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Using the economics of the pass-through in proving antitrust injury in Robinson-Patman cases.

I. Introduction

In a famous footnote, the Supreme Court in J. Truett Payne Co., Inc. v. Chrysler Motors Corp. (1) stated that one (but not only) way to establish that price discrimination injured the plaintiff is to demonstrate that the favored buyer "passed on" the price advantage in a lower retail price:
   If the favored purchaser has lowered his retail price, for example,
   the disfavored purchaser will lose sales to the extent it does not
   match that lower price. Similarly, if the disfavored purchaser
   matches the lower price, it will lose profits. (2)


In earlier cases, the Supreme Court refers to price advantages passed on. (3) Yet the authors are aware of no case law that explains when pass-on should occur.

In this article, we present an overview of what economic theory has to say about the existence and the determinants of the magnitude of pass-through. We begin by presenting a standard microeconomic theoretical model of the cost pass-through rate that measures the magnitude of a price change following a firm experiencing a change in costs. Then we examine how various real-world features that are not explicitly incorporated in the standard model affect the pass-through rate. We show that, except for a few very particular circumstances, the pass-through rate is always positive: if there is a price differential, it will be passed on to consumers, resulting in diversion of sales. We then show how various features of the industry and of the product affect the magnitude of the pass-through rate.

In addition to Robinson-Patman cases, the concept of the pass-through rate is also extensively used in indirect purchaser litigation and merger analysis. Suppose several manufacturers form a cartel. Often, these manufacturers do not sell directly to consumers, but rather they sell through retailers. Thus, if the cartel harms competition, the cartel harms only the retailers directly. Final consumers are harmed only indirectly: to the extent that the wholesale price increase due to the cartel's existence is passed on to the final consumers. If the pass-through rate on the retail level is close to zero, then consumers are barely harmed. On the other hand, if the pass-through rate on the retail level is close to one (100% or full pass-through), then consumers are harmed almost as much as they would have been had they been buying from the cartel directly.

In Hanover Shoe, the U.S. Supreme Court decided that indirect purchasers cannot recover claims against the cartel. (4) Similarly, in Illinois Brick, the Supreme Court confirmed the decision. (5) However, later the Supreme Court legitimized provisions passed by many states allowing indirect purchaser actions. (6) Similarly, many international courts allow indirect purchaser actions as well. (7)

The pass-through rate is also used extensively in merger review. (8) The upward pricing pressure index is the opportunity cost of a price cut taking away sales from another product owned by the same firm. (9) This opportunity cost is the extent to which a merger would incentivize a firm to raise its prices unilaterally postmerger. The pass-through rate in this case is the proportion of this opportunity cost that gets passed on to consumers in terms of increased prices. Thus, getting the pass-through rate right is integral in predicting whether the post-merger prices increase by 5% or more (or any other threshold).

II. Analysis of a Basic Model and Conclusions

A. A Model of a Monopolist Firm

Before diving deeper into the effect that different demand and supply side factors have on the pass-through rate, it is informative to review the standard monopoly model of pass-through rates. Much of the intuition in models that include competition and other variations is an extension of the relatively straight-forward intuition of this basic model.

Let us start by analyzing a monopolist with a linear demand function of

D(p) = a - bp,

where p is the price that the firm charges (for example, retail price of gas) and a > 0 and b > 0 are parameters (intercept and slope) of the demand function. The linear shape of the demand curve is chosen mainly for analytical convenience; empirically, the linear form provides an approximation to the actual shape of demand only if prices vary within a small range.

Say that the firm has a constant marginal cost c (for example, the wholesale price of gas that the firm has to pay to the refinery or the wholesaler) and a fixed cost F. Then, the firm's profit is

[pi](p) = D(p)p - D(p)c = (a - bp)(p - c) - F.

The firm chooses its price to maximize its profit, resulting in (10)):

[p.sup.*] = a/2b + 1/2 c.

The pass-through rate is the extent to which price reacts to changes in cost. In the case of linear demand, the equation above tells us that the pass-through rate is 50%. For a dollar increase in cost, the price increases by 50 cents; and for a dollar decrease in cost, the price decreases by 50 cents.

What happens if the demand function is not linear, say a more general function D(p)l In this case, the firm chooses the price to maximize its profit

[pi](p) = D(p)p - D(p)c - F.

in the same manner as with linear demand (again, via solving [partial derivative][pi](p)/[partial derivative](p) = 0 for p), except that the expression becomes a little harder to interpret:

[p.sup.*] = c + D([p.sup.*](c))/-[D.sup.']([p.sup.*](c)),

where the symbol of prime denotes derivative of the demand function. If the marginal cost changes, so does the price. If the price changes, so does the quantity demanded. Therefore, both the numerator and the denominator of the fraction in the equation above depend on marginal cost.

