FIRST Degree: The firm knows that it faces different individuals with different demand functions and furthermore the firm can tell who is who. In this case the firm extracts all the consumer surplus, usually with a two-part tariff (with P = MC, thus the same price for everybody, but with different tariffs for different individuals).
The economic intuition behind our findings is straightforward: The monopolistic platform operator is maximizing her profit by inducing a self-selection process among both types of agents on market side 1. Therefore, the bundle of platform access and payment that is sold to low-demand agents ceteris paribus contains less platform access than under complete information as this allows the platform operator to extract additional consumer surplus from high-demand agents. This result is well-known from second-degreepricediscrimination on one-sided markets. However, the reduction of n 1 L induces an additional effect on the opposite market side as the demand of market side 2 agents was supposed to depend on n 1 L and n 1 H . For instance, assume a positive network externality exerted on market side 2. Then, a reduction of n 1 L shifts the demand function n n n 2 ( 1 L , 1 H , p ) inwards, which reduces the optimal price p ** that is charged on market side 2. This in turn makes a marginal increase in n 1 L even less profitable, so that the profit-maximizing extent of platform access for low-demand agents is strictly smaller under incomplete information. In addition, the reduction of p ** also affects
In this article we study second-degreepricediscrimination by a two-sided monopoly platform. We find novel distortions that arise due to the two-sidedness of the mar- ket. They make the standard result “no distortion at top and downward distortion at bottom” not holding. They generate a new type of non-responsiveness, different from the one found by Guesnerie and Laffont (1984). We also show that the platform may mitigate or remove non-responsiveness at one side by properly designing price discrimi- nation on the other side. These findings help to address our central question, i.e., when pricediscrimination on one side substitutes for or complements pricediscrimination on the other side. As an application, we study the optimal mechanism design for an advertising platform mediating advertisers and consumers.
Defining the demand function, or quessing it, will be left for suggestions to future research.
To form the two type second-degreepricediscrimination two-part tariff model for comparison of these three packages, we also need marginal cost c for comparison.
Merchants’ marginal cost in reality is constructred from transaction fees and device costs such as payment terminal and tablet, but at this comparison we take it as constant. Even though transaction cost is volume based. There also may be big differences in that cost for service providers, for example if the service provider is producing part or most parts of the transaction card payment activities by itself. For that reason it wouldn’t have to pay so much margins to another party or parties. Also such factors as retention rate and acquisition cost will be left outside of this analysis.
regulated …rm could increase the universal access problem.
Therefore, this paper attempt to demonstrate that in a context of WAPC regulation and second-degreepricediscrimination, allocative ine¢ciencies and some kind of monopolist’s avoidance behavior arise. In the presence of these problems, it is recommended to design a regulatory scheme involving the regulation by Price Cap of a single plan (e.g. the "Classic Line" plan 17 ), excepting that this regulated plan must always be o¤ered by the monopolist as part of his menu of plans 18 . This will provide some ‡exibility to the monopolist to o¤er alternative plans but with the caveat that be incentive compatible with the regulated plan 19 , thereby avoiding losses in consumer welfare.
In this paper we present an example where the generally accepted superiority of ad valorem taxes does not hold. We study a monopoly with Pigouvian second- degreepricediscrimination and find that, under certain conditions, unit taxes are not only welfare but also Pareto superior. This is not meant to be a general result contradicting accepted wisdom, but a theoretical example suggesting that the commonly held view deserves more careful consideration. In fact, it is possible that this result may be extended to other settings. On the one hand, the superiority of ad valorem taxes over unit taxes has long been established to be greater in monopoly than in other market structures. Given the result presented here for a monopoly, further investigation of the welfare effects of taxes in different settings may be interesting. Similarly, other types of non- Pigouvian second-degreepricediscrimination, such as nonlinear pricing, may be worth investigating.
Consumer surplus for each consumer is shown in figures 1a and 1b. Beard-b- Gone knows the demand functions of the two consumers, and so they know how much CS each consumer gets from using razors and razor blades to shave.
When determining the price of razors, Beard-b-Gone will try and extract as much of the CS as it can. If Beard-b-Gone wants to sell to both consumers, it can’t set the price of razors any higher than $16. That is the CS of the consumer with the lowest valuation (consumer 2). If the price of razors were
The rest of the paper is structured as follows. In the second part, the main assumptions are made and two models are developed. The …rst one characterizes the solution to be reached if there were a social planner, who, not having asymmetric information about costs and/or demand and only knows the distribution of consumers types, may set socially optimal prices with zero pro…ts for the monopolist. This model will be used as benchmark to compare e¢ ciency gains. The second model presents the problem of the monopolist, who besides being able to price discriminate in second-degree, has to face the WAPC constraint. The inclusion of this restriction in the monopolist’s optimization problem generates plans more distorted than the second-best outcome, even distorting the high-valuation consumer’s plan. Finally, the third part presents some conclusions. The formal proofs are presented in the appendix.
Second-Degreepricediscrimination – The monopolist has incomplete information, he knows that there are different types of consumers and knows their tastes but cannot tell them apart ex-ante, i.e. before purchase. He must use self-selection devices to set the right price- quantity or price-quality packages.
It is an imperfect form of first degreediscrimination. Instead of setting different prices for each unit it involves pricing based on the quantities of output purchased by individual consumers.
