E-learning in the market for higher education: Competition and regulatory implications
Adel BEN YOUSSEF
Thomas LE TEXIER
Ludovic RAGNI
Université de Nice Sophia-Antipolis, GREDEG – UMR 6227 CNRS 250, rue Albert Einstein, F-06560 Valbonne Cedex
Université de Rennes 1, CREM – UMR 6211 CNRS 7, place Hoche, F-35065 Rennes Cedex
[email protected] ;
[email protected] ;
[email protected] Third draft – Please do not quote – July 2010
Abstract E-learning is often depicted as an attractive counterpart to the traditional learning activity inasmuch as it is perceived to be a main engine to both diffuse and acquire knowledge assets at a rapid pace and with lesser constraints than that supported by ‘brick’n mortar’ learning organizations when providing learning services. This article aims at analyzing the adoption patterns that apply on the market for educational services when two types of learning providers – namely, the traditional learning organization and the e-learning organization – compete by providing educational programs. Building on the theoretical spatial linear framework developed by Hotelling (1929), we present a duopoly model to identify optimal quality-based and pricing strategies and ensuing profits by taking into account the case in which the market for educational services is fully-served and that in which such a market is partially-served. A welfare analysis is also carried out to see to what extent ‘pro e-learning’ public subsidies are relevant from a social viewpoint. We find that public subsidies are likely to generate a strategic convergence between the two types of providers and to ‘equalize’ the competition game. However, our results reveal that the setting out of such policies may not be sufficient enough to lead to the disappearing of the learning gap and suggest thus that longer-term public policies should also be carried out.
Keywords: Competition; Price; Quality; Education; E-learning; Public subsidies. JEL Codes: I20 – I28 – L13 – L38
Corresponding author. Tel.: +33(0)223233006; Fax: +33(0)223233509. E-mail address:
[email protected] (T. Le Texier).
1. Introduction The advent of ICTs – notably the Internet – nowadays represents a main evolution in the way productive activities and service deliveries are carried out. Moreover, the so-called ‘e’ – electronic – trend has not only led to the setting up of newer market-based – commercial – schemes but it has also driven the providing of digital services which are likely to spin off from traditional ones. As a striking illustration, e-learning is often depicted as an attractive counterpart to the traditional learning activity inasmuch as it is perceived to be a main engine to both diffuse and acquire knowledge assets at a rapid pace and with lesser constraints than that supported by ‘brick’n mortar’ learning organizations when providing learning services. As such, an increasing number of people is today adopting online technology-based training and courses (Wirt et al., 2004) and e-learning systems and interfaces are becoming popular in an open framework in which physical boundaries can easily be overcome when virtual networks are designed. The popularity of e-learning is undoubtedly closely related to the way universities have intended to develop such sets of tools to foster learning access (Goldfarb, 2006). At the same time, the advent of e-learning underlines major challenges to be pointed out and thus suggests – from both academic and practical viewpoints – research tracks to be dealt. One first research line aims at analyzing to what extent ICTs have deeply modified both learning practices and teaching patterns in the provision of university-leveled educational services. Notably, e-learning has been shown to enable teachers and learning staff to develop pedagogical innovations (Becker and Watts, 2001; Rivkin et al., 2005), leading thus some first-mover universities to extend their learning supply to attract a higher number of adopters (i.e., students). However, the main share of such contributions only appears to deal with elearning services from a managerial point of view and intends to identify potential key factors to explain why some e-learning projects success while others fail (Webster and Hackley, 1997; Piccoli et al., 2001; Johnson et al., 2008; Lee and Lee, 2008; Tao, 2008; Cukusic et al., 2010). Amongst many critical factors, some authors have pointed out the importance of heterogeneity in the adopters’ ability to assimilate technological artefacts to understand the ‘productivity paradox’ one may easily observe when focusing on virtual educational services (Brown and Liedholm, 2000; Hoskins and van Hooff, 2005; Ben Youssef and Ragni, 2008). To some extent, this suggests that digital divides are still likely to apply (Wan et al., 2008)
2
and directly affect adoption patterns and students’ performance (Romer, 1993; Durden and Ellis, 1995). In the same fashion, additional analyses have revealed mixed results when estimating the impact of the size of classes on performance (Hanushek, 1986; Bradley and Taylor, 1998; Lazear, 2001; Dustmann, 2005) while the physical presence of learning staff is not systematically found to be performance-improving (Brown and Liedholm, 2002). Dealing with education economics, a second research track aims at studying the competition dynamics which are likely to apply when several learning organizations (i.e., schools, universities) are faced off. As such, a dominant trend in the literature has been to consider elearning as a substitute of the traditional learning activity rather than a complementary activity (Alberto and Dumont, 2002). For this purpose, empirical investigations have been carried out reveal somehow contrasted results when measuring the effect of competition intensity on individual – public and/or private – school performance. Indeed, Friedman (1962), Hoxby (1994; 2000), West (1997), Dee (1998) and Jaag (2006) find that educational mobility (i.e., ability/authorization for a student to select her learning provider, independently from her living location) leads learning organizations to provide higher-leveled quality for their programs whereas less optimistic results are obtained by Epple and Romano (1998), Hoyt and Lee (1998), Jepsen (2002) and McMillan (2004). Although the impact of the competition effect on learning quality remains unclear, such contributions