FIRM SIZE AND MARKET BEHAVIOR: A THEORY OF THEIR RELATIONSHIP Julian L. Simon Determining precisely what people do who are not in equilibrium is not one of the notable achievements of economics. (Schultz, 1975, p. 829) I. INTRODUCTION Why does the maker of Seagrams 7 Crown whiskey price its brand at $6 a fifth and spend millions to advertise it, whereas the maker of Guckenheimer whiskey prices its fifth at $3.50 and advertises not at all? Both courses of conduct may be considered successful strategies in that both have continued for decades and presumably are profitable. Production cost does not explain the phenomenon, because the two whiskies are made with a standard process and are indistinguishable, as are the glass bottles in which they are contained. Why do new department stores and entrants into many other fields often adopt a policy of low prices and no frills, whereas more established merchants tend to provide more services and charge higher prices, while both kinds of stores are selling the same merchandise? Neither demand nor supply arguments throw any light on these matters because there is no reason to suppose that either supply or demand (the latter thought of in a conventional sense) are different for Seagrams 7 Crown than for Guckenheimers, or for a new department store than for an old one. Recently, such concepts as implicit contract have entered into economic discourse to help explain behavior by one entity that is different from other entities. And the notion of strategy has filtered into economics from marketing as a normative device to guide a firm into the most profitable activities by taking advantage of its particular organizational and other non-physical assets. But neither of these ideas helps explain the set of phenomena to be examined here. Even more important, neither of these notions provides any systematic predictions about firm behavior based upon quantifiable criteria. Yet it is ever more crucial that we confront the variety of forms that economic units take, and the variety of ways that they conduct their businesses. Sellers of identical products not only choose different combinations of price and advertising but also choose different combinations of product quality and R&D along with price and advertising to reach similar markets. Also relevant is the bewildering array of devices such as cents-off coupons, lotteries, special promotions, special services, and so on that we observe firms using. Why does one firm use one sort of device at one time, whereas another firm uses another? The paper tries to shed light on this question. Our general aim is to understand the phenomena at hand without resorting either to psychological arguments regarding the characteristics of the decisionmakers, or to historical explanations that depend upon the prior experiences of the firm, because such variables are difficult or impossible to measure systematically and therefore invite ad hoc argumentation. Instead, the size of the firm's sales volume, which is amenable to empirical and theoretical work and which is easier to integrate with standard economic theory, seems to offer a powerful explanation of these "strategic choices." It should be noted, however, that the size variable is unusual in that it suggests differences in the "nature" of two firms, or of the same firm at different moments, whereas the only difference between firms found in standard theory is a difference in cost functions. The discussion section deals with this matter in greater depth. The key idea is that there is a fundamental difference between two classes of competitive variables. While obtaining more customers, some competitive variables do not affect the revenue gained from existing customers whereas other variables do affect the amount received from customers who would buy anyway. To avoid getting sidetracked into the wilds of oligopolistic and game- theoretic head-to-head conscious interaction, we will not focus the discussion upon such homogeneous products in narrow markets such as Guckenheimer and Seagram 7 Crown, but rather upon such firms as Crain Publishing's magazine Advertising Age, a fast-food chain such as Pizza Hut, a seller of art books such as Harry Abrams, Inc., L.L. Bean's sporting goods offerings, semi-conductor manufacturers, Kawasaki motorcycles, Britt Airlines' route from Champaign-Urbana, Illinois to St. Louis, and a university extension course on "Corporate Planning with a Marketing Focus." None of these goods is sold in a narrowly defined market with a homogeneous physical product, as is whiskey or builder's sand. But since the comparison is to itself, with the single difference in the two conditions that its sales volume is larger versus smaller, there is no analytic difficulty concerning homogeneity of the product or other conditions of sale. The commonly used concepts of market and market share are difficult to define meaningfully for such firms. Therefore, in place of market share this paper works with a firm's "loyal custom," defined as the number of customers at any one moment who have some loyalty to the firm from the previous period to the upcoming period. And, in place of the concept of a market, the paper uses "potential market," meaning the number of additional customers the firm could expect to have with varying combinations of price and other variables. More specific definitions follow later. Consider as an example magazine A aimed at the general science public. Another magazine B in a somewhat-related field has just gone out of business and has sold its customer list for five dollars per subscriber to magazine A. Magazine A has the responsibility of providing issues to the end of B's current subscriptions, and then has the opportunity of soliciting "continuations" to A. Based on long experience in the magazine industry, it is estimated by A that perhaps half of the subscribers to B will then buy A. These names are sufficiently valuable to A as to each be worth $5 plus the cost of completing the subscriptions because the rate of sales to lists of non-subscriber "cold" names that are ordinarily rented in a subscription campaign is perhaps 2%, in contrast to the 50% rate expected by A from the ex-subscribers to B. It is clearly revealed from A's purchase of the list that the subscribers to B will be "committed" to A to a considerable extent; they will be part of its "custom." That is, the probability of B's subscribers buying A in the future is very different than