In seconddegreepricediscrimination, price varies according to quantity sold. Larger quantities are available at a lower unit price. This is particularly widespread in sales to industrial customers, where bulk buyers enjoy higher discounts.
+ Q 2 *
) = 60*40 + 130*55- 2,000 - 20*95 = 5650.
Remark 1: Use this example to understand the ideas behind pricediscrimination: in order to maximize profits, the firm is charging $60 to first group and $130 to the second for each unit of the product. Although, the price to the second group is more than twice the price to the first it would be a mistake to conclude that the firm should increase sales to the second group. Why? The key indicators are the marginal revenues. In order to maximize profits, the firm equates the marginal revenues, not the prices, of the different groups. We can look at the problem from a different point of view. We have defined “cost of sale” as the difference between price and marginal revenue. In the previous example the marginal revenue of the first group computed at Q 1 * = 40 is
elasticity type, and both inelastic. We will show that, within a whole range of values of the parameters a and b, proposition WO is no longer true. To prove it, we present three propositions in this example. The first one provides some useful results for the Cournot oligopoly. The second states that total output is always reduced with the introduction of pricediscrimination for all the relevant parameter values. And the last result says that welfare is reduced for some values of the parameters.
Even though the products are complements, a similar logic can apply to the prop- erty of pricediscrimination. When the products are complements, the price changes and the associated production changes are large due to the greater elasticity created by com- plementarity. In fact, welfare loss is larger in the fourth case (where the strong market has a higher value of price elasticity than the weak market does) than in the third case ( j 0:0123] > j 0:0022 j ). As to the changes in equilibrium aggregate output, it is positive in our second and third cases but negative in the other two. These results are consis- tent with Proposition 2: an increase in the aggregate output is necessary for welfare to be improved by pricediscrimination, as in the case of monopoly.
Quantity discounts: This occurs when the per-unit price for a specific product decreases as the number of purchased units increases. A simple–and easy implemented–instance of this is a two-part tariﬀ, whereby a buyer must pay a fixed charge in return for the right to purchase any quantity at a constant marginal price. There are two distinct motives to use nonlinear tariﬀs. First, nonlinear tariﬀs provide a more eﬃcient means by which to generate consumer surplus. With linear pricing, the only way to make profit is to set prices above costs, which entails deadweight losses. With a two-part tariﬀ, however, a firm can extract profit using the fixed charge, while leaving marginal prices close to marginal costs (which then maximizes the size of the “pie” to be shared between consumer and firm). This role for nonlinear pricing exists even if all consumers are similar. A second role emerges if consumers have heterogeneous tastes for a firm’s products. In this case, a nonlinear tariﬀ can be used to sort diﬀerent types of consumers endogenously (so-called second-degreeprice
Quantity discounts : This occurs when the per-unit price for a speci ﬁ c product decreases as the number of purchased units increases. A simple–and easy implemented–instance of this is a two-part tariﬀ, whereby a buyer must pay a ﬁxed charge in return for the right to purchase any quantity at a constant marginal price. There are two distinct motives to use nonlinear tariﬀs. First, nonlinear tariﬀs provide a more eﬃcient means by which to generate consumer surplus. With linear pricing, the only way to make proﬁt is to set prices above costs, which entails deadweight losses. With a two-part tariﬀ, however, a ﬁ rm can extract pro ﬁ t using the ﬁ xed charge, while leaving marginal prices close to marginal costs (which then maximizes the size of the “pie” to be shared between consumer and ﬁrm). This role for nonlinear pricing exists even if all consumers are similar. A second role emerges if consumers have heterogeneous tastes for a ﬁ rm’s products. In this case, a nonlinear tariﬀ can be used to sort diﬀerent types of consumers endogenously (so-called second-degreeprice
3.3 Seconddegree PD (arbitrage and screening)
Note that the absence of direct signals empowers consumers with the ability to engage in personal arbitrage. Perfect PD is, in general, not possible. However, even when there is no exogenous information (direct signals) for the monopolistic producer to tell the consumers apart, a monopoly can still extract some consumer surplus. Let’s first go through a common way of 2 ◦ PD — the two-part tariﬀ.
…rst, pricediscrimination causes a misallocation of goods from high to low value users (that is, output is not e¢ ciently distributed to the highest-value end); second, pricediscrimination a¤ects total output. Therefore, since pricediscrimination is viewed as an ine¢ cient way of distributing a given quantity of output between di¤erent consumers or submarkets, a necessary condition for pricediscrimination to increase social welfare is that it should increase total output. 3 In consequence, in order for pricediscrimination to increase welfare a positive output e¤ect must o¤set the negative e¤ect of distributional ine¢ ciency.
Meanwhile, an important stream of literature has been discussing pricediscrimination from the standpoint of ver- sioning (Shapiro and Varian 1999; Ulph and Vulkan 2000;
Acquisti and Varian 2005; Bandulet and Morasch 2005) or customizing (Bandulet and Morasch 2005). However, although versioning and customization may lead to a mar- ket outcome similar to first-degreepricediscrimination, it is not, per se, first-degreepricediscrimination. Indeed, they necessarily imply different products (versions) sold, which leads, at best, to an extreme case of market segmentation, where each consumer has become a market segment. This makes versioning closer to second-degreeprice discrimina- tion (where consumers self-select the ‘formula’ best-suited for them). The present article, in contrast, focuses on the ability firms may have to charge different prices for the exact same good or service within the same time frame.