have opened alternative paths to study the delivering of educational services. Moreover, these contributions suggest that it is possible to consider a market for learning services, depicting thus both supply (i.e., learning organizations) and demand (i.e., students) sides (Levin, 1974; Knudsen and Servelle, 1978; Vaughan and Baxter, 1988; Borland and Howsen, 1992; Blair and Staley, 1995; Allen and Shen, 1999; Belfield and Levin, 2002; Brasington, 2003; Musselin, 2008). Consequently, such an approach tends to apprehend learning organizations as potential commercial entities whose goals are profit-driven, especially when dealing with higher education – mostly private – institutions. Although a large body of the literature has focused on the managerial aspects of the e-learning way of diffusing and acquiring educational knowledge, fewer contributions have really analyzed the competition dynamics which apply on the market for educational services. Such a research direction yet appears to be of major interest since the developing of e-learning platforms is all the more likely to influence the shaping of adoption patterns. In particular, in an open context in which students are less likely to face mobility constraints through the developing of e-learning services, it is relevant to study how ‘brick’n mortar’ learning 3
providers and virtual ones interact from a competitive way. Indeed, these organizations differ in the costs they have to face when they establish their for-profit activities and one may wonder what the competitive consequences are on (i) the quality of the educational programs they provide, as well as on (ii) their pricing schemes. Such an approach may provide complementary insights to deeply analyze the effect of ICTs (i.e., e-learning platforms) on the students’ performance, thus validating or not validating previous findings (Dutton et al., 2002; Brown and Liedholm, 2002; Sosin et al., 2004). The aim of this article is thus to analyze the adoption patterns that apply on the market for educational services when two types of learning providers – namely, the traditional learning organization and the e-learning organization – compete by providing educational programs. We develop a spatial duopoly model ‘à la’ Hotelling (1929) to introduce product differentiation for learning services and to identify adoption dynamics in the market for education. Although such a framework is often used to analyze competition outcomes on a wide range of markets (e.g., software market, telecommunication market, information market, see Dixit, 1979; Singh and Vives, 1984; Tirole, 1988; Vickers, 1995; Shy, 1996; Belleflamme and Peitz, 2010), it has – to our knowledge – never been used before to deal competition outcomes on the market for educational services. Our approach is twofold. We first analyze the outcomes (i.e., optimal prices, qualities and profits) reached out by both providers by distinguishing two cases, namely the case in which the market is fully-served and shared (case 1) and the case in which the market partiallyserved and shared (case 2). Indeed, we focus on these two cases to introduce both endogeneous and exogeneous factors to better identify optimal strategies for both types of organizations to see to what extent market structures do shape strategic convergences or divergences. We secondly measure the impact of public subsidies for e-learning providers to evaluate the conditions under which the learning gap eventually pointed out in case 2 can be fully-covered. A welfare analysis is introduced to estimate the relevancy of such ‘pro elearning’ public policies. A first main result is that the quality of the educational services which are provided by the ‘brick’n mortar’ organization are likely to higher-leveled than that of the virtual organization whereas their pricing strategy is lower-leveled than that of the e-learning provider. We secondly show that public subsidies enable the e-learning organization to provide qualitybased and pricing strategies which tends to be similar to that of the ‘brick’n mortar’ organization, equalizing then the competitive game between the two types of players. 4
However, our welfare analysis underlines contrasted results about the relevancy of such shortterm public policies inasmuch as they may not always lead to the disappearing of the learning gap. From this third result, we suggest that public authorities should rather design a mixing of short-term (e.g., public subsidies) and long-term (e.g., educational campaigns) public policies to eventually lead to the disappearing of ‘learning divides’, although such policies are obviously found to generate potential coordination difficulties. The organization of the paper is as follows. We first present the settings of the model (2.). We secondly identify optimal quality-based and pricing strategies, as well as ensuing optimal profits, by considering two cases (i.e., fully-served market and partially-served market) (3.). We thirdly analyze the impact of public subsidies on both competition outcomes welfare when the market for educational services is fully-served and shared (4.). We fourthly conclude and provide directions for further research (5.).
2. The model – Settings We present a market in which two commercial – education-related – organizations act as duopolists when providing learning services. Although each organization provides learning services, their activities differ in their intrinsic nature. As such, we introduce two types of learning providers, namely traditional – brick’n mortar – campuses (type 1) and virtual campuses (type 2). From an output-related point of view, we state that traditional organizations are more likely to provide mass-oriented services whereas virtual ones rather provide customized services to better match the needs of the students. These two types of organizations also differ in the nature of the constraints students have to face when adopting one of the two services. Indeed, adoption outcomes have to be interpreted as answers to the ‘traditional-virtual’ dilemma which points out potential digital access constraints and varying interactive learning expectations. We therefore develop a model in a ‘à la’ Hotelling framework in which each learning provider sells a differentiated, the traditional campus (resp. the virtual campus) being located at 0 (resp. 1).