is the probability for uncommitted "cold names" of non-subscribers in its "potential market." For convenience, we shall model the state of commitment as a non- probabilistic 100% commitment, but it will be obvious to the reader how that assumption could be made weaker and probabilistic without affecting the analysis. And it should also be obvious how a similar process of commitment is at work in almost every other line of business. Established customers behave differently, and therefore must be thought of differently, than do non-customers of department stores, soft drinks, airlines, and almost every other business situation. For convenience, we will also consider an additional committed customer as having newly arrived in the market and become a purchaser, in order to abstract from issues such as the diminution of the pool of potential new customers which occurs when magazine B's subscribers are sold to A, and such as the issue of head-to-head competition. Firms in narrowly-defined markets, for whom the notion of market share is more appropriate, are more difficult to think clearly about in this connection because of the conscious interactions among them. But the ideas developed here for the non-interactive situation probably can be extended to narrowly-defined markets as well. Size differences are taken as exogenous. Studying the effects of the differences makes sense because differences are found in the world. Discussion of this fact of economic life may be found in the appendix. The heart of the analysis is contained in the discussion of Proposition 1 in Section II and its proof. All the rest of the proofs are similar. II. ADVERTISING VERSUS PRICE Consider two firms of different size operating under similar market conditions but where we can safely ignore any interaction between them. Why does one of them cut its price and another increase its advertising? A psychologist or sociologist may attribute the difference to the personalities or the ethnic backgrounds of the managers, while marketers call it a "characteristic strategy" of the firm. Either may really be just another label for the competitive choices the firm habitually makes. Neither sort of explanation is satisfying to economists. Many writers (e.g., Stigler, 1968) have noticed a fundamental difference between advertising and price as competitive variables: advertising to get more customers has no negative effect upon the firms' existing customers, and perhaps has a positive effect upon them, whereas a price-cut to increase market share reduces revenue from the firm's existing customers. But the implications of this difference for understanding a firm's behavior in terms of the firm's present situation seems to have been overlooked. This section shows that it follows from this difference that the larger the firm's present custom, ceteris paribus, the greater its propensity to use advertising and the less its propensity to use price cuts. The analysis bears a relationship to Adams' analysis (1977) of advertising as a device which permits the firm to discriminate -- that is, to treat each customer or class of customers differently -- whereas ordinary commercial pricing of many goods does not permit such discrimination. It is in somewhat the same spirit as the famous Dorfman- Steiner paper (1954), but it is formally quite different and reaches different sorts of conclusions. This paper may be viewed as producing the sort of conclusion that Dorfman-Steiner should have produced but did not. More on this may be found in the Discussion in Section VI. One can quickly prove that when price is considered in isolation, the smaller firm has a greater propensity to cut price than the larger firm. But the same can be shown for an increase in advertising considered in isolation. The question is: why is the price cut relatively more attractive than advertising when the firm is relatively smaller?1 Proof That The Firm With the Larger Loyal Custom Will Prefer Increased Advertising to Price Cutting The aim of this section is to prove the following proposition: Proposition 1: A firm having a larger loyal custom will have a greater propensity to increase advertising than to cut price, whereas a firm with a smaller loyal custom will prefer a price cut, ceteris paribus. Now some more specific definitions: By "loyal custom" (Mt) or just "custom" is meant the number of persons who bought from the firm in period t-1 and who will also buy from the firm in period t if there is no increase in price, even if the firm does no advertising (all other promotional activity being ignored for the time being). In the example below, the attachment force that underlies market share will be a contract which binds the person for certain. More realistic forces include customer inertia, the cost of changing one's behavior, habit formation, sentimental loyalty, or any of the related forces as they are described in the marketing literature. And these inertial forces operate probabilistically and can be modeled as a Markov process; the difference between a probability of repeat buying, and repeat buying for certain, does not affect the analysis, as discussed earlier. By "potential market" (D) is meant the function (1) Dt = f(Pt, At, Bt, ...) where Dt = number of sales that will be made in period t, apart from present custom Mt, assuming one sale per customer Pt = price At = total advertising expenditure Bt = product quality and where other marketing variables may be added if the decision-makers consider them relevant to a particular decision. Again, we recognize that the distinction between the persons making up the firm's "loyal custom" and its "potential market" are not well-demarcated, but that is not unusual for a distinction newly introduced into a particular field. We are sure, however, that ignoring the difference between these two classes - which is a fundamental fact of business life - would prevent us from analyzing important strategic choices made by firms. The analysis will be an exercise in comparative statics examining a firm which can assume that both its loyal custom and its demand function with respect to price or advertising (i.e., its potential market) may be taken as given for the decision period. This is possible because the analysis abstracts from all competitive interaction among firms and focuses only on the shortest-run tactical choices. We present two kinds of proofs. The first is an orthodox equilibrium analysis which arrives at the conclusion