If cost changes are relatively small, we can obtain the pass-through rate by implicitly differentiating the equation above with respect to marginal cost. Skipping a few steps of algebra, we obtain:

[partial derivative][p.sup.*]/[partial derivative]c = 1/2 - [D.sup."] D/[([D.sup.']).sup.2], (1)

where double prime denotes the second derivative of the demand function. Both the demand function and its derivatives are calculated at the original price, that is, the price that prevailed before any cost increase.

B. Conclusions from the Model

Now that we have done the hard work, let us see what conclusions can be established.

The first notable conclusion is that the pass-through rate is the rate of pass-through of marginal cost only. Fixed cost does not determine the optimal price; therefore, any decreases or increases of fixed cost are not reflected in the price level. In other words, the pass-through rate of fixed cost is always zero. From now on, whenever we refer to the pass-through rate, we are implying the pass-through rate of marginal cost. Similarly to fixed cost being irrelevant for price calculations, the only component of the average cost that matters is the marginal cost; thus, it is difficult to discuss pass-through of average cost.

The second thing to note is that linear demand is a knife-edge case. Examining the terms in the equation above, it is easy to see that if the demand function is concave ([D.sup."] < 0), then the pass-through rate is lower than 50%, but if the demand function is convex ([D.sup."] > 0), then the pass-through rate is higher than 50%. The linear function is at the boundary (since [D.sup."] = 0), and thus the pass-through rate is exactly 50%. Thus, the second derivative (concavity) of the demand function determines whether a monopolist's pass-through rate is above or below 50%. (11)

By the way of example, suppose that again that [D.sup.'] = -1/2, for example, demand falls by 0.5 units following a price increase of one dollar. Now suppose that the price has increased by another dollar. If demand falls by yet greater amount, say by 0.8 units, then it is said that the demand function is concave ([D.sup."] < 0). If, on the other hand, demand falls by a smaller amount, say by 0.3 units, then we say that the demand function is convex ([D.sup."] > 0). Whether demand for a given product is concave or convex is an empirical question.

The third finding is that concavity is the only factor that determines whether the rate is above or below 50%. Three factors are jointly responsible for just how much above or below 50% the pass-through rate is: concavity of the demand function (second derivative), slope of the demand function (first derivative), and the quantity demanded.

The upshot of these conclusions is that one has to be extremely careful when estimating the pass-through rate in practice, since often the functional form used in estimation will determine the pass-through rate almost regardless of the actual data used. For example, assuming a linear demand model while estimating the pass-through rate automatically results in a pass-through rate of 50%. Various economic and marketing articles note issues that could arise when not using flexible demand forms and arguing that demand forms that are generally considered flexible are not sufficiently flexible for estimating the pass-through rate. (12)

Given how difficult it is to pinpoint the exact shape of the demand curve, can we at least put any limits on how far away from 50% different concavity/slope/quantity combinations can push the pass-through rate? It turns out that it is possible, but only in one direction. From an introductory calculus class, one might remember that for any optimization problem, second-order conditions must be satisfied to ensure that a finding is indeed a maximum as opposed to a minimum or a saddle point. Standard monopolist second-order conditions ensure that the pass-through rate cannot fall below zero. Note that almost every economic model makes this assumption, either implicitly or explicitly. Thus a pass-through rate of zero is a limiting case: a result that raises doubt about whether the right model is used. On the other hand, it is possible for the pass-through rate to be above 100%, for example, for certain parameters of the constant elasticity of substitution function, which is another popular choice in demand estimation. More generally, for a monopolist with linear cost, any log-convex demand function results in the pass-through rate of over 100%. (13)

One important observation is that the pass-through rate is the same regardless of why costs actually changed. Costs could change because the upstream supplier is in a different bargaining position vis-a-vis the firm. Alternatively, costs could change because the upstream supplier and the firm changed their contracting relationship to a two-part tariff (note that the size of the lump sum part of the tariff does not matter since it is, a possibly negative, fixed cost). Yet another possibility is that the costs changed because the upstream supplier is providing a one-time promotional incentive. There is a multitude of reasons for why costs change. The end result is the same: the firm passes-through according to the principles described above.

C. Incorporating Nonlinear Costs

Just like a linear demand function, a linear cost (constant marginal cost) is a convenient assumption. However, this assumption is frequently not satisfied in reality. (14) To analyze this case, let's consider the following profit function:

[pi] = D(p)p - K (D(p)) - cD(p) - F,

where K is a nonlinear cost function. Again, we can derive the optimal price (via solving [partial

derivative][pi](p)/[partial derivative]p = 0 for p), and differentiate the resulting expression with respect to c. The resulting expression for the cost pass-through rate is

[partial derivative][p.sup.*]/[partial derivative]c = 1/2 - [D.sup."] D/[([D.sup.']).sup.2] - [K.sup."], (2)

Note that concavity of demand ceases to be the sole factor determining whether the pass-through rate is above 50%. For example, a sufficiently concave cost function can push the pass-through rate below 50% despite a convex demand function. Despite that, the pass-through rate of zero is still a limiting case, for exactly the same reason as above: the monopolist's problem stops being well defined. (15)