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On the demand side, we consider adopters who are uniformly distributed on the Hotelling line and whose total mass N is equal to 1. They adopt at most one product (i.e., learning service) that is provided by either the traditional campus or the virtual campus. We define x as the location of each product on the line ( x 0;1 ). Consumers whose x is close to 0 exhibit preferences for the traditional learning programs provided by the brick’n mortar organization whereas consumers whose x is close to 1 are more interested in adopting the e-learning programs provided by the virtual organization. Utility functions are defined as follows:
r q1 tx p1 U x r q2 t 1 x p2 0
if adopts from the traditional campus if adopts from the virtual campus
1
if does not adopt
r ( r 0 ) is the gross utility adopters derive from learning services. We here suppose that its level is the same for any potential adopter. tx (resp. t 1 x ) is the transportation disutility adopters get from adopting the learning program provided by the traditional campus (resp. the virtual campus). t is the traditional transportation cost parameter used when formalizing product differentiation. Moreover, transportation cost t captures the nature of the constraints which lead students to adopt at most one of the two educational services. Such constraints are related to both technical features (e.g., equipment) and abilities (e.g., competences) to use one of the two types of service. To put it differently, transportation cost t here refers to the exogeneous set of parameters which shapes adoption patterns. In contrast, x (resp. 1 x ) represents the distance between any adopter’s ideal product and that provided by the traditional campus (resp. the virtual campus). As such, x characterizes the likelihood of the adopters to eventually select one learning provider and should be seen as an endogeneous variable in our model. p1 ( p1 0 ) is the price the brick’n mortar provider charges to students when adopting their learning programs and p2 ( p2 0 ) represents the price students have to pay to adopt the e-learning programs provided by the virtual campus. q1 ( q1 0 ) (resp. q2 ,
q2 0 ) is the level of quality that is provided by the traditional provider (resp. the virtual provider) when releasing its learning programs. Such levels are positively appreciated by adopters when adopting one of the two learning services. We here interpret learning qualities as the efforts carried out by the organization to hire high-leveled learning staff (e.g., teachers) and to contribute to the provision of high-leveled diploma for the students to meet their career-related expectations. The qualities of learning providers appear to be relevant in a
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context in which the ranks of such organizations may be taken into account by the students when they intend to adopt learning programs. However, we suppose in our model that the content of learning programs provided by the two types of learning organizations is the same. As such, product differentiation can only be measured by the – material or virtual – way educational services are released. Both learning providers are driven by pure for-profit motives to develop learning programs. The levels of profit they are likely to reach out depend on both the price they individually charge to their students and the quality they set out for their learning programs. We define the producers’ objective functions as follows: 1 2 1 n1 p1 F1 2 q1 n p n f 1 q 2 2 2 2 2 2 2 2
2
1 (resp. 2 ) is the profit function of the traditional learning provider (resp. the virtual learning provider) when supplying its programs. We define n1 ( n1 0;1 ) as the mass of the students who adopt the programs provided by the brick’n mortar campus whereas n2 ( n2 0;1 ) represent the mass of the students who adopt e-learning services. The two organizations both have to face costs, but their cost structures are not the same. Indeed, the traditional learning provider has to support fixed costs F1 to carry out the provision of learning services inasmuch as the setting out of brick’n mortar activities requires buildings to be allocated and both teaching and administrative staffs to be paid. Nevertheless, let us note that the mass of the students who adopt traditional learning services are not likely to strongly affect the levels of costs of the learning supplier since her activity is based on a massconsumption scheme. For simplification purposes, we set the level of marginal costs to zero in the case of commercial traditional learning activities. The provider of e-learning programs has to face marginal costs when carrying out her activity inasmuch as it is based on a customization-based approach. Indeed, since each student is likely to be individually provided a specific learning program and teachers are likely to be more involved in participating to personal trainings, marginal costs f 2 have to be taking into account when providing learning services. In contrast with the brick’n mortar provider, we however suggest that fixed costs are much lower-leveled in the case of commercial e-learning activities. Again, for simplification,
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we set the level of fixed costs to zero in the latter case. As generally assumed, we eventually suppose that both producers face innovation production costs whose shapes are quadratic. Such costs lead both learning providers to design suitable pricing and quality strategies to maximize their – positive – profits. We define the adoption decision process as a four-step game: -
at step t 0 , both the traditional organization and the virtual organization decide whether to provide or not to provide learning programs;
-
at step t 1 , both organizations simultaneously set their qualities q1 and q2 ;
-
at step t 2 , both organizations sets their prices p1 and p2 ;
-
at step t 3 , the students decide to adopt or not to adopt the product released by either the brick’n mortar organization or the virtual campus.