quickly and compactly. Offsetting these virtues is the difficulty of interpretation arising from the fact that the maximization is timeless and does not explicitly portray the transitions 1) out of equilibrium due to a change in firm size, and then 2) back into equilibrium again with newly-chosen magnitudes. To clarify the step-by-step process, an unorthodox disequilibrium proof is also presented. It has the virtue of showing the steps explicitly, but it is prolix and seems strange in its novelty; the reader who is satisfied with the equilibrium approach may rest with it. The disequilibrium method may also be found to be useful in some other contexts, however, where the equilibrium approach is not feasible. Equilibrium Analysis To frame the problem, assume that "our" brand is now in equilibrium. That is, price and advertising have been chosen so as to maximize our profit. Suddenly immigrants arrive, and we consider adjusting price by cutting price or raising advertising. How does the size of our brand influence which of the two variables are likely to change? Assume constant marginal cost in the neighborhood of the decision. The profit function (Z) to be maximized is (2) Z = MP + P[D(P,A)] - C1M - C1[D(P, A)] - C0 - A where A = advertising C1 = incremental unit cost, a constant C0 = fixed cost M = number of loyal customers P = price D = potential market Differentiate with respect to price and advertising (3) dZ = M + ( dD )P + D(P,A) - ( dD )C = 0 dP dP dP 1 (4) dZ = ( dD )P - ( dD )C - 1 = 0 dA dA dA 1 Equation 4 implies (5) ( dD )(P - C ) = 1 dA 1 Substituting a rewriting of (5) into a rewriting of (2) we get (2a) ( -dD )/( dD ) = M + D dP dA This implies that the larger the loyal custom, M, the more that advertising will be increased for a given reduction in price. This is not precisely the same as saying that a firm is more likely to choose an increased advertising strategy rather than a decreased price strategy when M is larger -- which is the proposition to be proven -- but the two statements are at least consistent with each other. The solution also goes through nicely for a non-linear cost function (C2, C0). (2b) Z = MP + P[D(P,A)] - C2[M + D(P, A)] - C0 - A (3b) dZ = M + D(P,A) + P(dD) - C2[M + D(P,A)] dD = 0 dP dP dP (4b) dZ = P(dD) - C2[M + D(P,A)] - 1 = 0 dA dA (5b) dD (P - C2[M + D(P,A)] = 1 dA Disequilibrium Analysis The equilibrium analysis above embodies a paradox: When the firm is in equilibrium, neither price nor advertising will be changed. And increasing the firm's custom M does not move a firm from equilibrium to disequilibrium in the analysis. Yet we desire to analyze how the size of M influences decisions about P or A - which are changed only when the firm is out of equilibrium. To get at the matter explicitly, a different and novel approach must be used. Consider a firm F that is now planning its operations for the coming period. The firm has tentatively chosen a price of P and an advertising budget of A. Assume that this combination of (P, A) is very close, as close as one wishes, to the profit-maximizing point for the firm as estimated by the firm's decision-maker2. Now let the decision-maker consider reducing the firm's price an amount p to (P-p) or increasing its advertising an additional amount a to make a total (A+a). Assume that either small change would be marginally profitable if the market-potential function is D; this function refers to customers who will not "automatically" buy from firm F at price P and advertising level A, and either change under consideration would bring one new customer. For a firm at the point of maximization, the expenditure a equals the drop in revenue from the M customers that the firm would have at (P,A) if it drops price to (P-p), together with the difference between P and (P-p) charged to the additional customer; this overall "loss" equals (M+1)p, which just equals aby assumption, by simple Dorfman-Steiner reasoning for a profit-maximizing point. The firm is therefore indifferent between the strategy of advertising (A+a) and the strategy of setting price (P-p), both of which are preferable to doing neither. The firm is also indifferent between these two options and no change at all. (We shall assume that it would not be profitable for the firm to both lower price to P-p and raise advertising to A+a, and that any further drop in price or increase in advertising would not be profitable.) To simplify, a zero cost of production is assumed; production with constant marginal cost clearly leads to the same result, however. In any case, production costs will be brought into the picture in the section on product quality. The firm's choices with their associated present values (V) may be shown as follows, where the alternative is the superscript of V, the present market-potential function is the first subscript, and the term "no contract" should be ignored for now. The period subscript in the control variables is omitted for convenience. A+a (6) VD, no contract = PM + PD + P(1) - (A+a) where the first term on the r.h.s. represents the revenue obtained from the loyal customers; the second term is the revenue obtained from the new customers that would be obtained with (P,A); the third term is the revenue from the "additional" one customer obtained by advertising A+a rather than A, along with P; and the fourth term is the expenditure on advertising. P-p (7) VD, no contract = (P-p)M + (P-p)D + (P-p)(1) - A A+a P-p (8) VD, no contract = VD, no contract which is the same as writing (9) a = (M + D + 1)p.3 Now consider that, for some exogenous reason, a person who had not previously been part of the potential market moves into the area and signs a contract with the firm. Or, alternatively, we might think of the change in putative circumstances as an upward revision by one customer in the decision-maker's estimate of the firm's potential sales, as a result of additional scanning of the market environment; this interpretation would seem particularly congenial to "Austrians." That is, the firm's custom becomes "bigger" by one more customer. The firm will then still be indifferent between advertising (A+a) and advertising A. But if the firm lowers price to (P-p), it will now be in a considerably less profitable situation than remaining at (P,A) or going to (P, A+a). This may be seen in the comparison of the two profit functions [N. B. eqs. 10 and 11 are in footnote 3]: A+a (12) VD,contract = PM + PD + P(1) + P(1) - (A+a) P-p (13) VD , contract = (P-p)M + (P-p)(1) +(P-p)D + (P-p)(1) + (P-p) - A Subtracting (13) from (12) shows that the advertising strategy now yields p greater profit. It may be illuminating4 to rewrite (9) as (9a) a/p = M + D + 1. This suggests that the relative effectiveness of a price cut and additional advertising depend upon the size of the custom, M. Loosening the implicit assumption that the quantity of advertising has no effect on presently loyal customers only strengthens the result obtained so far. This can be seen by assuming that the benefit of a advertising in strengthening the attachment of present customers is worth v. We can then find some new a' which (to a small approximation, which could be made more precise quite easily) is equal to (a - v), and hence a' = p. If we now add one customer to the custom, there will be some additional benefit from a'due to its effect on the additional (M + D + 1)th customer, hence leaving advertising at least as attractive an alternative as it is with (M + D) customers, whereas the reduced benefits to p of adding the (M + D + 1)th customer are not affected at all by this adjustment.5 To recapitulate, we see that the attractiveness of an increase in advertising relative to a price reduction is affected by the firm's custom (by which we mean the number of customers bound to the firm by one force or another). This corroborates the casual observation that the larger the firm, ceteris paribus, the greater the propensity to advertise. The underlying reason is that the more loyal customers that a firm has, the more it "loses" on these customers when it reduces price. In contrast, a change in the absolute number of uncommitted customers in the market need not influence the choice between advertising and price reduction, though one could undoubtedly create plausible response functions that would show the effect going in either direction. Please notice that after the addition of a customer to the firm's custom, there will again be some near-profit-optimizing combination of P and A, say P1 and A1, where the firm is indifferent between using more advertising or a price cut to achieve one more customer, were it to decide to go after one more customer. If we now subtract one customer from the firm's custom, the firm will no longer be indifferent between increased advertising and reducing price, by exactly the opposite logic as given above; it will now find it more profitable to reduce its price. That is, we see that adding a loyal (M + 1)th customer leads to increased advertising and decreased propensity to cut price. There is then a new profit-maximizing point. If at that point, the process were reversed and the (M + 1)th customer were lost, it would then be relatively more profitable to reduce price than to increase advertising relative to the profit-maximizing combination with M + 1 customers. This logic would also apply to each point between M and M + 1 customers, and hence we have proven that moving from the firm's equilibrium at M to the firm's equilibrium at M + 1 reduces propensity to cut price relative to the increased-advertising alternative. The analysis now comes close to meeting Machlup's description (see footnote 2) of an equilibrium analysis for the firm (though not for an analysis of market equilibrium or general equilibrium, of course). We examine the firm near its profit-maximizing equilibrium, apply the shock of an additional customer, and observe in that neighborhood an increased propensity to use advertising in comparison to a price reduction. We also see that when the firm settles down to its new equilibrium, a reversal of the shock would result in a decreased propensity to advertise relative to price reduction. From this it seems fair to conclude that the addition of a customer reduces the firm's propensity to cut price relative to increased advertising. An obvious corollary of proposition 1 is that the smaller the firm's custom, the more likely it is to cut prices. The proposition proven above, as well as all the other propositions in the paper, might be shown more elegantly by writing explicit sales-response functions with advertising, price (and later, product quality) and lagged sales as arguments, and then comparing the profit results under various assumptions. But there is a great variety of reasonable functions that could be written, few of them simple, and the analysis would surely be complicated mathematically. Even more important, the generality of the conclusion would be limited to the functions specified. The analysis given above refers to any functional forms, which is a considerable degree of generality. Hence the simple form of proof given above has advantages which we hope outweigh its mathematical inelegance. Illustration of the Analysis The analysis offered in this section explains the famous "wheel of retailing." This is the phenomenon of a new set of stores in a given trade -- appliances, say, or food -- entering the market with rock-bottom prices but without advertising. (A similar analysis applies to lack of services and well-appointed establishments, phenomena which relate to the analyses below.) After a period of success winning substantial custom from the well-established competitors, the "discounters" then begin to advertise (and offer extras) while raising prices somewhat. As they "move up," there soon arises another wave of "discounters," and the "wheel of retailing" continues to turn. Relationship to Market Equilibrium Concerning the relationship of the behavior analyzed in this paper to market equilibrium, as distinguished from firm equilibrium: The analysis begins with firms that differ in size, which is the state of affairs in all markets at all times and hence needs no further justification; the cause of such size differences may be myriad. But in the absence of differences which are fixed by law or nature, one wonders whether there will be a movement toward obliteration of the differences and hence similarity in competitive behavior, a state which one might call an equilibrium (though it would not necessarily or likely be an equilibrium in which there is no competitive behavior). As noted earlier, it is easy to prove that the smaller firm has a greater propensity both to cut price and to increase advertising than a larger firm; both propensities flow from its larger potential market (some of which is the larger firm's custom). The proof for advertising follows from the empirically-observed monotonically diminishing