III. Demand Factors

A. Availability of Alternatives

We now expand on our simple monopolist model by introducing competition from other firms that offer similar products. Having one more firm in the model immediately raises an important question: if there is a cost change, does the cost change just for one (or some) of the firms, or do the costs change for each Finn in the market? In the context of examining the pass-through of taxes, tariffs, or compliance costs with regulation, typically all or most of the firms in the market are affected. This is also the case that most of the academic literature addresses. (16) For example, the analysis of pass-through based on the standard supply-demand diagram implicitly assumes that each firm in the market experiences a cost change. Similarly, most of the analysis of Cournot quantity competition models in the earlier literature also deals with the case of each firm experiencing a cost increase. (17)

Suppose a firm's costs decreased. Regardless of whether the firm's competitors' costs decreased as well, the firm's margin became larger, and therefore, the firm wants to sell more product. This incentivizes the firm to cut prices, similar to the intuition in the monopolist case above. (18)

For antitrust purposes, however, we are generally concerned with one firm experiencing a cost change, while its competitors do not. In this case, there are two reasons why a pass-through rate in the presence of competing products is different from the pass-through rate of a monopolist.

The first reason is that prices of substitute products sold by different firms are strategic complements: if I increase my price, my competitor's best response is to increase her price as well; and vice versa, if I decrease my price, my competitor's best response is to decrease her price. (19) Now, suppose that my cost decreases. In this case, I should, according to the monopolist model, decrease my price by some factor. However, this price decrease prompts my competitor to decrease her price as well. In turn, her price decrease prompts me to decrease my price even further. This incentive produces a higher pass-through rate: due to responding to my competitor's best response to my initial reaction, I will pass through more of the cost change. (20)

The second reason is that the relevant parameters of demand that determine a monopolist's pass-through rate--concavity of demand, slope of demand, and quantity demanded--all depend on the competitor's price.

What happens with the pass-through rate as the number of competitors increases? Typically a firm's demand becomes more elastic when its customers have more alternatives. (21) However, this change in elasticity does not immediately imply a lower or higher pass-through rate, as it also depends on the concativity of demand. Except in special cases such as linear demand, (22) there are no theoretical results regarding the relationship between the number of competitors and pass-through. It remains an empirical question and must be resolved on case by case basis. For completeness' sake, if all competitors experience the cost change, then the intuition remains similar. (23) Note that the special case of perfect competition is defined by

D(p) = S(p - t),

where D is the demand function, S is the supply function, and t is the cost increase or tax that all the firms in the markets incur. In this special case, via implicitly differentiating the equation above with respect to t,

[partial derivative][p.sup.*]/[partial derivative]t = 1/1 + [[epsilon].sub.D]/[[epsilon].sub.S],

where [[epsilon].sub.D] is the elasticity of demand and [[epsilon].sub.S] is the elasticity of supply. This equation confirms the familiar intuition that in a perfectly competitive market the relatively inelastic side of the market bears any cost/tax increases. In particular, in a perfectly competitive market where each firm's cost is linear (and, thus, supply is infinitely elastic), there is full pass-through: a dollar of a cost increase is a dollar of a price increase. Note that it is often difficult to generalize intuition from the perfectly competitive market to imperfectly competitive markets (the markets that would generally be discussed in either Robinson-Patman or merger cases). While the differences between the pricing implications of the two market structures are well understood, the differences between the pass-through rate implications are not.

B. Price Points

So far we have abstracted in our discussion and analysis from a particular real-world friction: price points. However, in many markets, price points matter. One only needs to watch a few consumer product good advertisements to realize that prices that end with 99 cents, or perhaps 9.99 are important factors. Similarly, in cell phones with contracts, a "free" cell phone seems a focal price point and in TVs, tablets, and personal computers, hundreds or dollars serve as price points. (24)

It might seem that an environment with price points serves as a road block to price adjustments: after all, a small cost change should not entice a firm to jump from one price point to another, and should result in a pass-through rate of zero. (25) However, this intuition is incomplete. The firm might have been close enough to jumping from one price point to another so that this last cost change was the proverbial straw that broke the camel's back.

Thus, while it is true that the probability of the pass-through rate being zero increases (in cases where the firm was far from jumping to another price point), it is also true that in some cases the pass-through rate actually ends up being higher (in cases where the firm was close to jumping to another point anyway). In most cases, the intuition stated above is completely right: if the cost change is relatively small, the firm will not want to jump to a different price point. However, in a few cases, the firm might have already been close to changing its price, and thus the small cost change results in an abnormally large pass-through rate given the cost change. (26) The additional difficulty is that we cannot know a priori whether the firm was already close to changing the price.

