Market share analysis between MNO and MVNO under brand appeal based segmentation

Transcription

1 Market share analysis between MO and MVO under brand appeal based segmentation Merouane Debbah Alcatel-Lucent Chair in flexible adio SUPELEC, Gif-sur-Yvette,France Loubna Echabbi IPT, Madinat El Irfane 2, av Allal El Fassi, abat, Morocco Chahinez Hamlaoui Alcatel-Lucent Chair in flexible adio SUPELEC, Gif-sur-Yvette,France Abstract We are interested in this paper by the competition between MO and MVO on a population of heterogeneous customers, with different perceptions of operators offer. The MVO buys resources from MO at the wholesale price and offers an added value supposed to be better and at a lower price compared to the incumbent operator. In such a scenario, the rational customer behavior is to choose the virtual operator offer. However, we consider that the market is segmented into two different populations: the first segment is defined by customers attracted by the brand appeal of the MO as the incumbent operator and the second segment of customers more sensitive to the added value proposed by the MVO. Thus, the choice of customers will rather depend on their preferences and retail operators offers. We model this problem considering game theory tools and we distinguish three possible situations depending on customers preferences. For each situation, we calculate the market share of each of the operators and the ash equilibrium given by the MO s wholesale price and the MVO s margin. A mobile virtual network operator MVO is, in the broadest sense of the term, an operator that provides mobile phone services without owing a radio spectrum license or a network infrastructure. For this purpose, the MVO must contract with a mobile network operator MO with frequencies and mobile network infrastructure. This contract allows the MVO to buy wholesale resources from the MO and to resell in retail to subscribers. Unlike ordinary resellers, the MVO relies on its brand image and reputation gained in other business to sell its mobile service[1. MVO offers are usually proposed as a bundle including, in addition to the mobile service, an added value related to their core business, as bonus points, discounts on music CDs or theater tickets. Through its original core business, the MVO can directly target a specific segment of the mobile market, in other words a niche. We refer for example to Virgin Mobile offers which target a relatively young In population. Thus, a market that can be segmented regarding customer preferences, make the substitutability of operators offers a key factor in competition in the mobile market. Mobile operators are faced with strategic issues when it comes to decide whether to accommodate or to foreclose the entry of the MVO in the market. [3 and [4 consider a model with two vertically integrated MO and one MVO competing in a downstream market. In [3 Bourreau and all, analyze the price competition between two integrated firms and a potential downstream rival and show that at the equilibrium, the downstream rival is not foreclosed. Upstream firms have two motivations to give the access to the downstream firm. First, the wholesale generates additional revenues. Second, serving firm with high upstream price mitigates competition on the downstream market. Yu-Shan lo [4 studies a similar model while incorporating the demand-side investment. The objective is to study how the MVO behaves when facing entrant of different abilities. Hence, in Yu-Shan Lo model, users preferences are represented by a quasi-linear utility that depend on the product differentiation and the flat fee, which in turn depends on the added value. Another relevant question is should MOs be enforced to open their networks to MVOs or not by the regulator for example. Indeed, the introduction of MVOs aims to lower retail prices through competition and use the extra resources that are not used by the MOs. In [5 authors show that enforcing the MO to open its network to MVOs has a negative effect due to the fact that intense competition reduces the return on investment of MO and therefore reduces the incentive to invest in its network. The MO is indeed alone to bear infrastructure costs. The authors also show that semi-collusion in the investment increases the