captured in Fig. 1, where DBF is assumed to be the present demand curve. Since B is assumed to be the intersection point for the current price-output profit-maximizing combination MN, the marginal cost curve, has been placed so as to be consistent with this assumption. The effect of alternative assumptions as to the placing of this curve are explored in the next section. With MN given in Fig. 1, any costless increase in the slope of the demand curve, assuming that the current

Quantity of product

Figure. 1. Rotation of demand curve on the price-output profit-maximizing point for a monopolist.

price-output combination is a pivot, always leads to increased profitability. The reason for this is that the current price-output combination is the maximum point of the concave profit function. Pivoting the demand curve still leaves the current price-output combination on the profit curve but, obviously, at some point other than the maximum of the new profit function. It follows that profit increases as the demand curve rotates around the initial price-ouput profitmaximizing position towards either the horizontal or the vertical. This is by no means an intuitively obvious conclusion. Of course, the finding is only relevant where demand curve can be pivoted without cost. Clearly, any conventional or actual demand curve only maintains its current slope because of the implicit assumption that changing that slope would be costly. One implication of the discussion is that, surprisingly enough, little is gained in launching into a discussion of the effects of a change in the slope of the demand curve by beginning the analysis from the 'obvious' starting point, namely the current priceoutput combination. For a costless change in the slope of the demand curve, the most suitable starting point is the assumption that the firm either accepts the demand curve as it is revealed in circumstances where the firm is unable to influence the quantity purchased except through changes in the price demanded for the product or it is contemplating the market possibilities of a new product by considering solely the relationship between sales volume and price demanded. On this interpretation any change in the slope of the demand curve for an established product can only be costly, and any costly change in the slope of the demand curve for an established product has the purpose of attempting to influence the quantity purchased. The analysis of a costless change in the slope of the demand curve has a role to play in the context of the launching of a new product. This will be demonstrated in the next section.

CHOOSING THE SLOPE FOR A NEW PRODUCT Launching a new product involves the choice of an appropriate management strategy. Managers are assumed to have a choice of three alternative demand curves for their product. The situation for a purely arbitrary choice of a pivot point is shown in Fig. 2. Curve DBF is drawn to represent a self-centred (nonsocially influenced) type of demand curve. This can be regarded as the demand curve which would prevail in the absence of any specific marketing strategy and on the assumption that the quantity demanded of a produt by individuals is independent of the quantity purchased by others. Curve ABC is an alternative, a snob-type curve, and curve EBG is another alternative, a bandwagon-type curve. Since the firm is assumed to have a choice of marketing strategies (or no strategy), each represented

PROFIT MAXIMIZATION AND MARKETING STRATEGIES

A

&2b

- type

,

Bandwagon-type

\

&If -centred type

C

0

Quantity of product

X

Figure 2. Some alaternative possible demand curves.

0 x,

xzx3

x4

I x5

c X

Quantity of product Figure 3. The optimality of bandwagon or snob directed marketing from management's point of view depends on the firm's level of marginal cost of production.

by a different demand curve, the outside boundary of the alternative demand curves is the relevant demand curve for the firm's planning purposes. In the case shown in Fig. 2, the relevant demand curve corresponds to ABG. I t implies maximum possible revenue at each possible price for the product, the firm being treated as ii price-maker. The relevant demand curve ABG is shown in Fig. 3 and is kinked at point B. The accompanying marginal revcnue curve has a gap below point B and is represented in Fig. 3 by AHJK. Since the marginal cost curve has no longer to be drawn to be consistent with the hypotheses that B is the currcnf price output point on the current demand curve DBF, we explore the implications of differing levels of marginal cost. Three different types of situations are worth considering: ( 1 ) The marginal cost curve is sufficiently high to interscct the marginal revcnue curve only once and this occurs on its segment AH. The marginal cost curve MC, illustrates this case. The firm maximizes its profit by charging P , per unit for its product and producing x , of it. Management finds that it