Our model stands in a framework in which the agents (i.e., commercial providers and potential adopters) have full and common knowledge of the production outcomes, whether they concern prices and qualities. We here suppose that their expectations about the way prices and qualities are defined do apply. We consider two cases in our duopoly model. In the first case (case 1), the market is fullyserved and shared by both the traditional learning organization and the virtual learning organization. In the second case (case 2), the market is partially-served and shared by both learning providers and no-adoption patterns may apply. Put it differently, we distinguish the case in which the gross utility adopters derive from getting access to learning services (i.e., r ) is sufficiently large for the market for education to be fully-served from the case in which r is low so that the access to learning services is limited. As such, we raise the question of full accessing for educational services in a context in which learning providers are likely to compete. Our approach is motivated by the fact that access to educational programs differ from one country to another. Indeed, although some countries are likely to facilitate access to higher education-related services to a large scope of potential students (e.g., France) by providing institutional support (e.g., fellowships, studying loans…), other countries rather appear to restrict such an access (e.g., the U.K.), the latter being too expensive for a large body of potential adopters to eventually adopt learning services. Adoption patterns also appear all the
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more to depend on domestic job-market dynamics as well as the rate for students to successfully achieve their studies. As a consequence, we distinguish two cases in which adoption patterns are structurally shaped according to both the cultural and political landscapes of the countries in which learning services are provided. We analyze the competition outcomes which emerge when case 1 (resp. case 2) applies, notably quality and pricing outcomes. Moreover, our model aims at analyzing to what extent public authorities may reduce educational divides while not radically affecting competition outcomes by taking into account one may call a ‘cultural diversity for (higher) education learning services’. The impact that public policies may have on the levels of learning qualities is here next widely investigated.
3. Optimal strategies and competition outcomes
We here identify the optimal quality strategies of both learning organizations as well as their optimal pricing strategies when maximizing their specific profit functions. To do so, the fourstep game we previously presented is solved by backward-induction. We clearly distinguish the case in which intrinsic valuation for learning services is high (case 1) to that in which such a valuation is found to be low (case 2). By pointing out these two cases, we suggest that areas (e.g., countries) differ in the willingness of their populations (e.g., citizens) to adopt learning programs. Commercial outcomes (i.e., optimal quality strategies, pricing strategies and related profits) are thus analyzed depending on the competitive environment in which both learning organizations may evolve. In the first case, competition intensity is shown to be high-leveled since the market is fully-served and the organizations strategically interact to reach out their optimal states. In the second case, competition intensity is lower-leveled. As the market is partially-served, the two learning providers act as ‘local’ monopolists in their respective – traditional and virtual – markets for education and strategic competitive interactions do not occur. We consider values for transportation costs t , fixed costs F1 and marginal costs f 2 which are the same in either case 1 and case 2. Assumption 1a. Transportation costs t are large so that t 1 .
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Assumption 1a is introduced to restrict our analysis to a framework in which transportation costs are large enough to take into account the fact that lock-in effects may apply. Mobility is limited so that there exist adoption constraints which do not allow the potential adopters to easily switch from one learning provider to the other one. Assumption 1b. Marginal costs f 2 are lower-bounded so that f 2 t .
Assumption 1b is introduced to restrict our analysis to a framework in which marginal costs are low-leveled enough so that the e-learning provider may generate a positive profit from her commercial activity. We present the optimal strategies and competition outcomes reached out in case 1 (3.1.) and case 2 (3.2.).
3.1. Case 1: fully-served market We here consider the case in which the market for education is fully-served, that is to say the case in which the potential adopters have a high intrinsic valuation for learning services whether they are traditional or virtual ones (i.e., r is sufficiently large).
Figure 1. Adoption patterns – case 1
The adopter’s choice is considered at step t 3 . The adopter who is indifferent between the two learning services is located at location x , given by:
r q1 t x p1 r q2 t 1 x p2 We find that
10
1 q q p p2 x 1 2 1 2 2t 2t
3
All the adopters who are characterized by parameter x x adopt the learning program that is provided by the traditional campus and all the other adopters adopt the product that is provided by the virtual campus. At this step, n1 and n2 can be expressed as 1 q q p p2 1 q q p p2 and n2 1 x 1 2 1 . Let note that n1 x 1 2 1 2 2t 2t 2 2t 2t transportation costs t have to be sufficiently large for the market to characterize a fullyserved state (i.e., 0 x 1 ). From assumption 1a, we suppose that such a condition is satisfied. At step t 2 , we identify the optimal pricing strategies p1* p1* (q1 , q2 ) and p2* p2* (q1 , q2 )
for both learning providers. We find that * q1 q2 1 p1 (q1 , q2 ) t f 2 3 3 p* (q , q ) t 2 f q1 q2 2 2 1 2 3 3
4
Let us note from 4 that the quality gap q1 q2 has an opposite impact on the willingness of the two organizations to design price strategies. However, we cannot identify at that stage the real effect (i.e., positive or negative) such a quality gap has on each provider’s pricing scheme. One can easily verify that they depict maximum states and that such equilibria are unique and stable. At step t 1 , we identify the reaction functions for quality: * 3t 1 1 q1 (q2 ) 9t 1 f 2 9t 1 q2 9t 1 q* (q ) 3t f 1 q 1 2 1 2 1 9t 1 9t 1 9t 1
5
, and we find optimal levels for qualities, prices and adoption: 3t ** 1 1 ** q1 3 f 2 9t 2 p1 t f 2 9t 2 q** 1 f 1 p** t f 2 3t 1 2 2 2 2 3 9t 2 9t 2
** 1 3 n1 f 2 2 2(9t 2) 3 n** 1 f 2 2 2 2(9t 2)
6
11
Again, one can easily verify that they such levels depict maximum states and that such equilibria are unique and stable. Besides, from assumptions 1a, 1b and 2, the levels for p1** ,
p2** , q1** , q2** , n1** and n2** are all positive. Consequently, when designing optimal quality and price strategies, the brick’n mortar learning organization and the virtual learning organization reach out the following optimal levels for profit: 9t 1 ** 2 1 18 9t 2 ** 9t 1 2 18 9t 2 2
9 f 22 6 f 2 (9t 2) (9t 2) 2 F1
7
3 f 6 f 2 (9t 2) (9t 2) 2 2
2
Lemma 1. When potential adopters have a high intrinsic valuation for learning services, the
traditional
learning
organization
generates
a
2 1** 9t 1 18 9t 2 9 f 22 6 f 2 (9t 2) (9t 2) 2 F1
strategies
p
** 1
organization
by
; q1** t f 2 3t / 9t 2 ; 1 3 f 2 1/ 9t 2 reaches
level
out
a
level
setting and
for
profit
out
optimal
the
e-learning
for
profit
2 1** 9t 1 18 9t 2 3 f 22 6 f 2 (9t 2) (9t 2)2 by setting out optimal strategies
p
** 2
; q2** t f 2 2 3t 1 / 9t 2 ; 1 3 f 2 1/ 9t 2 .