social welfare semi-collusion in the sense that the MVO participates in the investment costs. Hence, one can expect the difficulty to introduce the first MVO and once the market is open more MVO can enter the competition. The French market for example has experienced its MVO revolution in July 2004, hosting the first MVO Debitel. Virgin Mobile s entry on this market took place in 2006 and the total number of MVOs has finally reached forty in 2010[6. These operators are beginning to attract more and more market share especially young population which is more sensitive to added value proposed by MVOs. We will focus in this paper on MO behavior when facing a segmented downstream market where users have an

2 heterogeneous preferences and have a different sensitivity to operators offers. It can be the case, of a market where for example old users trust the incumbent operators Orange, SF, Bouygues and where young users prefers the added value proposed by an MVO like Virgin Mobile. In that case, an important policy question is whether an MO is likely to offer access to its network on a voluntary basis. I. A MODEL FO CUSTOMES PECEPTIOS OF OFFES BASED O BAD APPEAL AD ADDED VALUE We are interested in the competition between MO and MVO over a population of heterogeneous customers, with different perceptions of operators offers quality added value of each offer. The MVO buys MO resources at the wholesale price and offers an added value supposed to be better at a lower price than the MO. In such a scenario, the rational behavior of customers is to choose the virtual operator offer. However, we believe that customers, at least part of them, rely also on the brand appeal while making their choice. Thus, in this paper, we consider that the market is segmented into two populations of different customers: customers that are attracted, at least to a certain level, by the well established brand of the incumbent operator and customers that are more sensitive to the added value offered by the MVO. Thus, the choice of customers will rather depend on their preferences and operators retail offers. We consider that MO and MVO are caracterized by the following parameters: and model resp. the added value of the MO and MVO. Since MVO is supposed to innovate on added value we will consider that <. p 1 and p 2 model resp. the unitary price charged by MO resp. MVO to customers that choose its offer. We consider again that MVO should propose lower prices in order to attract customers. Hence, we consider p 1 > p 2. I 1 and I 2, the brand appeal of the MO and MVO. As the MO is the incumbent operator we consider that it is more attractive with respect to brand appeal, thus I 1 > I 2 w is the unitary whole price charged by the MO to the MVO. A rational behavior expected from the MVO is to set its retail price at least to the wholesale price in order to ensure a positive benefit. The market is composed of customers. We consider that this market is segmented into two segments S 1 and S 2 where S 1 refers to customers that are more sensitive to brand appeal and thus more likely attracted by MO offers. Whereas S 2 refers to customers that are more sensitive to added value and thus more likely attracted by MVO offers. We denote i the market share of segment S i. Each customer is caracterized by two parameters α i and β where: α i is the customer perception of brand appeal. Indeed, as the market segmentation is defined by brand appeal perception, we will consider only two possible values for this parameter each related to the segment to which the customer belongs. This parameter is thus indexed by the related segment. β is customer perception of added value. In order to cope with lack of information about actual perception of added value, we will suppose a uniform distribution on a bounded interval [0,. However it is possible to consider other laws to capture different perceptions of added value on both segments. For simplicity sake is supposed to be the same for both segments, but again we can consider different values which will slightly modify market share computation. Each customer will choose to subscribe to the operator that maximizes his surplus. We are inspired by the original formulation of Mussa and osen [7 to express the surplus of each customer. Thus, the