The models which I have examined in the last couple posts assumed the simplest possible context for a commercial enterprise: a business with a single plant, employing a single variable input, producing a single product, which is sold in a single market, and which is run by a single manager. The organization of the market varied in structure and complexity, ranging from pure competition through monopolistic and oligopolistic competition to pure monopoly. But there are very few real-world businesses which are so simple.
Business enterprises typically produce a multiplicity of goods and services which often can be organized into lines of complementary and sometimes competing items. Occasionally the goods produced by the business are conglomerated in the sense that there are no apparent relationships among them. Often the multiple goods are joint products resulting from a common production process. And commercial enterprises often sell their products in a multiplicity of separable market areas. They employ a great many variable inputs bought or hired from different resource markets. It is not unusual for a business to have several production facilities or plants, and each plant may be subdivided into several assembly lines, each of which can function as a more-or-less autonomous production unit. And the management of the business may include many decision makers, each with limited areas of expertise, decision-making authority, and responsibility. They may be organized into multiple, hierarchical tiers of authority. The facets of intricacy and complexity of the modern business enterprise are almost innumerable.
How can the simple-minded models elaborated previously be relevant to any real-world business organizations other than those which match the models in simplicity? The great virtue of such simple contexts is that they allow us to peer through the haze of complexity in order to come to understandings of the principles governing the behaviors of revenues, costs, profit, production, and competition itself without the encumbrances of a plethora of detail. They may serve their academic purposes well, but from a practical perspective, the applicability of such simple models is still not apparent.
There are three planes upon which the models which I have been examining may be beneficial to practical decision contexts. First, the general principles discovered and learned by examining the models in an academic setting can be used as guides to what I shall call “seat-of-the-pants” decision making (see Fritz Machlup, “Marginal Analysis and Empirical Research,” in Essays in Economic Semantics, W. W. Norton & Company, 1967, pp. 154-155). Here the decision maker proceeds from an accumulation of experience in similar circumstances to an assessment of the present situation. A rational decision is made by comparing the best available information about the situation to the decision criteria discerned in the academic study of the principles. While this decision-making procedure may sound a bit loose and uncertain, I believe that the vast majority of all business decision makers who have engaged in any formal study of economic principles are likely to proceed in just this fashion.
The second plane upon which simplistic models can be used is to simulate small parts of the complex business decision context. For example, if a business has one plant in each of several completely separate markets, and each plant produces several mutually-exclusive products for sale in the market where that plant is located, it should be possible to specify a revenue and a cost function for each of the products in each of the markets in order to establish the relevant marginal decision criteria. This approach becomes cumbersome and costly in the case of a wholesale distributor which regularly carries 30 thousand different items (in the case of screws, each combination of thread pattern, head design, finish, diameter, and length constitutes a separate item) in its warehouse. The approach breaks down entirely if some of the items are jointly-produced, or if they are produced in a single plant for sale in several markets, or if they are produced in multiple plants but sold in a single market.
On the third plane the simplistic models must be elaborated to handle the intricacies of the situation. The model builder attempts to make the assumptions underlying the model ever more realistic, the structure of the model ever more accurately descriptive of the real context which is being modeled, and the parameters of the model ever more closely tailored to the particular circumstances of the required decision. The progressive elaboration of a model inevitably increases its complexity and detail. The number of equations in the model increases, and particular equations may have to have more and higher-ordered terms in them.
Economists have traditionally valued simplicity in models, for after all is said and done a model is intended to be a simplified representation of a more complex reality. But economists have also debated the importance of the realism of assumptions and the descriptive accuracy of the structure of their models. Most inevitably have come to the conclusion that it may not be possible to construct a simulation model which is perfectly realistic in its assumptions and accurately descriptive in its structure without making it as complex as the real situation from which it is supposed to be an abstraction. This of course would defeat the purpose of attempting to structure a simplified representation of the more complex reality.
A respected economist, Milton Friedman, has argued that the realism of assumptions and the accuracy of the structure of a model are of lesser importance than is the predictive ability of the model (“The Methodology of Positive Economics” in Essays in Positive Economics, University of Chicago Press, 1953). The acid test for a model is how it performs in doing what it was designed to do. According to Friedman, a simplistic model based on unrealistic assumptions may perform satisfactorily; what is important is whether people behave as if the assumptions of the model are realistic, even if the assumptions bear little or no resemblance to the reality.
An “economic” perspective on the process of elaborating a model to make it more specific to the context being modeled would examine the benefits and the costs of the elaboration process. A more complex model based on more realistic assumptions may indeed yield better decision criteria, but the process of specifying any model is costly in terms of time and effort, and in money terms if the expertise has to be hired from outside the organization. The cost of specifying an ever more complex model probably obeys the principle of diminishing returns (or its variant, the law of increasing costs) no less so than does any other real production phenomenon. Model-building costs rise at an increasing rate the farther the model builder attempts to go in detailing the model. The relevant economic question then is whether the value of the additional effectiveness of the model is worth the extra cost of improving the fit.