We have to analyze if profit levels 1** and 2** are positive or negative to identify production (i.e., provision of learning services) patterns at step t 0 .
Proposition 1. Both learning providers reach out positive profits and fully serve the market
for education when potential adopters have a high intrinsic valuation for learning services. Proof of proposition 1. From assumption 1a, one can easily observe that the traditional
learning provider generates a positive profit from her activity provided that fixed costs F1 are sufficiently small. In a similar fashion, it can be shown that the e-learning provider reaches out a positive profit level for any value of f 2 ( 0 f 2 t ) (see proof in Appendix 1). ■
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Proposition 1 highlights that both providers are able to make positive profits within the analytical framework we previously defined. It stresses that the provision of differentiated learning services always leads the two learning organizations to – here fully – serve the market at step t 0 . As such, traditional learning and e-learning activities are both found to be sustainable inasmuch as their respective optimal levels of profit are always shown to be positive. A preliminary analysis can be carried out when comparing the price and quality levels of both learning providers.
Proposition 2. When the market for education is fully-served, the traditional learning
organization sets out higher (resp. lower) quality (price) levels for their learning programs than the ones which are provided by the e-learning organization. Proof of proposition 2. From assumptions 1a and 1b, it is straightforward to show that
3t 2 2 p1** p2** f 2 0 and q1** q2** f 2 0. ■ 9t 2 9t 2 Proposition 2 highlights that transportation costs t play a critical role in adoption patterns to explain a market-shared situation inasmuch as the traditional learning organization appears to have advantages (i.e., lower-leveled price strategy and higher-leveled quality strategy) over the e-learning one. Intrinsic preferences for either virtual or brick’n mortar services here strongly affect adoption issues. Hence, proposition 2 stresses that the e-learning provider is likely to provide a lesser quality and a higher price than the ‘brick’n mortar’ provider in a market in which access to higher education programs is originally set to be wide. Within such areas, the traditional learning services are more likely to be attractive than the virtual ones.
3.2. Case 2: partially-served market We now consider the case in which the market for education is partially-served. Indeed, we now suggest that potential adopters may have a low intrinsic valuation for learning – traditional or virtual – services and/or constraints to access educational services are high so
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that no-adoption patterns are introduced. We hence here focus on the specific case in which r is low so that some potential adopters eventually decide not to adopt learning programs. 1
Figure 2. Adoption patterns – case 2
The adopter’s choice is considered at step t 3 . The adopter who is indifferent between the traditional learning service (resp. e-learning service) and no-adoption is located at location x1 (resp. x2 ), given by: r q1 t x1 p1 0 r q2 t (1 x2 ) p2 0 We find that r q1 p1 x1 t x2 1 r q2 p2 t
8
All the adopters who are characterized by parameter x x1 adopt the learning program that is provided by the brick’n mortar campus whereas all the adopters whose value for parameter x is so that x x2 adopt the e-learning program. Adopters who are characterized by parameter x x1 ; x2 decide not to adopt a learning program. At step t 3 , n1 and n2 can be expressed
r q2 p2 r q1 p1 . Let note that both transportation costs t as n1 x1 and n2 1 x2 t t and r have to be sufficiently large for the market to characterize a partially-served market for
1
However, we here restrict our analysis to ‘reasonable’ values of r . Indeed, if r is shown to be ‘too’ low, global no-adoption patterns are likely to apply on the market for education. We do not analyze such a case in this article.
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education. As such, an additional assumption is introduced to cope with our framework when dealing with case 2.
Assumption 2. The intrinsic valuation for learning – traditional or virtual – services r is
defined so that 0 f 2 r
1 2t 1 f 2 . 2
Assumption 2 presents the conditions for values of r we have to consider for the market for education to be partially-served. Values for r are therefore lower-leveled in case 2 than in case 1. Let us stress that assumption 2 can be extended and expressed so that 0 f 2 r 1 2 2t 1 f 2 2t 1 2t 1 f 2 .