An apt analogy is a short trip on a road with a traffic light. Most of the time, going a little faster does not result in getting there any quicker; it just results in waiting for the traffic light to change for a longer time. However, sometimes increasing the speed just by a little can make the trip much faster due to just making green as opposed to spending minutes waiting for the light to change.

It turns out that, on average, the increased speed helps as much on a road with a traffic light as it does on a road without one or, in the context of the pass-through rate, the average pass-through rate is the same with or without the price points. (27) However, there is a high chance of a zero pass-through rate combined with a low chance of an abnormally high pass-through rate.

Note that while the expected pass-through rate is the same, it might mask variation that is relevant for this particular case. A particular case is actually more likely to have a pass-through rate of zero, and that has plenty of consequences for damages both in individual and in class actions cases. (28)

Finally, we note that the intuition above holds for any demand function, and it holds for monopoly as well as for market structures involving strategic competition.

C. Costly Search

Standard models of competition typically make an implicit assumption that consumers are fully informed, that is, they know about all available varieties and their prices before deciding what to buy. In many markets, however, this assumption is not adequate. When the number of products is large (such as airline transportation), or product characteristics are complex (such as camcorders), or prices change frequently (such as gasoline markets), consumers typically find it necessary to shop around before making a purchase. Because shopping involves time and effort, the extent of price comparison is usually limited, so that a consumer ends up making a purchase without full knowledge of available choices. Both the fact that consumers search before they buy and the fact that they do not search enough have implications for incentives of firms to pass through cost changes.

To see the effect of limited consumer knowledge on pass-through, consider an individual consumer entering a given shop, say of firm A. This could be the very first shop visited by the consumer, in which case firm A is essentially a monopolist, as there are no other options in consumer's consideration set. More generally, a consumer may have visited A other shops prior to firm A, in which case firm A has N competitors in the "market" for this consumer's purchase decision. The larger is N, the higher is probability that his consideration set contains a better alternative, and therefore the larger is the elasticity of demand. Aggregating over all visitors of firm A, we conclude that the total demand consists of a mixture of consumer types, according to the number of shops already visited, where parameters of the mixture are determined by the distribution of search costs among potential visitors. As a result, the elasticity of search-generated demand depends both on the elasticity of individual demand and on the shape of the search cost distribution. Both need to be empirically estimated in order to reach conclusions regarding the pass-through rate in search markets.

So far we have considered search costs as a determinant of the number of competitors of firm A once a consumer has reached the firm A's store. The story does not end here. The fact that a consumer has visited firm A does not mean that he will stop there and, crucially, the decision to continue shopping (and leave the shop) will depend on firm A's offer. By charging a higher price, firm A not only it makes its product less attractive relative to other products that the consumer has found so far, it also makes the consumer more motivated to search further. (29) This factor further increases the elasticity of demand, particularly among consumers with lower search cost. (30)

In addition to search costs, consumer beliefs regarding the distribution of prices in the market are another factor that determines the elasticity of search-generated demand. Consider, for example, the incentives of a retailer to pass through the trade promotion--a temporary decrease in wholesale price of a product. Producers often use trade promotions as a way to expand market share and increase brand awareness. By initiating a price discount, the retailer makes extra sales, but only to consumers who learned about the discount. Due to limited search, it will take time for other consumers to learn about the lower price, thus reducing the benefits of the promotion. (31) The retailer may counter this negative effect by establishing a reputation by offering promotions more frequently: this will improve consumer beliefs regarding the likelihood of finding a good deal, and will motivate consumers to shop more often.

If the price cut comes as a surprise--something the consumer did not expect to find during price comparison--it might make the consumer to become more optimistic about prices of similar products offered by other retailers, inducing him to leave the shop and search further. For example, this may happen if the consumer infers, quite reasonably, that manufacturers of competing products have also launched trade promotions. More generally, a lower price might induce the consumer to think that the retailer's margins are higher than previously thought, and hence there is more scope other retailers to offer discounts. (32) In both cases, lower price induces more search and reduces the benefit of the promotion.

To conclude, the interactions between costly search and demand elasticity are complex. The purpose of the above discussion was to highlight the main forces that differentiate the elasticity of search-generated demand from the demand under full information. Generally, positive search costs make demand less elastic, although there is a possibility of opposite effects coming from consumer beliefs. Once the concavity of individual demand is established, one can translate these effects into pass-through rate: according to equation (1), if the second derivative of individual demand is positive, lower elasticity will imply lower pass-through, mutatis mutandis for establishing convexity of individual demand.

IV. Supply-Side Factors

A. Menu Costs

A menu cost is a cost that a firm incurs to change its price. (33) There is evidence that menu costs are an important component of pricing decisions of firms. In particular, an older survey showed that for a random sample of firms in the northeast of the U.S., with yearly sales of over $10 million, menu costs were either important or very important for 43% of firms. (34)

The intuition of the effect of menu costs on pass-through rates seems relatively straight-forward: the pass-through rates should be lower when menu costs are present, since a firm would rather not pass through a small cost change so that it does not incur the menu cost. However, just like in the case of price points, this logic is deceiving.