Our advice is to apply Occam’s Razor to the model-building context. Under this principle, one should (use the Razor to) “cut off” the unnecessary complexity of a model: let suffice the simplest model which will perform satisfactorily. When several needles are lost in a haystack, rational behavior on the part of the tailor is to search until he finds one which is sharp enough to do the sewing job, not until he has found the absolutely sharpest one. But, this is not a recommendation to make no enhancements to the model. Some models are “simply too simple” to fit the realities under analysis. Our purpose in the next section of this post is to point the reader in the directions of some potentially productive model elaborations. But I do caution the fledgling model builder to take an economic approach by comparing the possible benefits with the likely costs.
Economists focus almost obsessively upon price as the primary determinant of demand. Previously I postulated a more general demand function with several quantity determinants, any one of which could be moved to the head of the queue to serve as the primary determinant. Once any one of them has been designated the primary determinant, others are assumed constant. This procedure enables the construction of a two- or (at most) three-dimensional graphic model to illustrate and analyze the demand relationship. A change of any of the assumed-constant determinants (i.e., the ones not represented explicitly on any of the coordinate axes) results in a shift of the curve (in two dimensions) or the surface (in three dimensions). If such a change occurs without being recognized by the analyst, an “identification problem” arises. The decision-significance of the occurrence of an identification problem is that the decision criteria will tend to be over- or understated, and could thereby lead to erroneous decisions.
Economists, in structuring the kinds of models I have examined, usually assume price to be the primary determinant of quantity demanded, but it is also a convenience to have a deterministic variable which is directly comparable to average and marginal costs. Business decision makers attempting to employ the economic models should pay attention to the non-price demand determinants because autonomous changes in any of them can shift the company’s demand curves in unexpected ways. While these are phenomena to be aware of and prepared to adjust to, it may also be possible to make the non-price determinants of demand into components of the firm’s promotional strategy. For example, a successful advertising campaign (promotional effort is one such non-price determinant of demand) should have the effect of increasing the company’s demand (i.e., shifting the demand curve to the right), or at least preventing it from decreasing (shifting left) in the face of a competitor’s promotional effort.
Economists also focus almost exclusively upon quantity produced as the primary determinant of cost. But I also noted that non-quantity determinants of costs may be incorporated into the cost function. Possible candidates are the market prices of the labor and materials inputs which the firm purchases. It is a convenience to take costs primarily to be functions of quantity produced because this allows direct comparison of per-unit costs (average and marginal) with price and marginal revenue. A change in any of the non-quantity determinants of costs can be expected to shift the per-unit cost curves upward or downward.
As in the case of the non-price determinants of demand, it may be possible to incorporate the non-quantity determinants of costs into the company’s production and marketing strategies. For example, one way to gain a “leg-up” on the competition would be to develop a more productive (i.e., lower cost) technology, or to find or negotiate lower-priced sources of supply of the materials or labor inputs than competitors can employ. This would certainly increase the company’s profits (or reduce its losses) by shifting its per-unit cost curves downward. If the company’s average variable cost curve shifts far enough downward, the manager may be encouraged to initiate a price war.
The markets in which a firm sells can be classified on at least four bases: product, geographic, demographic, and temporal. I shall defer consideration of multiple products to a subsequent section. The geographic market for a particular product is the locale within which the company sells, and where there is effective competition by other companies selling closely competitive products. For most products, the geographic market is almost certainly not the world or even the whole geographic of area of a country. Most companies sell in multiple geographic markets which are separated by distance and the cost of transport so that clienteles are effectively compartmentalized. Furthermore, the company may face varying intensities of competition in its different geographic markets: it may be a monopolistic competitor in some markets, an oligopolist in some, and a nearly-pure monopolist in a few. It may need to pursue different marketing strategies according to the nature and intensity of competition faced.
Varying demand conditions make price differentials among the markets feasible. The charging of different prices for the same item where there are no differences in the costs of serving the different customers constitutes price discrimination which is prohibited under law in most western societies. By the same token, the charging of the same price where there are different costs of serving different customers is also price discrimination, but this form of price discrimination usually escapes detection or prosecution under the law. For example, many companies deliver products in their own trucks instead of using third-party shippers. Often the costs of own-truck delivery are not charged explicitly, but rather absorbed in the product prices. To the extent that this occurs, the delivered price is the same to the nearby customer as to the distant customer. Price discrimination results as a consequence of charging the same price to the different customers. The antitrust authorities would likely never finish if ever they decided to start prosecuting this form of price discrimination. Although the law usually prohibits the practice of overt price discrimination where there is no cost justification for the price discrimination, price discrimination between markets should be expected to emerge as a normal concomitant of different demand elasticities in the different markets.