returns to advertising; the proof for price-cutting follows from the key element of this paper, that a price cut produces a greater "loss" in revenue from already-attached customers for a larger than for a smaller firm. Hence it is reasonable to expect that in the long run in a stable environment, firms would arrive at an equilibrium of equal size and therefore similar competitive behavior. The differential propensity by size of firm to cut price and increase advertising analyzed here would not affect this directional tendency toward market equilibrium. It would affect the relative importance of differential advertising and price in moving the firms toward equilibrium, but this second-order effect would not seem to be of sufficient importance to call for exploration here. This comment on the tendency toward market equilibrium generalizes straightforwardly to other competitive variables such as product quality discussed below. Other Pricing Behavior The analysis given above immediately leads to additional propositions. In this section we deduce Proposition 2: The larger the firm's custom, ceteris paribus, the more likely it is to raise price rather than to decrease advertising. This proposition can be deduced by running in reverse the equations in proposition 1. It is consistent with the observation that "leaders" in price rises tend to be larger "dominant" firms (e.g., Scherer, 1970, pp. 164-166). As to the choice between raising price and increasing advertising, this is really of a different nature than the choice between lowering price and raising advertising, because an increase in price reduces the number of customers whereas a rise in advertising increases the number of customers. This means that now we are faced with the complication that one of the price-rise alternatives affects both the number of loyal customers who will buy as well as the number of potential customers who will buy, whereas the advertising alternative affects only the latter. The price-rise-versus-advertising-increase choice may be analyzed as follows, in the manner of (6) and (7) and assuming that the increase in price to (P+p) loses m loyal customers (that is, loyal at price P) and also loses n of the customers it would get with (P,A). (14) VA+ano contract = PM + PD + P(1) - (A+a) P+p (15) Vno contract = (P+p)(M-m) + (P+p)(D-n) - A (16) Let [P + p(M - m) + p(D-n)] = a so that the two alternatives are equal at first. Now add one customer by contract from outside the market A+a (17) Vcontract = PM + PD + 2P - (A+a) P+p (18) Vcontract = (P+p)(M-m) + (P+p)(D-n) + (P+p) - A Subtracting (18) from (17), and using the left side of (16) to substitute for a, we find that the price-rise alternative has a present value higher by p than the advertising-increase alternative. And hence we see Proposition 3: A price rise is relatively more attractive than an increase in advertising when the firm's custom is larger, ceteris paribus. IV. PRODUCT QUALITY AND PRICE CHANGES Proposition 4: The larger a firm's custom, the less likely it should be to raise quality in preference to increasing advertising. This proposition obviously follows from proposition 1 if we index quality by the cost of production, because the increase in quality must be provided to all customers, both new and loyal; and the larger the number of loyal customers, the less attractive is the quality increase to the firm, ceteris paribus. Here we must bring the cost of production into the analysis. Let C be the production cost per unit, the same at all levels of production. A reduction in quality of c is defined as a reduction in production costs of c dollars per unit; an illustration is a reduction in proof of liquor, a simple dilution with water equivalent to selling less of the product per quart sold, and an increase in quality is an increase in proof. Let us compare an increase in quality of c to an increase in advertising a, where Mc = a, and where the resulting change in profit will be the same given the firm's custom. A+a (19) Vno contract = (P - C)M + (P - C)D + (P - C)1 - (A+a) C+c (20) Vno contract = PM - (C+c)M + PD - (C+c)D + P(1) - (C+c)(1) - A Assume a = (M+D+1)c so that the two alternatives are equal in value. Now let us consider what happens if the firm's custom increases by one person formerly outside the market who now signs a contract. Following (12) and (13) A+a (21) Vcontract = PM - CM + PD - CD + 2P - 2C - (A+a) C+c (22) Vcontract = PM - (C+c)M + PD - (C+c)D + 2P - 2(C+c) - A Subtracting (22) from (21) leaves a c advantage with the advertising alternative, showing that the larger custom makes it relatively less attractive to increase quality as a device to increase profit when the firm has additional loyal customers. A corollary of this proposition is that the smaller is a firm's custom, the more likely it is to increase quality as a business strategy, in comparison to increasing its advertising. Proposition 5: The larger a firm's custom, the more likely it should be to lower quality in preference to decreasing advertising. This proposition follows immediately from Proposition 4. Propositions 4 and 5 could both be tested very neatly on the proof-changing behavior of liquor brands. The liquor market also would provide a good test because each firm owns many brands, and these propositions should predict for the brand but not for the firm as a whole. V. RESEARCH AND DEVELOPMENT STRATEGIES Research and development expenditures are not one strategy; rather, R&D encompasses a variety of business strategies. Among the important R&D strategies are: (a) R&D to reduce costs of the existing product; (b) R&D to increase the product's quality (say, for simplicity, with the same production cost), and (c) R&D to produce new products. The firm's custom should influence which of these strategies the firm should choose. Let us consider them one at a time. Proposition 6: The larger a firm's custom, the more likely it will be to invest in R&D that will reduce production costs, rather than engage in an increase in advertising. Such R&D is like an increase in price, and the proof is identical to that given above for proposition 3. Proposition 7: R&D to cut costs should also be relatively more desirable than an advertising increase or a price cut, the larger the firm's custom, by rather obvious and similar logic. Proposition 8: R&D to increase quality should be relatively more likely if the firm's custom is relatively small. The argument for proposition 8 is identical