Just like in the case of price points, menu costs make it more likely to observe a zero pass-through rate in many cases. However, the firm might have already experienced many cost and demand changes that were incentivizing it to change its price in a particular direction, except that these changes were not sufficient to actually incur the menu cost. Finally, this last change was sufficient to incur the menu cost and change the firm's price--the proverbial straw that broke the camel's back, exactly like in the price points discussion above. (35)

Despite the seeming similarities between price points on the demand side and menu costs on the supply side, there are differences between them. The first difference is that with price points a firm might overshoot with its reaction to cost change: while the cost change does not justify switching the price all the way from 1.99 to 2.99, the cost change might be sufficient so that the profit at 2.99 is higher than the profit at 1.99. However, with menu costs, the firm will get it just right: if the profit at 2.57 justifies incurring the menu cost, and that is the actual optimal price, then the firm incurs the menu cost and charges 2.57. Because the firm does not overshoot, even the expected pass-through rate is lower in the presence of menu costs than it would have been without menu costs. (36)

The second difference is that firm's manager's expectations matter much more for menu costs. If the managers expect that more changes are forthcoming, then maybe even though it would have made sense to change the price in the static environment, it makes more sense to change the price next period once that change comes. Due to the expectations, it is again possible that even the expected pass-through rate is lower in the presence of menu costs than it would have been without menu costs. (37)

The third difference is related to the second difference. If the cost change is temporary and sufficiently small relative to the menu cost, then it does not make sense for the firm to pass it through. In this scenario, the firm simply pockets the extra profit from any cost decrease and absorbs any change stemming from a cost increase. (38)

Again, the reader should note that while the expected pass-through rate is still positive, it might mask variation that is relevant for this particular case. A particular case is actually more likely to have a pass-through rate of zero, and that has plenty of consequences for damages both in individual and in class actions cases.

B. Multiproduct Firms

So far we have been dealing only with firms that sell a single product. However, this assumption is not always true. Occasionally, a firm's products are not related either on the demand side or on the production side. In this case, our analysis from above applies. But if the products are related either on the production side or on the demand side, our analysis has to be somewhat adjusted.

Multiproduct firms have to be concerned about cross pass-through: the pass-through of product A's cost change onto product B's price. In the economics literature, this topic is generally explored only tangentially, generally in merger analysis. (39) However, in the quantitative marketing literature, this topic is at the forefront. Every retailer has to solve this problem, and any manufacturer that engages in trade deals (for example, temporary wholesale price discounts) has to be concerned not only with the effect of the trade deal on retail prices on its own products, but also with the effect of trade deals on competitors' prices. Thus, it is not surprising that there is both theoretical and empirical literature in marketing that explores cross pass-through rates. (40)

The cross pass-through rate depends on the relationship between the products sold. In particular, two factors affect cross pass-through rates. The first factor is the "substitution" factor. (41) Suppose products A and B are substitutes (say, basic and premium versions of an electronic equipment). If product A's cost decreases, then product A's price decreases (by the intuition from the monopolist model), which in turn leads to lower quantity demanded of product B. Lower quantity demanded of B leads to a lower price on B--a cost decrease of A leading to B's price decrease, a positive cross pass-through rate.

The second factor is the "margin" factor. (42) Lower cost of A made A more profitable. Therefore, product B's price should increase, since some of the consumers that stop buying B will switch to a now more profitable A. In other words, A's cost decrease leads to B's price increase, a negative cross pass-through rate.

These factors point in different directions and, in general, the cross pass-through rate can be either positive or negative. Only in special cases the cross pass-through rate is zero. (43)

The interdependence of products also leads to changes in their own pass-through rates. The intuition in the multiproduct case is similar to the aforementioned result of higher incentive to pass through when there are competing products. Suppose the prices of two products of a multiproduct firm are strategic complements, as they would be for a firm selling differentiated substitutes. Product A's cost decrease leads the firm to decrease that product's price. However, since the prices of two products are strategic complements, product A's price decrease prompts the firm to decrease product B's price as well. In turn, product B's price decrease prompts the firm to decrease product A's price even further? (44)

C. Changing Quantity and Quality Together with Price

Instead of changing the product's price, a firm might change the quantity or the quality of the product. There is plenty of anecdotal evidence of firms changing the quantity or the quality offered in response to either supply or demand shocks. In particular, firms offer smaller packages and lower quality in developing countries. (45) During a recession or when commodity prices are high, firms do the same in the United States. (46)

Estimating the pass-through rate in these cases can be particularly challenging. For example, when a firm decreases its package size, oftentimes it decreases the price as well. In this case, a cost increase leads to a price decrease--a negative pass-through rate, something that we mentioned is impossible to get in the monopolist model. However, this seemingly counterintuitive result is easily resolved. Instead of focusing on the effect of cost on price, in cases like this one should focus on the effect of cost on quantity adjusted price. Thus, if one considers the pass-through rate of cost on price per unit of product (say, price per ounce of yogurt), then the intuition behind pass-through rates returns to what we considered in the monopolist section above. (47)

The same argument applies to firms that can adjust the quality of their products. Note that the argument continues to hold when the firm can price discriminate by offering a menu of options (in the multiproduct framework like the one above). (48) Also, if there is a menu adjustment cost of changing the quantity or the quality of the product, for example changing the package size might require spending some money and it is arguably easier to change the price of the product than it is to change its size or quality, then before the cost is incurred and the package is changed the firm's price should follow the standard intuition of the monopolist model described above.