The company may also sell to separate temporal and demographic markets within the same geographic market. The bases for demographic market separation may include age, race, ethnicity, religion, place of birth, citizenship, etc. Price (and any other kind of) discrimination based on race or ethnicity are usually prohibited by law. The most common demographic forms of price discrimination are by age and citizenship. Theaters typically offer lower-priced children’s tickets, even though the seat is as fully occupied by the child as by an adult, and even though the adult really didn’t want to see the children’s feature. Restaurants as well as theaters may price differently through the day (the “luncheon menu” vs. the “dinner menu,” the “afternoon matinee” vs. the “evening feature”). State universities often price-discriminate against citizens of other states who apply for admission and denominational colleges occasionally price-discriminate in favor of their own members or the offspring of their ministers and missionaries. Airlines and hotels conventionally price discriminate by days of the week and from one season to the next.
Commercial classification may constitute yet another basis for price discrimination. Wholesalers usually identify “legitimate” retail vendors who then are eligible to buy “at wholesale” whereas members of the general public can qualify only for the higher retail price. Some wholesalers as well as some manufacturers maintain several customer classifications, each of which is eligible for a certain price level or discount from the company’s standard price (wholesalers often express their price schedules as various levels of discount from manufacturer’s suggested retail price). Such classification schemes break down when a buyer classed in one group has access to someone classed in another group. Most of us know “a guy who’s got a brother-in-law who can get it for us at wholesale.” Also, the recent advent of “wholesale buying clubs” has served to obscure the distinction between retail and wholesale.
Any of these forms of price discrimination is enabled only because demand elasticity varies among groups or from time to time, and it is not feasible for a prospective client to jump from one group or time frame to another. If clients can jump market segments, the basis for price discrimination is destroyed. It can be shown mathematically that if two conditions can be met, the company can increase its profit by price discriminating across its markets: (a) demands are of different elasticities in the different markets; and (b) there is some means segmenting markets and keeping customers in the different market segments from jumping segments or from buying for one another.
Demand in Market A is somewhat more inelastic than is demand in Market B. When the demands are summed (horizontally), Dc (the combined demand) has the appearance of a bend where Db is joined to Da, so that the marginal revenue curve, MRc is as drawn in panel (c). The firm has a single plant for which its marginal cost curve is MC. The intersection of MC with SMR identifies the quantity Qc and price Pc which would maximize profits without price discrimination. The total revenue will be the area 0PcTQc. Suppose now that the manager of the company identifies the quantities and prices in the two markets separately for which MR in each is equal to MC, the common marginal cost. On this criterion, Q1 can be sold at Pa in market A, and Qb can be sold at Pb in Market B. Pa is higher and Pb is lower than Pc. A careful examination of total revenue rectangles 0PaRQa and 0PbSQb should reveal that the sum of their areas is greater than that of total revenue rectangle 0PcTQc. Thus, whatever the firms costs happen to be, its revenues with price discrimination will be greater than its revenues without price discrimination, so price discrimination will yield more profit than can be realized without price discrimination.
The managerial implications are clear. The manager of an imperfectly competitive company may by price discrimination increase the company’s revenues, but only by incurring the costs of establishing and enforcing market separation, and often by risking antitrust prosecution. It may be very troublesome (and trouble translates into costs) to seal off the markets from one another. The costs of enforcing market separation may be greater than the additional revenue realized from discrimination. What does it take to certify that a person really is under thirteen years of age in order to qualify for the child’s price, or over 55 years of age to qualify for the senior citizen’s discount? How much does it cost to verify each prospective customer’s claimed authorization to buy at wholesale? What is the probability of incurring antitrust prosecution, and what is the likely fine if the verdict is “guilty?” As with any other managerial decision, the rational approach is to compare the expected benefits with the likely costs before deciding to proceed.
Suppose that the manager of a company which has a single plant thinks that it might be more profitable to divide the market into two segments in order to price discriminate. In order to ascertain the appropriate quantities to ship into each sub-market and the prices at which to sell them, the company must estimate its demand functions in the form of P = f( Q / … ) and then find the total revenue function by multiplying the demand function through by Q, or TR = P x Q (alternately, the company might first estimate its total revenue function, then derive the average and marginal functions mathematically):
TR1 = P1 x Q1 = Q1 x f(Q1), and
TR2 = P2 x Q2 = Q2 x f(Q2).
It must also estimate its cost function, TC = f(Q), where
Q = Q1 + Q2.
It must then compose its total profit function as TN = TR1 + TR2 – TC, so that the two marginal profit expres-sions can be computed by partial differentiation,
MN1 = dTN/dQ1
MN2 = dTN/dQ2.