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maximizes profit by opting for a snob-focus in marketing its product. Indeed, if the marginal costs of production are sufficiently high, it is only possible to make a profit from the product by marketing it with snob-appeal. The marginal cost curve may intersect the marginal revenue curve only once but intersect its lower segment JK. In this case in which the marginal costs of production are low, management maximizes profit by concentrating on bandwagon-marketing. In the case illustrated when the marginal cost curve is represented by MC3, the firm maximizes its profit by producing x5 of the product and selling it at price P o . Marginal costs may be of an intermediate amount and, as shown by curve MC, may interscct the marginal revenue curve twice. In this case, profit has two local maxima, and each corresponds to these intersection points. I t is necessary to evaluate each of these local maxima to determine which gives the greater profit, but, the higher is marginal cost, the more likely is the one associated with the snob demand curve to yield the absolute maximum, whereas, conversely, the lower marginal costs the more likely is the bandwagon-strategy to do this. In this last case, the firm's maximum profit as a function of its output is shown by the type of curve in Fig. 4, indicated by LMNQR. Given the reentrant nature of the profit curve in the neighbourhood of x3 (which corresponds to the kink of the demand curve), market choices at the kink (and within some neighbourhood of it) do not maximize profit. An inert area or avoidance area (compare with Tisdell and De Silva, 1983; Leibenstein, 1978) exists at B (and in its ncighbourhood) as can be seen by referring back to Fig. 3. Consequently, in this case, the firm never finds it optimal to foster a selfcentred or other than socially influenced strategy to marketing its product. The special conditions assumed about relationships between alternative demand curves will be relaxed in

Snob dominonce

Wit

0

LI

Quantity of output

Figure 4. Profit function with cusp at N corresponding to kink in the demand curve. The curve LMNQR can be considered as the upper boundary of two profit functions-one for snob demand and one for bandwagon demand.

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C. J. AISLABIE AND C. A. TISDELL

the fifth section of this paper, but it is worthwhile making some additional observations about this case. We have already observed that the higher are the marginal costs of producing or supplying the product, other things equal, the more likely profit is to be maximized by a snob demand strategy. This implies that firms with higher per-unit marginal costs of production are more likely to opt for a snobstrategy in marketing their products than those with low per-unit costs. The latter are likely to find the bandwagon-emphasis more profitable. Furthermore, when a company is selling in more than one market or market area it may find different strategies optimal in diferent markets, depending upon its cost of supplying these. When the per-unit cost of supplying a distant market is high because of transport costs or tariffs on imports, the company may find it profitable to promote the product in the home market appealing to bandwagon-effects, but promote it in distant markets (overseas or foreign markets) by emphasizing snob-appeal. This would be a rational response, and casual observation indicates that this in in fact done with some products (for example, cars). A second observation also seems to be in order. Other things equal and if per-unit costs are similar at very low volumes of production, a snob-marketing strategy is more likely to maximize profit if increasing marginal costs of production prevail than if decreasing marginal costs of production prevail. Indeed, if decreasing marginal costs of production prevail there is a strong tendency for bandwagon-marketing strategy to be optimal. In the former case the chances are that the marginal cost curve will only intersect the upper branch of the marginal revenue curve (such as that shown in Fig. 3). In the latter case the chances are that the decreasing marginal cost curve will only intersect the lower branch of the marginal revenue curve. Thus bandwagon-marketing strategies may be more commonly associated with decreasing cost industries than with increasing cost industries.

A COMPARISON OF APPROACHES

It is desirable to stress the differences between the approaches adopted in the two previous sections. In the third section there is no particular relationship between the pivot point and the marginal cost curve, whereas in the second section the prior determination of the marginal cost curve determined the pivot point. Consequently, in the second section it is meaningless to ask what the most suitable strategy is in the light of information as to the pivot point, and the level of marginal costs as this information has all ready been taken into account in determining the pivot point. Knowledge of the current price-output combination in the second section avoids the need to gloss over a problem that is implicit in our analysis in the third. While a purely arbitrary choice of pivot lends gener-

ality to the analysis it does raise two dificult questions. These are: (1) Is the concept of a pivot point meaningful from the

point of view of a manager who is expected to undertake the pivoting exercise? (2) Can (or should) a pivot point be chosen in an optimal fashion? Answering these questions throws further light on what is involved in pivoting the demand curve. The alternative to pivoting (with or without a common intersection) is merely to compare alternative slopes of the demand curve. The concept of pivoting involves the recognition that points on demand curves which are being compared in this way may involve common priceeoutput combination. The slope of the demand curve without knowledge of the intercept is of limited use because it does not spell out which priceoutput combinations are likely to be of interest. However, it is impossible to speculate about that priceoutput combination at which the new product would sell without coming to a prior decision about the level of marginal costs. As we know from the analysis in the second section, once that prior decision about the level of marginal costs has been taken, the current priceoutput combination is known and then speculation about pivoting is not useful. Nevertheless, it may be useful to realize that if a pivot point is being considered that is above the likely level of marginal costs then the adoption of a bandwagon-strategy is a possible alternative to consider, while if a pivot point is being considered that is below the likely level of marginal costs then the adoption of a snob-appeal strategy is a possible alternative. What this means from the point of view of a management trying to reduce its product position problem to its bare essentials is that the initial demand curve to consider is the non-socially influenced type of demand curve. In recognizing that this curve can be pivoted, the manager has to accept that both the new slope and the new intercept have to be selected. Our analysis helps him here to some extent in that he will realize that the pivot point implied by the choice of intercept will determine, with the likely level of marginal costs, which way it will pay to pivot the demand curve. In other words, the point where the marginal cost curve cuts the non-socially influenced type of demand curve has a previously unrecognized significance, because it is that point, as much as the arbitarily selected pivot point, that determines the likely direction of pivoting.