surplus of customer i regarding the offer made by operator j is modeled by the following amount: β V j α i I j p j, where j = 1 for the MO and j = 2 for the MVO. Let us note however that a customer still have the choice to refuse to subscribe or to delay the subscription process if the offers are not interesting enough i.e the price is too high, the added value or the brand appeal are not sufficient to compensate the raise of the offer price. This can be captured by the fact that the surplus is negative. We will refer to that case by index 0 as none of the operator are chosen. Taking into account the proposed model for capturing customers perceptions of brand appeal and offer added value, we will compute the market share between the MO and the MVO. II. THE MAKET SHAE OF MO/MVO Let us consider a customer of the first segment : Such a customer prefers not to have access to the service rather than having the MO as provider iff: α 1 I 1 β p 1 < 0 That is β < p1 α1i1 The customer prefers not to have access to the service rather than having the MVO as a provider iff: α 1 I 2 β p 2 < 0 That is β < p2 α1i2 The customer prefers having the MVO rather than the MO as a provider iff: α 1 I 1 β p 1 < α 1 I 2 β p 2 that is β < p1 p2α1i2 I1. let us sort this three thresholds: β 1 = p 1 α 1 I 1 ; β 2 = p 2 α 1 I 2 and β 3 = p 1 p 2 α 1 I 2 I 1. Indeed their order is very important when computing the market share. This order is defined by prices set by each operator and may change in function of them. We will see that different order are possible but some of them are not valid as they imply absurd situations. Let us note i j or

3 symetrically j i if a customer with a given sensitivity β prefers j among i where i, j {, MO,MVO} case 1: β 1 β 2 β 3 : is valid for β < β 1 customer prefers not to join any provider for β 1 < β < β 3 customer prefers to join the MO. for β 3 < β < customer prefers to join the MVO. case 2: β 1 β 3 β 2 : is not valid. Indeed if β 3 < β < β 2 than there is a cycle which is absurd. case 3: β 2 β 3 β 1 : is not valid. Indeed if β 2 < β < β 3 than there is a cycle case 4: β 2 β 1 β 3 is not valid. Indeed if β 2 < β < β1 than there is a cycle which is absurd. case 5: β 3 β 2 β 1 : is valid for β < β 2 customer prefers not to join any provider for β > β 2 customer prefers to join the MVO. case 6: β 3 β 1 β 2 is not valid. Indeed if β 1 < β < β2 than there is a cycle Let us prove that it is sufficient to consider case 1 and case 5 by comparing β 3 and β 2. Indeed we have only two cases either β 3 β 2 or β 3 β 2. Let us suppose that β 3 β 2 and prove that β 3 β 1 necessiraly. β 3 β 2 p 1 p 2 α 1 I 2 I 1 p 2 α 1 I 2 That is : p 1 p 2 α 1 I 2 I 1 p 2 α 1 I 2 By expanding and simplifying, we get : p 1 α 1 I 1 p 2 α 1 I 2 After further simplification: p1 α1i1 p2 α1i2. That is : β 2 β 3 β 1 β 2 β 1 β 3 1 This relates to case 1 where β 1 β 2 β 3. ow, let us suppose that β 3 β 2 and prove that β 3 β 1 necessarily β 3 β 2 p 1 p 2 α 1 I 2 I 1 p 2 α 1 I 2 That is p 1 p 2 α 1 I 2 I 1 p 2 α 1 I 2. By expanding and simplifying, we get : p 1 α 1 I 1 p p 2 α 1 I 2 After further simplification: 1 α 1I 1 p 2 α 1I 2. That is: β 3 β 2 β 1 β 2 β 3 β 1 2 This relates to case 5 where β 3 β 2 β 1. ow let us analyse the situation for segment S 2 taking into account the situation of segment S 1. ote that for segment S 2 the thresholds are defined with α 2 instead of α 1. Suppose That segment S 1 is in case 1. Intuitively, customers in segment S 2 may be either in case 1 or 5 depending on their sensitivity to added value. However if segment S 1 is already in case 5 then segment S 2 is definitely in the same case. Indeed, if customers giving priority to brand appeal choose the MVO than definitely customers from S 2 will do so. Let us analyse this case more carrefully. First suppose that S 1 is in case 1 that is p 1 α 1 I 1 p 2 α 1 I 2 p 1 p 2 α 1 I 2 I 1. For simplicity sake, we will consider in the following : a 1 = p 1 / ; a 2 = p 2 / ; a 3 = p 1 p 2 / ; b 1 = I 1 / ; b 2 = I 2 / ; b 3 = I 1 I2/. We have then for segment S 1 : a 1 b 1 α 1 a 2 b 2 α 1 a 3 b 3 α 1. ow we will analyse which case is valid for segment S 2 by comparing a 1 b 1 α 2 ; a 2 b 2 α 2 and a 3 b 3 α 2. First, we have a i b i α 2 > a i b i α 1 for i = {1, 2} since α 1 > α 2. However a 3 