As in many cases above, we find that the intuition from the simple monopolist model introduced at the beginning of the article applies, however, it is easy to get perverse results if one is not careful. For example, if the firm that experiences a cost increase simply decreases the size of the package without changing the price, one would observe a zero pass-through rate. However, this zero pass-through rate is simply an artifact of not measuring the pass-through rate correctly, and one should adjust the price to the size of the package to get the correct answer.

V. Conclusion

We summarized the intuition of pass-through rates using microeconomic theory. We first analyzed a standard monopolist case, and then we examined several demand and supply side factors that could influence the pass-through rates. The pass-through rate is generally strictly more than zero, and could even be higher than 100%. Table 1, while skipping several important details and nuances, summarizes our analysis concisely.

Now we summarize our conclusions for a Robinson-Patman case. In a Robinson-Patman case, we are generally concerned with the existence of the pass-through for liability purposes. In some cases, the size of the pass-through could be a factor in a damage model. With respect to liability, there is always a positive pass through assuming firms maximize profits except in the few exceptional cases explained above: there is a probability of a zero pass-through if the firms have menu costs of changing prices or have to adhere to price points like.99 price endings; however, the expected pass-through rate is still positive. The size of the pass through is far more difficult to draw generalizations, as shown in Table 1, and it is highly dependent on the specific market frictions and on how the market departs from the base theoretical model described in Section II.

DOI: 10.1177/0003603x15602402

Authors' Note

The views expressed are those of the authors and do not necessarily represent those of the Director of the Consumer Financial Protection Bureau nor those of the staff. Authors can be contacted at alexei01@gmail.com and sergei.koulayev@gmail.com.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

(1.) 451 U.S. 557 (1981).

(2.) Id. at n. 4.

(3.) See, e.g., Perkins v. Standard Oil Co. of Cal., 395 U.S. 642, 649 (1969) (Evidence showed "Signal received a lower price from Standard than did Perkins, that this price advantage was passed on....").

(4.) See Hanover Shoe, Inc. v United Shoe Machinery Corp., 392 U.S. 481 (1968).

(5.) See Illinois Brick Co. v. Illinois, 431 U.S. 720 (1977).

(6.) See California v. ARC America Corp., 490 U.S. 93 (1989); see also George Kosicki & Miles B. Cahill, Economics of Cost Pass Through and Damages in Indirect Purchaser Antitrust Cases, 51 Antitrust Bull. 599 (2006) (discussing this and other cases related to Hanover Shoe).

(7.) See, e.g., Frank P. Maier-Rigaud, Towards a European Directive on Damages Actions, 10 J. Competition L. & Econ. (2014).

(8.) See, e.g., Gregory J. Werden, A Robust Test for Consumer Welfare Enhancing Mergers Among Sellers of Differentiated Products, 44 J. Indus. Econ. 409 (1996); Daniel P. O'Brien & Steven C. Salop, Competitive Effects of Partial Ownership: Financial Interest and Corporate Control, 67 Antitrust L. J. 559 (2000).

(9.) See, e.g., Joseph Farrell & Carl Shapiro, Recapture. Pass-Through, and Market Definition, lb Antitrust L. J. 585 (2010).

(10.) Via solving [partial derivative][pi](p)/[partial derivative]p = 0 for p.

(11.) See Rajeev K. Tyagi, A Characterization of Retailer Response to Manufacturer Trade Deals, 36 J. Marketing Res. 510 (1999); Paul L. Yde & Michael G. Vita, Merger Efficiencies: Reconsidering the "Passing-On" Requirement, 64 Antitrust L. J. 735 (1996).

(12.) See Jeremy 1. Bulow & Paul Pfleiderer, A Note on the Effect of Cost Changes on Prices, 91 J. Pol. Econ. 182 (1983); Michal Fabinger & E. Glen Weyl, A Tractable Approach to Pass-Through Patterns (Working Paper No. 2194855, 2014), http:// ssm.com/abstract=2194855.

(13.) A function is log-convex when the natural logarithm of that function is convex.

(14.) See, e.g., Susanto Basu & John G. Femald, Returns to Scale in U.S. Production: Estimates and Implications, 105 J. Pol. Econ. 249 (1997).