At step t 2 , the optimal pricing strategies p1* p1* (q1 ) and p2* p2* (q2 ) of both learning providers are identified. Let us remind that the two learning providers here act as ‘local’ monopolists. Optimal pricing strategies do not take interaction features into account and the traditional learning provider (resp. the e-learning provider) does not consider the level of price set out by the e-learning (resp. the traditional learning provider) when designing her optimal pricing strategy. By expressing first-order conditions, one can easily find that 1 * p q ( ) r q1 1 1 2 p* ( q ) 1 r q f 2 2 2 2 2
9
From 9 , we unsurprisingly observe that optimal price levels positively depend on the level of quality decided by both organizations when providing learning programs. We also note that the marginal costs f 2 positively affect the level of price p2 that the e-learning provider charges to her students. Second-order conditions show that 9 characterizes Nash equilibria at step t 2 . From assumptions 1a, they depict maximum states and are can easily be found to be unique and stable. At step t 1 , due to the market structure we consider in case 2, we obviously see that the optimal price strategy of the traditional learning provider (resp. e-learning provider) does not depend of that of the e-learning provider (resp. traditional learning provider). We identify optimal levels for quality, prices and adoption patterns:
15
r ** q 1 2t 1 q** r f 2 2 2t 1
tr ** p 1 2t 1 tr p** f 2 (t 1) 2 2t 1
r ** n 1 2t 1 n** r f 2 2 2t 1
10
We see that marginal costs f 2 only affect the optimal level for quality, price and adoption of the e-learning provider (their impact is widely analyzed in section 4.). This results from the partially-served nature of the market for education we have here introduced. As already been pointed out in case 1, from assumptions 1a, 1b and 2, one can easily see that levels for p1** , p2** , q1** , q2** , n1** and n2** are all positive. Consequently, when designing optimal quality and price strategies, the brick’n mortar learning organization and the e-learning organization reach out the following optimal levels for profit: ** r 2 1 t F1 1 2t 1 2 2 ** r f 2 1 2 2t 1 t 2
11
Lemma 2. When potential adopters have a low intrinsic valuation for learning services so
that the market for education is partially-served, the traditional learning organization generates a level for profit 1** r 2t 1 t 1 2 F1 by setting out optimal strategies 2
p
** 1
; q1** tr 2t 1 ; r 2t 1 and the e-learning organization reaches out a level for
profit
p
** 2
1** r f 2 2t 1 t 1 2 2
by
setting
out
optimal
strategies
; q2** tr f 2 t 1 2t 1 ; r f 2 / 2t 1 .
Again, we have to analyze if profit levels 1** and 2** are positive or negative to identify production (i.e., provision of learning services) patterns at step t 0 .
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Proposition 3. Both learning providers reach out positive profits and partially serve the
market for education when potential adopters have a ‘low’ intrinsic valuation for learning services. Proof of proposition 3. As already stressed in case 1, one can easily observe from
assumption 1a that the traditional learning provider generates a positive profit from her activity provided that fixed costs F1 are sufficiently small. In parallel, it is straightforward to show that the profit of the e-learning provider is positive at the optimal state for any value of f 2 ( 0 f 2 t ). ■ Proposition 3 highlights that both providers are able to make positive profits within the analytical framework we defined for case 2. The provision of learning services always leads the two learning organizations to – here partially – serve the market at step t 0 . As a consequence, traditional learning and e-learning activities are both found to be sustainable inasmuch as their respective optimal levels of profit are always shown to be positive.
Proposition 4. When the market for education is partially-served, the traditional learning
organization sets out higher (resp. lower) quality (price) levels for their learning programs than the ones which are provided by the e-learning organization. Proof of proposition 4. From assumptions 1a and 1b, one can easily find that
1 t 1 0 and q1** q2** f 2 p1** p2** f 2 0. ■ 2t 2 2t 1 Proposition 4 somehow highlights the same findings reached out in case 1. Transportation costs t are found to be critical to explain adoption patterns since the traditional learning organization appears to have advantages (i.e., lower-leveled price strategy and higher-leveled quality strategy) over the e-learning one. Intrinsic preferences for either virtual or brick’n mortar services are once again shown to strongly affect adoption issues. Again, the traditional learning provider appears more likely to attract a higher scope of potential adopters. Nevertheless, let us remind that no-adoption patterns apply due to the structure of the market for education.
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Competition outcomes have been analyzed by either introducing a duopoly framework (case 1) or a ‘local’ monopoly one (case 2). In the latter case, we have suggested that ‘learning divides’ are likely to occur when levels of valuation for learning programs (i.e., r ) are low. We next analyze the effects of policies that public authorities may undertake to reduce such a ‘learning gap’.