b 3 α 2 < a 3 b 3 α 1. ow given those constraints let us show which situations are valid for segment S 2. We will check if segment S 2 may be in case 1 too. This is depicted in figure 1. Fig. 1. Case 1-1 This situation is valid if the situation of the market is such that a 1 b 1 α 1 a 1 b 1 α 2 a 2 b 2 α 1 a 2 b 2 α 1 a 3 b 3 α 2 a 3 b 3 α 1. In such a situation segment S 2 will be in case 1 and thus some customers will choose the MO and some of them will choose the MVO. We will relate to this case in the following as case 1-1. Since both segments have customers eventually interested in both operators, One can expect that in such a case the proportion of customers choosing the MVO in segment 2 is more important than customers from segment S 1. This is confirmed by figure 2. Let us note that the proportion of customers who will not choose either the MO or the MVO is less important in segment S 1 which can be explained by the fact that the brand appeal is much more a compensation in that segment. ow let us check if segment 2 may be in case 5 that

4 Fig. 2. Market share of operators each operator. First, we will consider the demand for MO from the first segment in Case 1: D MO 1 = 1 p 1 p 2 α 1 I 2 I 1 p 1 α 1 I 1 With 1 = and 2 = 1, and 0 1 then: D MO 1 = [ p 1 p 2 α 1 I 2 I 1 p 1 α 1 I 1. In a similar way we have for segment 2 : is all clients in that segment are only interested in the MVO. Let us first note that we have a 2 b 2 α 2 > a 2 b 2 α 1 since α 1 > α 2 > 0,and whatever the order of a i b i α 1 compared to a i b i α 2 for i= 1 or 3, It is valid for segment S 2 to be in case 2 as depicted in figure 3. We will relate to this case in the following as case 1- Fig. 3. Case In such situation the MO looses all customers in segment S 2. An important proportion of customers is lost as they do not choose either the MO or the MVO. ow suppose that segment 1 is in case 2 that is all customers from S 1 choose the MVO and let us show that so will be the case for customers from segment 2. As segment 1 is in case 2 than a 2 b 2 α 1 a 1 b 1 α 1. Let us suppose by contradiction that segment 2 is not in case 2 that is a 1 b 1 α 2 < a 2 b 2 α 2. we have then : a 2 b 2 α 1 a 1 b 1 α 2 < a 1 b 1 α 1 a 2 b 2 α 2 thus : b 1 α 1 α 2 < b 2 α 1 α 2 which is a contradiction as α 1 α 2 is positive and b 1 b 2. Hence both segment 1 and segment 2 are in case 2 and choose either the MVO or nothing. We will refer to that case as 5-5. A. Case 1-1 Let us remind that case 1-1 refer to the case where both MO and MVO are in case 1 that is when there are customers from both segments maybe interested in their respective offers. ow, we will compute the total demand of D MO 2 = 2 = p 1 p 2 α 2 I 2 I 1 p 1 α 2 I 1 1 [ p 1 p 2 α 2 I 2 I 1 p 1 α 2 I 1. Hence, the total demand on the MO is given by: D MO = D1 MO D2 MO = [ p 1 p 2 α 1 I 2 I 1 p 1 α 1 I 1 1 [ p 1 p 2 α 2 I 2 I 1 p 1 α 2 I 1. By denoting : C 1 = [ α1 α 2 I 2 I 1 α 1 α 2 I 1 α 2 I 2 I 1 I 1 p 1 cst And after simplification we get: D MO = p 2 C 1 In an another hand the demand received by the MVO from segment 1: MV O D1 = βmax 1 p 1 p 2 α 1 I 2 I 1 = [ p 1 p 2 α 1 I 2 I 1 In a similar way, the demand received by the MVO from segment 2 is given by: MV O D2 = 2 = βmax p 1 p 2 α 2 I 2 I 1 1 [ p 1 p 2 α 2 I 2 I 1 Hence the total demand on MVO is given by: D MV O MV O = D1 D MV O 2

5 D MV O = [ p 1 p 2 α 1 I 2 I 1 1 [ p 1 p 2 α 2 I 2 I 1 By denoting : C 2 = I 2 I 1 α 1 1 α 2 p 1 cst Then after simplification we get: : D MV O = C 2 p 2 ow, to define the best response of the MVO to the MO strategy, we derive its profit with respect to µ : MV O π µ 2 = 0 µ ω C 2 = 0 The optimal response of the MVO is given by the margin µ as function of ω : µ = I 2 I 1 α 1 1 α 2 p ω 4 At the equilibrium, both ω and µ are best response to each other. After substitution of µ in 3 by its value from equation 4 and after simplification we get: ω = I 2 I 1 α 1 1 α 2 p 1 3 Similarily, after substitution of ω in 4 by its value from equation 3 and after simplification we get: ow, we will compute the profit for both operators under case 1.1, then define the optimal strategies for each. Given that the MVO price is set while taking into account the wholesale price ω and an eventually positive margin µ then the MO profit can be written as : π MO = D MO.p1 D MV O.