These marginal profit expressions may then be set equal to zero (because the slope of the profit function is zero at its peak),
dTN/dQ1 = 0
and dTN/dQ2 = 0,
allowing for solution of values for Q1 and Q2. Then, using these values in the estimated demand functions, values for P1, P2, TR1, and TR2 may be found. And finally, the maximized profit, TN, may be computed.
As I have already noted, if the company produces multiple products for sale in as many product markets, its production and marketing operations in each product market can be modeled separately. For short-run decision making purposes, this analysis can be handled without reference to the overhead costs since they are irrelevant to the price and output decisions (in the last section of this I will consider a model for pricing to cover fully-allocated costs).
In the long run the allocation of the overhead costs in a multiproduct plant becomes critical to the question of whether to delete any particular items from the product line, or to add new items if excess capacity exists. In order for any item currently in the product line to continue to be produced, its price must make an adequate contribution to its overhead costs as well as cover all of the direct costs of its production. This is not an argument for price to be set to cover overhead as well as direct costs; rather, once price has been determined with appropriate economic criteria (MR, MC), the question is whether or not it covers all relevant costs. Since there appears to be no objective criterion for allocating overhead costs among multiple products, this assessment must be based upon the judgment of the decision maker who, in any case of deleting or adding products, is engaging in an entrepreneurial decision.
If the company has excess productive capacity and is considering whether to add items to its product line, the decision maker must make a prior judgment (again, in an entrepreneurial capacity) as to whether the new item can be sold at a price which is high enough to cover all of its direct production costs and make some contribution to covering the overhead costs as well. It can be argued that since the excess capacity already exists, the overhead costs are in effect “sunk costs” and thus not pertinent to the question of adding the item to the product line. Yet, even if an item is added on the basis that its price will be sufficient to cover all direct costs plus some contribution to overhead costs, for the item to be retained in the product line in the long run it will have to be judged to be making an adequate contribution to overhead costs and profit. If the company is considering adding an item when it has no excess capacity, then the appropriate criterion is that the item should not be added unless it is possible to sell the item at a price which will cover both its direct costs and the overhead costs resulting from the added capacity. In any case, the rational entrepreneur should add items to the product line in descending order of perceived profitability.
The specification of decision criteria for jointly-produced products poses another difficult problem. Jointly-produced products are those which result from a common production process. Classic examples are beef and hides, gasoline and fuel oil, mutton and wool. Even where the objective is to produce one primary product, e.g., metal stampings for auto body parts, there are likely to be marketable by-products such as the metal scrap. In any short-run situation, such joint products are produced in fixed proportions. The relevant questions are what quantity of the output mix is to be produced and at what prices are the individual items in the mix to be sold. In the long run, the management often can vary the output proportions, so that the relevant question for the long run is the profit-maximizing output combination.
The short-run decision problem can be analyzed with a variant on the multimarket price discrimination model. The marginal revenue curves for the jointly produced products are summed vertically (they were summed horizontally in the price discrimination model) to construct the joint marginal revenue curve, MRJ. I note that for all outputs larger than Q2, MR1 is negative so that the MRj curve is coincident with the path of MR2. The relevant short-run decision criterion is the comparison of marginal cost with joint marginal revenue. The manager should increase output as long as joint marginal revenue exceeds marginal cost, or decrease output if joint marginal revenue is less than marginal cost. If marginal cost is given by MCA, the product 1 profit-maximizing price is P1 at which output Q1 of product 1 should be sold. Price P2 should be charged for product 2, and all units of both products should be sold.
If marginal cost should fall to MCB, it intersects the joint marginal revenue curve to the right of where MR1 has become negative. Since it would be irrational to sell so large a quantity of any product as to reduce total revenue (i.e, where MR is negative), output Q3 of both products is produced, but only Q2 of product 1 should be sold at price P4. The rest of product 1 (Q3-Q2) should be withheld from the market and possibly destroyed or “dumped” in another market (dumping is then a special case of price discrimination). All of product 2 produced, Q3, should be sold at price P3.
Plant managers typically have little discretion in varying the product mix in the short run. To alter the output mix usually requires a long-run adjustment to plant, equipment, and technology to be effected through capital investment. Without perfect prior knowledge of the costs and revenues of alternative product-mix combinations, the company’s manager, acting in an entrepreneurial capacity, can only proceed iteratively to try an alternative combination when the next occasion for capital reinvestment arises. If the new product mix increases profitability (a successful entrepreneurial decision), the manager can assume that an adjustment in the proper direction has been made.
The long-run decision to vary the proportions in which joint products are produced can be illustrated with an isorevenue map superimposed over an isocost map, similar to the isoquant-isocost analysis of production. I choose not to elaborate the theoretical isocost-isorevenue model in the text of this post because the ability to estimate the equations of surfaces from which isocost curves can be extracted requires near-perfect prior knowledge of the company’s multiple-product production possibilities. This is typically far more information than can be mustered in most real decision settings.