18
4. ‘Learning divides’ and public policies
In contrast to case 1, we have introduced case 2 as a case in which some potential adopters do not eventually adopt learning programs. As such, it exhibits sources of ‘learning divides’ which are likely to apply due to too ‘low’ levels of valuation for educational programs. Let us note r (resp. r ) the valuation for educational programs that all the potential adopters exhibit in case 1 (resp. case 2), r r 0 . No-adoption patterns are represented by the optimal mass of non-adopters, which is
n** 1 (n1** n2** )
1 2(t r ) f 2 1 2t 1
12
We obviously find that n** is positive for any value of t , f 2 and r under assumptions 1a, 1b and 2. Moreover, n** n** f 2 , r is unsurprisingly found to be an increasing function for f 2 and a decreasing function for r . Consequently, one may see appropriate to set up public policies which tend to make levels for marginal costs f 2 lower and levels for valuation for educational programs r higher. Although such policies are both shown to reduce the gap for learning access, they differ in the amount of time which is needed for positive outcomes to be reached out. Indeed, the setting up of information campaigns which are led to develop the intrinsic valuation for educational programs are somehow likely to be efficient in the long run whereas the provision of public – marginal – subsidies to the e–learning provider is generally found to be effective within a shorter time horizon. As educational campaigns are therefore shown to be uncertain, we restrict our public analysis to the example of public – here marginal – subsidies to the e-learning provider (e.g., public support to purchase IT terminals or computers). The total amount allocated by the public authorities thus depends on the number of adopters of e-learning services. Marginal public susbsidy is noted s ( s 0 ) and is defined so that f2 s 0 s
13
s refers to the amount which is allocated by public players to the virtual campus to develop
the providing of e-learning programs and to reduce the so-called ‘learning divides’. The impact of such a type of public policies can be measured by analyzing the effect that marginal
19
costs f 2 have on optimal price and quality levels, as well as on the resulting competition outcomes (i.e., profits and market shares). The level of marginal subsidy s is of course assumed to be lower to that of marginal cost f 2 (i.e., s f 2 ). We first analyze the effect of public subsidies on the optimal strategies we previously pointed out and on the optimal levels for profits (4.1.). A welfare study is then carried out to see to what extent public subsidies may be socially-improving by either considering fully-served or partially-served market structures (4.2).
4.1. Public subsidies and competition outcomes ** ** ** ** ** ** ** ** Let us note p1,1 , q1,1 , n1,1 and 2,1 the optimal levels we previous identified , p2,1 , q2,1 , n2,1 , 1,1 ** ** ** , p2,2 , q1,2 , when analyzing competition outcomes in case 1. In a similar fashion, we note p1,2 ** ** ** ** ** q2,2 , n1,2 , n2,2 , 1,2 and 2,2 the optimal levels we identified when analyzing competition
outcomes in case 2. ** ** ** We define Q1** q1,1 (resp. Q2** q1,2 q2,1 q2**,2 ) as the global quality effort which is jointly
provided by the two learning organizations when the market for education is fully-served (resp. partially-served). As we have supposed that educational programs are homogeneous products, one can interpret Q1** (resp. Q2** ) as a – yet preliminary – measure of the social outcomes that result from competition, whether public subsidies are considered or not considered. We show that ** 2 Q1 3 Q** 2r f 2 2 2t 1
14
The effect of public subsidies on the optimal pricing strategies of both learning providers are expressed as follows:
20
** p1,1 3t 0 f 2 9t 2 ** p2,1 2 3t 1 0 f 9t 2 2
15a
** p1,2 0 f 2 ** p2,2 t 1 0 f 2t 1 2
15b
Lemma 3. Public subsidies have a negative impact on the pricing strategy of both learning
providers when the market for education is fully-served. When potential adopters have a low intrinsic valuation for learning services, public subsidies have a negative on the pricing strategy of the e-learning provider whereas it has no effect on that of the brick’n mortar learning provider. Hence, lemma 3 stresses that the providing of public subsidies decreases the levels of the prices that are set out of both providers, except that of the brick’n mortar campus when the market for education is partially-served. The effect of public subsidies on the optimal quality strategies of both learning providers are defined by ** q1,1 1 0 f 2 9t 2 ** q2,1 1 0 f 9t 2 2
16a
** q1,2 0 f 2 ** q2,2 1 0 f 2t 1 2
16b
Lemma 4. Public subsidies lead the e-learning provider to increase the level of quality of her
learning programs, whether the market for education is fully-served or partially-served. In parallel, they lead the traditional provider to provide lower levels for quality in case 1, whereas they have no effect on her willingness to provide quality in case 2. 21
From lemma 4 we find that an opposite quality-based effect may apply when public supports are provided. Indeed, public subsidies are here found to enable the e-learning organization to provide higher quality levels for its programs whereas it may reduce the willingness of the traditional organization to provide high-leveled services. The effect of public subsidies on the optimal adoption levels of both learning providers are ** n1,1 3 0 f 2 2(9t 2) ** 3 n2,1 0 f 2(9t 2) 2
17a
** n1,2 0 f 2 ** n2,2 1 0 f 2t 1 2
17b
Lemma 5. Public subsidies enable the e-learning provider to attract more adopters, whether