to that for proposition 3, a direct increase in quality, except that the argument for proposition 8 must be phrased in terms of the probability of discovering a quality- increasing development rather than a quality improvement for certain. The analysis of R&D expenditures intended to produce new products is more complex than the analyses above. For new products the analysis must take into account both the effect of the new product upon sales of the old product (substitution) as well as the effect upon newly-attracted customers. In a simplified case where the prices of the old and the new products are the same, the result may be viewed as the net number of new customers (the total number of customers attracted by the new product less the number of old-product customers who switch to the new product) and the analysis is then the same as for advertising versus a price cut (Proposition 1) with the R&D similar to advertising. This would lead to Proposition 9: The larger the firm's custom, the more attractive is R&D to increase the number of products, relative to a price cut. VI. DISCUSSION 1. It is illuminating to compare our analysis with that of Dorfman and Steiner (1954). Their basic proposition is that at the profit- maximizing point the elasticity of demand with respect to price y = P dQ Q dP and the marginal value product of advertising z = P dQ dA are equal to each other y = z. where their Q is closer in meaning to our D than to our M. An increase in M decreases y, but leaves z unchanged. Dorfman and Steiner prove that when z > y, it pays to increase advertising and price. But in the situation in which custom M increases but market potential D does not change , the only cause of increased advertising is the price increase, which is a second- order difference; hence it is intuitively clear that the increase in advertising is "relatively" small compared to the indicated increase in price, in fact, nearly zero. (To show this rigorously would be a bit difficult, and would likely require complete specification of the market- potential function.) Dorfman and Steiner draw no conclusions about the relative impacts on advertising, price change, and quality that will result from a change in the firm's size. Their theorem offers no guidance about whether a price rise or an advertising increase will be more likely as the firm's custom increases and z > y. 2. A key element in this analysis is the inclusion -- implicit in the equilibrium analysis, explicit in the disequilibrium analysis -- of the effect of the firm's behavior in one period upon its market behavior in the next period, in contrast to comparative statics that excludes time- dependent effects. This inter-period effect arises because the choice of tactics in t influences the firm's custom in t+1, which then influences its choice of tactics in t+1. This multi-period effect is omitted from the Dorfman-Steiner analysis as well as the usual industrial-organization analysis of markets; an example is the timeless standard comparative- statics analysis of the "dominant" firm as a price leader (e.g. Scherer, pp. 164-166). This inter-period influence also must affect any attempt to derive a market equilibrium that begins by assuming the existence of differences among firms. If there were to be no additional changes in the environment, some stability would surely eventuate, cybernetic theory assures us, although it is not clear whether or not the result would be identity among firms in characteristics and tactics. But a continuous flow of changes in the environment is a central feature of the reality being studied here, and we speculate that the inter-period connection implies that these environmental changes will translate into continuing differences among firms, to a degree that would not occur if inter-period interaction were not present. 3. Though the firms are assumed not to be of equal size at the beginning of the analysis, a tendency toward an equilibrium of equal size is consistent with the analysis, as will be discussed below. The context is like that of "Austrian" disequilibrium, which views a market as in constant ferment due to a variety of disturbances from outside the market, together with necessarily imperfect attempts by entrepeneurs to take advantage of the profit opportunities that exist as a result of the disturbances outside plus the changes made by other firms trying to exploit opportunities for profit. (For discussion of the Austrian viewpoint on this matter, see Hayek, 1949, Chapter 5, or Kirzner, 1973, Chapter 1.) A similar view of firm size is expressed, justified, and used, by various other writers in very different contexts. For H. Simon, size of firm results from a growth process simply assumed without further discussion to be random. For Arrow, the cause of the differences is differences in information costs among firms. [T]he combination of uncertainty, indivisibility, and capital intensity associated with information channels and their use imply ...that the actual structure and behavior of an organization may depend heavily upon random events, in other words on history (1974, p. 49) When discussing the communication codes in use within firms with which employees communicate with each other Arrow says: [H]istory matters. The code is determined in accordance with the best expectations at the time of the firm's creation. Since the code is part of the firm's or more generally the organization's capital, as already argued, the code of a given organization will be modified only slowly over time. Hence, the codes of organizations starting at different times will in general be different even if they are competitive firms (p. 56). The recent literature on firm-specific phenomena is founded on the recognition that firms differ in their internal characteristics. For Hayek, the congeries of facts about competition (as he defines competition) necessarily lead to differences in size. That in condition of real life the position even of any two producers is hardly ever the same is due to facts which the theory of perfect competition eliminates by its concentration on a long-term equilibrium which in an ever changing world can never be reached. At any given moment the equipment of a particular firm is always largely determined by historical accident (1949, p. 101) The importance of these differences is also emphasized by Hayek: [U]tilization of dispersed knowledge is thus also made possible by the fact that the opportunities for