(15.) For the pass-through rate to approach zero, the combination of cost and demand functions must be such that the firm is virtually indifferent between any price that it might charge: clearly an atypical scenario.

(16.) See, e.g., E. Glen Weyl & Michal Fabinger, Pass-Through as an Economic Tool: Principles of Incidence Under Imperfect Competition, 121 J. Pol. Econ. 528 (2013); Simon P. Anderson, Andre de Palma, & Brent Kreider, Tax Incidence in Differentiated Product Oligopoly, 81 J. Pub. Econ. 173 (2000).

(17.) See, e.g., Jesus Seade, Profitable Cost Increases and the Shifting of Taxation: Equilibrium Response of Markets in Oligopoly (Warwick Economic Research Papers No. 260, 1988), http://www2.warwick.ac.uk/fac/soc/economics/research/ workingpapers/1978-1988/twerp_260.pdf.

(18.) Note that we are assuming Nash equilibrium behavior by firms: a belief that other firms do not change their prices. While conjectural variations (other beliefs about competitors' responses) were popular in the economic literature before the 1980s, they are generally not considered since then. But see Sonia Jaffe & E. Glen Weyl, The First-Order Approach to Merger Analysis, 5 Am. Econ. J.: Microeconomics 188, 188-218 (2013) (authors consider the standard Nash beliefs as well as conjectural variations).

(19.) See Jeremy I. Bulow, John D. Geanakoplos, & Paul D. Klemperer, Multimarket Oligopoly: Strategic Substitutes and Complements, 93 J. Pol. Econ. 488 (1985).

(20.) The same intuition often applies even if the firms' decisions are strategic substitutes. For both strategic complements and strategic substitutes, see Alexei Alexandrov & Ozlem Bedre-Defolie, Le Chatelier-Samuelson Principle in Games and Pass-Through of Local and Global Shocks (forthcoming Working Paper, Social Science Research Network, 2015).

(21.) But see, e.g., Yongmin Chen & Michael H. Riordan, Price-Increasing Competition, 39 RAND J. Econ., 1042, 1042-58 (2008).

(22.) See Paul R. Zimmerman & Julie A. Carlson, Competition and Cost Pass-Through in Differentiated Oligopolies (unpublished, Munich Personal RePEc Archive, Paper No. 25931, 2010), http://mpra.ub.uni-muenchen.de/25931/l/ MPRA_paper_25931.pdf. Zimmerman and Carlson study linear demand with differentiated products in Cournot and Bertrand, and find different results. In Cournot, PT increases with n, while in Bertrand it decreases. In an earlier paper, policy makers demonstrate that the effect of merger--which is one way to alter the number of competitors--on pass-through depends on the curvature of demand and cannot be determined solely on the basis of elasticity. See Luke Froeb, Steven Tschantz, & Gregory J. Werden, Pass-Through Rates and the Price Effects of Mergers, 23(9) Int'l J. Indus. Org. 703, 703-715 (2005).

(23.) Id.

(24.) See, e.g., Eric T. Anderson & Duncan I. Simester, Effects of $9 Price Endings on Retail Sales: Evidence from Field Experiments, 1 Quantitative Marketing & Econ. 93 (2003); Karen Gedenk & Henrik Sattler, The Impact of Price Thresholds on Profit Contribution - Should Retailers Set 9-Ending Prices?, 75(1) J. Retailing 33 (1999); Robert M. Schindler & Thomas M. Kibarian, Increased Consumer Sales Response Though Use of 99-Ending Prices, 72 J. Retailing 187 (1996) (evidencing the importance of pricing points).

(25.) See, e.g., John H. Johnson & Gregory K. Leonard, Frictions and Sticking Points: Applying the Textbook Model to the Analysis of Cost Pass-Through in Indirect Purchaser Class Actions, Antitrust Insights, Winter 2008, http:// papers.ssm.com/sol3/papers.cfm?abstract_id=1373793.

(26.) See Alexei Alexandrov, Pass-Through Rates in the ReaI World: The Effect of Price Points and Menu Costs, 79 Antitrust L. J. 349 (2013).

(27.) Id.

(28.) Id.

(29.) See Martin L. Weitzman, Optimal Search for the Best Alternative, 47 Econometrica 641-54 (1979).

(30.) See Sergei Koulayev, Search with Dirichlet Priors: Estimation and Implications for Consumer Demand, 31 J. Bus. & Econ. Stat. 226, 226-39 (2013).

(31.) For an application of this argument in the context of gasoline market, see George Deltas, Retail Gasoline Price Dynamics and Local Market Power, 56 J. Indus. Econ. 613, 613-28 (2008).

(32.) See Mariano Tappata, Rockets and Feathers: Understanding Asymmetric Pricing, 40 RAND J. Econ. 673, 673-87 (2009).

(33.) See, e.g., Andrew S. Caplin & Daniel F. Spulber, Menu Costs and the Neutrality of Money, 102 Q. J. Econ. 703 (1987).