ALTERNATIVE DEMAND CURVES WITHOUT A COMMON INTERSECTION POINT The case of three alternative demand curves with a common intersection point is a special but useful one

PROFIT MAXIMIZATION AND MARKETING STRATEGIES

for introducing this analysis. Keeping to the possibility of three alternative demand curves exhibiting similar relative slopes to the earlier ones, we can generalize the possibilities somewhat. Apart from the case already considered, the following may be worth study: The non-socially influenced demand curve dominates all others. It is dominated at low levels of output by a snobtype curve, dominates at medium levels of output, and is dominated at high levels of output by a bandwagon-type demand curve. A snob-type demand curve dominates at low levels of output but a non-socially influenced demand curve dominates at all other levels of output. A non-socially influenced demand curve dominates at low levels of output but a bandwagon-type demand curve dominates at high levels of output. If case (1) applies then, of course, a firm always maximizes profit by not marketing its product in a way emphasizing social considerations. If case (2) applies, its optimal strategy depends upon the level of its marginal costs of production, as in cases (3) and (4). In case (2), if marginal costs of production are sufficiently high, it pays to emphasize snob-elements in marketing, if marginal costs are at an intermediate level not to emphasize social effects in marketing and if marginal costs are sufficiently low to stress bandwagon characteristics in marketing. In case (3) if marginal costs of production or supply are sufficiently high it pays to stress snob-effects in marketing but otherwise not to appeal to social characteristics. In case (4), it pays to stress bandwagon characteristics if the marginal costs of production are sufficiently low but otherwise not to appeal to social characteristics. It may be useful to illustrate the conclusions for case (2),since case (1) is straightforward and cases (3) and (4) can be readily deduced from a consideration of (2).

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The demand curve for case (2) is like curve ARSG in Fig. 5. Its segment AR is that for which the snob curve dominates, RS is that for which the socially independent demand curve dominates, and SG is that for which the bandwagon curve dominates. The associated marginal revenue curve is the ‘saw-toothed’ one like ATUVWZ. It ‘jumps’ at x-values corresponding to each of the corner-points R and S of the relevant demand function. In the case shown, if the marginal cost curve of production is as indicated by MC,, the firm finds it most profitable to product x, of the product and sell it at a price of P,. In doing so, it is most profitable for it to foster the snob-effect. Similarly, if marginal costs of production are low enough, the firm’s marginal cost curve may only intersect the marginal revenue segment, WZ, corresponding to the bandwagon demand curve, in which case it is most profitable for the firm to foster the bandwagon-effect in marketing. Again, for medium levels of marginal costs, the marginal costs curve may only intersect the segment UV of the marginal revenue curve, in which case it is optimal for management not to stress social influences in marketing. As before, the marginal cost curve may intersect the marginal revenue curve more than once, in which case more than one local maximum of profit exists, and these have to be compared to determine the absolute maximum. Once again, and for similar reasons, values at or in the neighbourhood of the corner-points of the demand curve cannot be optimal.

CONCLUSION

The analysis indicates that firms with high marginal costs of production are more likely to find it profitable to foster snob-effects in marketing their products than those with low marginal costs of production, which are more likely to find a bandwagon-emphasis most profitable. It also appears that increasing such costs tends to favour an appeal to snob-effects in marketing, whereas decreasing them seems to favour a marketing bandwagon-strategy. Further, it seems that where a company is selling its product in a number of markets (for example, at home and in overseas markets) differences in its marginal cost of supplying these markets may result in its profit being maximized by appealing to bandwagon-effects in some markets, non-socially influenced demand elements in others and snob-effects in still others. This paper identifies a number of factors that influence or should influence managerial decisions in this regard.

Quantity of output

Figure 5. A relevant demand curve with more than one corner-point and its corresponding marginal revenue curve.

Acknowledgements The authors wish to thank anonymous referees for their comments on an earlier draft of this paper. The usual cuueat applies.

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