different individuals are different. It is because the circumstances in which the different individuals find themselves at a given moment are different, and because many of these particular circumstances are known only to them, that there arises the opportunity for the utilization of so much diverse knowledge -- a function which the spontaneous order of the market performs.. That at any given moment the position of each individual in society is the result of a past process of tentative exploration, in the course of which he or his ancestors have with varying fortunes pushed into every nook and corner of their (physical and social) environment, and that in consequence opportunities which any change in conditions creates are likely to be acted upon by someone, is the basis of that utilization of widely dispersed factual knowledge on which the affluence and adaptability of the Great Society rests. (1979, Vol. 2, p. 9) Whatever explanation or non-explanation one prefers of the differences in firm size assumed here, such an assumption accords with the observed fact that firms differ in size in any given industry. The disequilibrium method used in this paper might also assist Austrians in communicating some of the ideas that they ordinarily discuss with verbal logic only, and may therefore enhance their attempts to argue their point of view. The aim of this paper is, however, different than the central aim of the Austrians, if we understand them correctly. Whereas they wish to emphasize the fluidity and the indeterminate quality of the markets within which entrepreneurs operate, we wish to analyze in a determinant fashion the choices that particular firms make under particular conditions which differ from firm to firm. That is, what is noise for the Austrians is data for this paper. However, to show that the outcomes differ determinately when conditions differ, which then leads to changes in the market, which then alters the conditions of other firms and then of the firm under analysis as well, should fit comfortably with the Austrians' vision of the economy. The analysis offered here picks up the process of doing business at the point where relevant information has been collected and assimilated. But this is not intended to minimize the importance of the scanning process which such writers as Kirzner (1973, p. 35) refer to as "entrepreneurship." 4. The firm's choice of competitive variables is known as the firm's "strategy" to students of marketing, who routinely adduce the "character" of the firm in addition to the state of the market and competition when explaining the strategic behavior of firms. Economists have tended to look outside the firm at the characteristics of the market and the number of competitors, but in recent years this has been changing. For example, a study of product innovation and other competitive strategies in the semiconductor industry (Wilson, Ashton, and Egan, 1980) traces the causal links empirically from a number of characteristics of the firm (including capital availability, level of R&D spending, degree of risk taking, and the nature of top management and its organizational control, p. 37); to the firm's choice of strategies among product design, reliability, pricing and breadth of product lines (pp. 78-79) to the financial and social performance of the firm and the industry. But there has been absent a theoretical basis for predicting which strategies would be adopted by firms of different types, which is the lacuna this paper tries to fill. This paper suggests that the nature of the firm is indeed important, and should not be ignored. But many important relevant characteristics of the firm are understandable in terms of standard economic concepts, especially lagged responses to price and advertising; sunk costs of equipment, information, and advertising; and the levels of fixed and variable costs. The most salient of these concepts for the subject of market structure and behavior are the twin ideas of sunkness of costs and lagged consumer responses. These same concepts can also give us a more fundamental understanding of the phenomena usually explained by "barriers to entry," but that discussion must be pursued elsewhere. VII. SUMMARY AND CONCLUSIONS The aim of this paper is to explain the connection between firm size and business strategy, one of the more important links between market structure and market behavior. The concept of market share is frequently adduced in literary discussion by writers on industrial organization, but it is seldom, if ever, defined rigorously or used in formal analysis. The concept used here to measure firm size is "custom," by which is meant the number of a firm's customers in period t-1 who will buy form the same firm in period t=0 if price is not changed. This concept best fits firms that do not sell homogeneous goods in narrowly-defined markets, but rather sell products that are physically differentiated and have a wide variety of partial substitutes. page 1 /article8 firmsize/October 20, 1996 References Adams, Jr., Walter S., "What Makes Advertising Profitable?", The Economic Journal, Vol. 87, Sept. 1977, pp. 427-449. Arrow, Kenneth J., The Limits of Organization (New York: Norton, 1974). Bain, Joe S., Barriers to New Competition (Cambridge: Harvard University Press, 1956). Caves, R.E., and Porter, M.E., "From Entry Barriers to Mobility Barriers: Conjectural Decisions and Contrived Deterrence to New Competition," Quarterly Journal of Economics, Vol. 91, #2, 1977, pp. 241-261. Dorfman, Robert and Steiner, Peter O., 1954, "Optimal Advertising and Optimal Quality," American Economic Review 44, No. 5 (December 1954): 826-836, reprinted in Frank Bass, ed. et al., Mathematical Models and Methods in Marketing (Homewood, Ill.: Irwin, 1961). Hayek, Fredrick A., Individualism and Economic Order (London: Routledge and Kegan Paul, 1949). ___________, Law, legislature, and Liberty Vol. 2, The Mirage of Social Justice (Chicago: University of Chicago Press, 1979. John Hicks, Capital and Growth (Oxford: Oxford University Press, 1965/1972). Kirzner, Israel M. Competition and Entrepeneurship (Chicago: University of Illinois Press, 1973). Levy, Haim and Simon, Julian L., "Choosing the Best Advertising Appropriation When Appropriations Interact Over Time," in Jagdish Sheth (ed.), Research in Marketing, Vol. I (Greenwich: JAI Press, 1979). Scherer, Frederick M., Industrial Market Structure and Economic Performance (Chicago: Rand McNally, 1970). Schultz, Theodore W., "The Value of the Ability to Deal with Disequilibrium," Journal of Economic Literature, Vol. 13, September 1975, p. 827ff. Stigler, George J., "Price and Nonprice Competition," Journal of Political Economy, LXXII, February, 1961, reprinted in The Organization of Industry (Homewood: Irwin, 1968). Tull, D.S., "The Carry-Over Effect of Advertising," Journal of Marketing, 29 (April 1965), 46-53. Wilson, Robert W., Ashton, Peter K., and Egon, Thomas P., Innovation, Competition and Government Policy in the Semiconductor Industry (Lexington, MA: Lexington Books, 1980). 