(34.) See Alan S. Blinder, Why Are Prices Sticky? Preliminary Results from an Interview Study, 81 Am. Econ. Rev. 89, 90-94 (1991).

(35.) Alexandrov, supra note 27.

(36.) Id.

(37.) Id.

(38.) See Dennis Carlton, The Theory and the Facts of How Markets Clear: Is Industrial Organization Valuable for Understanding Macroeconomics?, 1 Handbook Indus. Org. 909, 909 -16 (1989).

(39.) See, e.g., Farrell & Shapiro, supra note 10.

(40.) While empirical literature is not the topic of this article, see, e.g., David Besanko, Jean-Pierre Dube, & Sachin Gupta, OwnBrand and Cross-Brand Retail Pass-Through, 24 Marketing Sci. 123 (2005). We provide cites to some of the theoretical literature below.

(41.) See Steven M. Shugan & Ramarao Desiraju, Retail Product-Line Pricing Strategy When Costs and Products Change, 77 J. Retailing 17 (2001).

(42.) Id.

(43.) Id.: see also Sridhar Moorthy, A General Theory of Pass-Through in Channels with Category Management and Retail Competition, 24(1) Marketing Sci. 110 (2005).

(44.) The same intuition often applies even if the firm's decisions are strategic substitutes. For both strategic complements and strategic substitutes, see Alexandrov & Bedre-Defolie, supra note 21.

(45.) See, e.g., Eric Bellman, Companies Court the Poor's Loyal Pennies, Wall St. J., July 23, 2012, http://online.wsj.com/ articles/SB 10001424052702303612804577530821179213842; John Revill, Food Makers Rethink Europe, Wall St. J., May 28, 2012, http://online.wsj.eom/articles/SB10001424052702304707604577422262832189148.

(46.) See, e.g., Katie Little, Chobani Yogurt Is Latest Victim in Shrinking Grocery Case, CNBC, Jan. 4, 2014, http:// www.cnbc.com/id/101309099.

(47.) See Alexei Alexandrov, Pass-Through Rates When Firms Can Vary Package Sizes, 10 J. Competition L. & Econ. 611 (2014).

(48.) Id.

Alexei Alexandrov * and Sergei Koulayev *

* U.S. Consumer Financial Protection Bureau, Washington, D.C., USA.

Corresponding Author:

Sergei Koulayev, U.S. Consumer Financial Protection Bureau, Office of Research, 1700 G St. NW, Washington, D.C. 20552, USA.

Email: sergei.koulayev@gmail.com
Table 1. Summary of the analysis in the article.

Scenario          Pass-through      Pass-through
Description       is lower if:      is higher         See more

                  Concave           Convex demand
                  demand (less      (more than        II. A and
Monopoly          than 50%).        50%).             II. B

Different         Fixed cost        Convex costs      II. C
  types of          (zero             (diseconomies
  costs             pass-through)     of scale).
                    or concave
                    (economies of
                    scale, low
                    nonzero pass-
                    through).

Competition       Less              More              III. A
                    competitive.      competitive

Price points      Same rate on      Same on           III. B
  (.99 endings)     average, but      average, but
                    there is an       there is a
                    effective         lower chance
                    lottery: the      of a zero
                    rate is zero      pass-through
                    sometimes and     rate when
                    really high       price points
                    other times.      are closer
                    There is a        together (as
                    higher chance     in have to
                    of a zero         end at .99 as
                    pass-through      opposed to
                    rate when         $999).
                    price points
                    are far
                    apart.

Costly search     Costly search                       III. C
                    makes each
                    firm's demand
                    more elastic.
                    Moreover,
                    passing costs
                    or promotions
                    through might
                    lead to
                    consumers
                    adjusting
                    their beliefs
                    regarding the
                    price
                    distribution
                    in the
                    market,
                    further
                    complicating
                    the
                    pass-through
                    intuition.

Menu costs        Lower rate on     Lower chance      IV. A
                    average, also     of a zero
                    an effective      pass-through
                    lottery as        rate when
                    with price        menu costs
                    points.           are lower.
                    Higher chance
                    of zero
                    pass-through
                    when menu
                    costs are
                    higher.

Multiproduct      Fewer             More              IV. B
                    products.         products,
                                      especially if
                                      decision
                                      variables are
                                      strategic
                                      complements.

Endogenous        Same              Same              IV. C
  package size      intuition as      intuition as
                    in the            in the
                    monopoly          monopoly
                    case, but         case, but
                    have to use       have to use
                    the per unit      the per unit
                    price (if a       price.
                    laundry
                    detergent now
                    has 4 ounces
                    less in the
                    bottle, its
                    per unit
                    price
                    increased).
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Title Annotation:To Defend or Reform? The Law and Economics of the Robinson-Patman Act
Author:Alexandrov, Alexei; Koulayev, Sergei
Publication:Antitrust Bulletin
Date:Dec 22, 2015
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