ω = ω µ C 1p 1 C 2 ω µω p 1 µ = ω2 c 2ω µp 1 C 1p 1 In order to define the best response of the MO to the MVO strategy we derive its profit with respect to ω : π MO ω = 0 2 ω p 1 µ v 1 C 2 = 0 The optimal response of the MO is given by the wholesale price ω as function of µ: ω = I 2 I 1 α 1 1 α 2 2p µ 3 The MVO profit is given by : = C 2 π MV O = D MV O µ = C 2 ω µ µ ω µ µ2 µ = I 2 I 1 α 1 1 α 2 3 By comparing µ and ω, we note that ω µ = p 1 in this case. Given the constraints that ω, µ 0 and ω p 1, then necessarily, ω = p 1. Hence the unique ash equilibrium in this game is given by ω, µ = p 1, 0. The MO chooses a foreclosure strategy by setting a wholesale price equal to its retail price. Thus, if the market is such that the competition between operators covers both segments, then the MO has more incentives to preserve its downstream market than to try to win on the wholesale market. MO acts aggressively by setting the maximum wholesale price such that the MVO can not make a profit. MVOs can not exist in such a market unless enforced by regulation. B. Case 1-5 ow let us consider case 1-5 where MVO is still active on both segments but MO is only active in segment S 1. We will compute the total demand for both operators. Similarly to Case 1-1, the demand received by MO and the demand received by the MVO from segment 1 are given by: D MO 1 = [ p 1 p 2 α 1 I 2 I 1 p 1 α 1 I 1. MV O D1 = [ p 1 p 2 α 1 I 2 I 1 However, for the segment 2, the MO does not attract any customers, Hence D MO 2 = 0 The demand received by the MVO for segment 2:

6 MV O 1 βmax D2 = p 2 α 2 I 2 MV O 1 D2 = [ p 2 α 2 I 2 v 2 Hence, the total demand of the MO is given by: D MO = [ p 1 p 2 α 1 I 2 I 1 p 1 α 1 I 1 where D MO = C 3 p 2 C 3 = [ p1 α 1 I 2 I 1 p 1 α 1 I 1 cst And the total demand on the MVO is given by: D MV O = C 4 Where: 1 p 2 C 4 = [ α 1I 1 I 2 p 1 1 α 2I 2 cst ow, we will compute the profit for both operators under case 1.5, then define the optimal strategies for each. First, the MO profit is given by: π MO = D MO.p1 D MV O.ω = [C 3 ω µp 1 [C 4 1 ω µω π MO = V 2 C 4 µ C 3 1 µ p 1 ω 2 1 p 1 To define the best response of the MO, we derive its profit with respect to ω. We obtain the optimal response of the MO given by the wholesale price ω as function of µ: C 4 ω = 2 1 p 1 2 In another hand the MVO profit is given by: π MV O = C 4 π MV O = D MV O µ µ 1 ω µ 6 µ π MV O = C 4 1 µ 2 1 ω To define the best response of the MVO, we derive its profit with respect to µ. We obtain the optimal response of the MVO given by the margin µ as function of ω: C 4 µ = ω 7 At the equilibrium, both ω and µ are best response to each other. After substitution of µ in 6 by its value from equation 7 and after simplification we get: ω = And similarily, µ = ω βmax C 4 µ 2p 1 v 1 8 3p There is a unique ash equilibrium ω, µ in this case given by 9 and 8. Both operators may reach that equilibrium where MO concentrates its effort on population which is sensitive to its brand appeal, by proposing appropriate offers and allowing MVO to access the market. We will see that this is the unique ash equilibrium where both operators have actual customers and their profit is non null. C. Case 5-5 In this case, in both segments the demand received by the MO is null. That is MO the price set by the MO is to high, its profit will be limited to the wholesale price charged to the MVO. We have : D MO = 0 The demand received by the MVO from segment S 1 is : ω MV O D1 = βmax p 2 α 1 I 2 MV O D1 = [ p 2 α 1 I 2 The demand received by the MVO from segment 2 is : MV O 1 D2 = βmax p 2 α 2 I 2 MV O 1 D2 = [ p 2 α 2 I 2 The total demand on the MVO is given by: D MV O = D MV O MV O = D1 D MV O 2 [ p 2 I 2 α 2 α 1 α 2