8-164 article8 2-17-9 page 2 /article8 firmsize/October 20, 1996 Acknowledgments William Baumol worked out a version of the maximand for the equilibrium analysis, showing that such a formulation was possible - valuable help, indeed. We appreciate the helpful criticism by Walter Primeaux, Edward Rice and James Smith. Simon enjoyed the opportunity of presenting an earlier version of the paper at the Marketing and Industrial Organization Workshops at the University of Illinois, and the Industrial Organization Workshop at the University of Chicago. Footnotes 1A related but more general question is: Why does a firm with a smaller market share in t-1 generally advertise less in absolute dollars than a firm with a larger market share? Manufacturing facilities and product cost certainly are not a sufficient explanation in many industries, e.g., cigarettes, nor is geographical limitation. Differences in the cost of capital may be important. But the forces discussed here must have a central role. 2These points may be thought of as an equilibrium position for the firm, according to Machlup's definition of "equilibrium, in economic analysis, as a constellation of selected interrelated variables so adjusted to one another than no inherent tendency to change prevails in the model which they constitute" (1958/1967, p. 54). Surrounding the terms "equilibrium" and "disequilibrium" is much confusion which Machlup (1958/1967, p. 43-72) illuminates.) Machlup's model of a model, embodying the notion of equilibrium, seems to fit the approach taken here: The following scheme illustrates the step-by-step working of a model; each step is described both in customary technical terms and in terms of catch-phrases in everyday language: Step 1. Initial position: "equilibrium," i.e., "Everything could go on as it is." Step 2. Disequilibrium Change: "new datum," i.e., "Something happens." Step 3. Adjusting Changes: "reactions," i.e., "Things must adjust themselves." Step 4. Final Position: "new equilibrium," i.e., "The situation calls for no further adjustments."... In a nutshell, we have here a mental experiment in which the first and last steps, the assumption of initial and final equilibria, are methodological devices to ensure that Step 2 is the sole cause and Step 3 contains the complete sequence of effects. The function of the initial equilibrium is to assure us that "nothing but 2" causes the changes under Step 3; the function of the final equilibrium is to assure us that "nothing but 3" is expected as an effect of the change under Step 2 (although the "completeness" of the list of effects will always be merely relative to the set of variables included in the equilibrium)." (Machlup, 1958/1967, pp. 47-49) 3It is not the size of the potential market--that is, whether a particular set of control variables produces D or D-1 customers--that influences the choice of advertising or price reduction; the firm in this example is indifferent between the strategies at either market size, to a small approximation. This may be seen in the following profit calculations for the two strategies with D-1 uncommitted potential customers at (P,A): A+a (10) V = PM + P(D-1) + P(1 * D-1) - (A+a) D-1, no contract D P-p (11) V = (P-p)M + (P-p)(D-1) + (P-p)(1) - A D-1, no contract Subtraction of (11) from (10) using (9) shows that the difference between them is (1/D)p, a very small number in comparison to the differences of order p we shall see when we alter the firm's custom. 4 John Gould pointed this out. 5 The basic proposition holds even if the additional customer comes from within the potential market, depleting that potential market of one of its potential customers rather than coming from outside. We first notice that the reductions in customer-getting effectiveness of both a and p are about the same near this profit-maximizing point: let us call the reduction e. Then (a + e) and (p + e) are the quantities needed to get one additional customer. And we may write, by analogy to (12) and (13) A+a (12a) V = PM + P(D-1) + P(1) + P[1 * (D-1)] - (A+a+e) D-1, contract D D P-p (13a) V = (P-p+e)M + (P-p+e)(D-1) + (P-p-e)(1) D-1, contract D + (P-p-e)[1 * (D-1)] - A D Subtracting (13a) from (12a) shows that the advertising strategy yields (p + e)[1 * (D-1)] higher profit. This is almost 2N times the D difference between (10) and (11), a point mentioned only to corroborate that (10) and (11) are roughly equal. page 3 /article8 firmsize/October 20, 1996 FIRM SIZE AND MARKET BEHAVIOR: A THEORY OF THEIR RELATIONSHIP Julian L. Simon and Haim Levy Abstract The aim of this paper is to explore the connection between firm size and business strategy, one of the more important links between market structure and market behavior. The paper offers proof of this set of propositions: (a) the larger a firm's custom, the greater the propensity to choose additional advertising in preference to a price cut; (b) the larger the custom, the greater the propensity to raise price rather than increase or decrease advertising or cut price; (c) the larger the custom, the greater the propensity to reduce quality rather than increase advertising or cut price; and (d) the larger the custom, the less the propensity to develop cost-increasing quality improvements rather than lower price or increase advertising. The fundament of the theory is that the larger the custom, ceteris paribus, the larger the number of "attached" customers who will pay more (less) if price is increased (decreased), and whose revenue could otherwise be counted on at the old price. Advertising does not affect revenue from the "attached" customers. Quality changes are similar in nature to price changes in this context. And the relationship of R&D activities to customer depends upon the type of discovery that is sought. 8-164 article8 2-17-9 page 4 /article8 firmsize/October 20, 1996 page 5 /article8 firmsize/October 20, 1996