7 Since the MO does not receive demand, its profit is given by: π MO = D MV O.ω = [ p 2 I 2 α 2 α 1 α 2.ω = [ I 2 α 2 α 1 α 2 ω µ ω To define the best response of the MO, we derive its profit with respect to ω. We obtain the optimal response of the MO given by the wholesale price ω as function of µ: ω = 2 [ I 2 α 2 α 1 α 2 µ 10 In the other hand, the MVO profit is given by: π MV O = π MV O = D MV O µ [ ω µ I 2α 2 α 1 α 2 µ = [ ω I 2 α 2 α 1 α 2 µ µ 2 To define the best response of the MVO, we derive its profit with respect to µ. We obtain the optimal response of the MVO given by the margin µ as function of ω: µ = 2 [ ω I 2 α 2 α 1 α 2 11 To compute the ash equilibrium ω, µ, we substitute 11 in 10 and get: ω = 3 [ I 2 α 2 α 1 α 2 Similarily, we substitute 10 in 11 and get: µ = 3 [ I 2 α 2 α 1 α 2 The only ash equilibrium in the case 5-5 is given by: ω, µ where: ω = µ = 3 [ I 2 α 2 α 1 α 2 ote that, at the equilibrium, the margin µ is equal to the wholesale ω. This means that profit of the MO is equal the profit of the MVO, since MO charge have no direct customers and make profit by selling wholesale resources. The equilibrium reflects a situation where both operators are satified by their profit as they obtain similar output. ote also that µ = ω in this case is only a special case of the equation 9 in case 1-5 as = 0 since the market share of the MO is null. Finally, we have to verify if this equilibrium can exist in our game, and what should be the retail prices p 1 and p 2 at the equilibrium. The exsitance of this equilibrium is verified if ω, µ > 0, which is the case. The retail price of the MVO at the equilibrum is given by: p 2 = ω µ = 2 3 [ I 2 α 2 α 1 α 2 12 To be in the cas 5 5, the retail price of the MO must be large enough so that even if some customers are attracted by the brandappeal of the MO they prefer to choose the MVO. This can be the case if: p 1 α2i1 > p 2 α2i2 p 1 > 2 3 [ I 2 α 2 α 1 α 2 α 2 I 1 I 2. Since I 1 V1 I 2 > 0 and α 1 > α 2, we should have 13 p 1 > 2 3 [ I 2 α 2 α 1 α 2 α 1 I 1 I 2 14 Hence, if MO wants to place itself in situation 5-5 he should announce a retail price that meets the condition 13. Its profits will be limited to the total wholesale price charged to the MVO. D. Brief discussion We have distinguish three cases : Case 1-1: Where MO acts aggressively by setting its retail price equal to the wholesale price. The MVO is unlikely to accept this situation unless it is sponsored otherwise advertisement for example. Case 5-5: where MO sets a very high retail price so that he have no actual customers. Its profit is limited to the wholesale price charged to the MVO. We can see this situation as the opposite extreme regarding case 1-1. Here the MO conserves its brand image since he does not sell off its price and still recover similar profit using the MVO. This might be an incentive to use MVO as interface in markets where he cannot set high prices without altering its image. Case 1-5: Both operators can set appropriate retail prices as shown previously so that they share the market. MO concentrates on the segment which is sensitive to its brand appeal and let the MVO access the market. This is likely the most viable scenario. III. COCLUSIO AD PESPECTIVES We have presented a competitive model operated by a mobile operator and a mobile virtual network operator, competing in a segmented market based on brand appeal. We have provided economic modeling of operator interactions and response of customers depending on their perception of the proposed offers. We have highlighted three possible market situations, two of them representing extreme situations where only one operator is really active and a situation where both

8 operators are active and we have computed the optimal prices for each situation. In further work, we explore different distributions of customer perception and their impact on the power balance between the incumbent and the virtual operators. EFEECES [1 G. Faulhaber and D. Farber, Spectrum management: Property rights, markets and the commons, elecommunications Policy esearch Conference, [2 J.Bertrand, Théorie mathématique de la richesse sociale, Journal des savants, [3 M.Bourreau, J. Hombert, J. Pouyet and. Schutz, Upstream Competition between Vertically Integrated Firms, Journal of Industrial Economics, 59-4, [4 Yu-Shan Lo, Incentive to supply the Mobile Virtual etwork Operators with Demand-Side investment, 2009 [5. Foros and B. Hansen and J. Sand, Demand-side Spillovers and Semicollusion in the Mobile Communications Market, Journal of Industry, Competition and Trade, Volum 2, , [6 K. Pousttchi, Y. Hufenbach, Analyzing and categorization of the Business Model of Virtual Operators, Eigth International Conference on Mobile BusinessICMB 2009, [7 M. Mussa and S. osen, Monopoly and Product Quality, Journal of Economic Theory, Vol. 18 o. 2, pp , 1978.