the market for education is fully-served or partially-served. They negatively influence the number of adopters of the traditional organization in case 1 whereas they have no effect on such a level in case 2. Lemma 5 evidences somehow similar results than those highlighted in lemma 4. The nature of the effect public subsidies have on the quality levels that are provided by both learning organizations is likely to shape adoption patterns. The effect of public subsidies on the optimal profits of both learning providers are expressed as follows: ** 1,1 9t 1 3 f 2 9t 2 0 3(9t 2) 2 f 2 ** 2,1 9t 1 f 2 9t 2 0 f 3(9t 2) 2 2
18a
22
** 1,2 0 f 2 ** 2,2 1 r f 0 2 2t 1 f 2
18b
Lemma 6. Public subsidies enable the e-learning provider to increase her profits, whether
the market for education is fully-served or partially-served. They negatively influence that of the traditional organization in case 1 whereas they have no effect on such profits in case 2. Lemma 6 unsurprisingly stresses that public supports always benefit to virtual campuses whereas it may be detrimental to brick’n mortar campuses. The effect of public subsidies on the global quality effort which is jointly provided by the two learning organizations is given by Q1** 0 f2 ** Q2 1 0 f 2 2t 1
19
Lemma 7. Public subsidies improve the level of global quality effort when the market is
partially-served. They have no influence on such a level when the market is fully-served. Lemma 7 provides first social insights about the providing of public subsidies. Indeed, we find that these lead to the provision of higher-leveled global quality effort for the two organizations to individually maximize their own profits when they act as ‘local’ monopolists. Lemma 7 somehow stresses that the providing of marginal subsidies does negatively impact on the joint level of quality delivered by both types of learning organizations. As such, public support to one of the two organizations (i.e., the e-learning provider) is likely to lead providers to offer higher-leveled services within a specific cultural framework, that is to say when access constraints to learning services apply. However, public subsidies are evidenced to have a neutral effect on the level of global quality effort when the two providers act as duopolists inasmuch as the increase of the level of quality provided by the e-learning provider is balanced by the decrease of that of the traditional learning provider.
23
Depending on the – partially-served or fully-served – market structure for educational services, lemmas 3 to 7 underline that the providing of public subsidies does not influence optimal outcomes and strategies the same way. Moreover, we see that public support may skew competition mechanisms while not improving outcomes (e.g., global quality effort). Public-resulting outcomes are thus shown to differ, depending on the level of intrinsic valuation for educational programs. A welfare analysis is next carried out to measure to what extent public subsidies may be socially-improving. This analysis notably integrates the social cost of public subsiding to better appreciate the effect of public support on overall social outcomes.
4.2. Public subsidies and welfare We discuss welfare outcomes to identify the effect of public subsidies on welfare when taking either case 1 or case 2 into account. Aggregate adopters surplus is equal to
AS ** AS1** AS 2** . The surpluses of both learning organizations are equal to the sum of the profit of the brick’n mortar provider 1** and that of the e-learning provider 2** . Welfare is defined by the sum of adopters and providers’ surpluses, as well as of the level of total public subsidy (i.e., public deficit) S S n2** s n2** . Indeed, we here consider that public authorities take rational decisions when designing public policies inasmuch as subsidies are allocated if and only if two conditions are met. These conditions state that (i) the impact of public subsidies on both the producers’ and consumers’ surpluses is shown to be positive, and (ii) public deficit S is overcome by the increase of the level of total surplus which results from the setting up of such a public policy. When public subsidies are provided to the e-learning organization, its marginal cost decreases to a level that is equal to f 2 s . We distinguish the impact of public subsidies on welfare in two cases, namely case 1 and case 2. In a framework in which the market for education is fully-served, we define the optimal level of welfare W1** as ** ** ** ** W1** AS1,1 AS2,1 1,1 2,1 S1**
24
** x
1
r q
** ** r q1,1 tx p1,1 dx
x 0
** 2,1
** ** ** t 1 x p2,1 dx 1,1 2,1 s 1 x
**
x x
**
,
After some calculations, we find that
8 9t f 2 s f 2 s W F1 r 45t 4 2 36 2(9t 2) 2
** 1,1
20
1 3 s f 2 s 2 2 9t 2
In a framework in which the market for education is partially-served, we define the optimal level of welfare W2** as ** ** ** ** W2** AS1,2 AS 2,2 1,2 2,2 S 2**
** x1
r q
** 1,2
** tx p1,2 dx
x 0
1
r q
** 2,2
** x x2
** t 1 x p2,2 dx
** ** ** 1,2 2,2 s 1 x2 ,
Again, after some calculations, we find that
r f2 s 2 1 1 2 W F1 3t 1 r r f 2 s s 2 2t 1 2t 1 2
** 2
21
One can find that levels for welfare W1** and W2** are positive, provided that fixed costs F1 are sufficiently small (see proof in appendix 2).
The impact of public subsidies on the level of welfare reached out in cases 1 and 2 are expressed as follows:
25
W1** 1 1 2 18t 2 f 2 9t 8 s 2 9t 2 s 2 ** 1 W2 r f 2 t s 1 t 2t 1 s
22
Proposition 5. Public subsidies are always detrimental to welfare when the market for
education is fully-served. When the market for education is partially-served, public subsidies are beneficial to welfare for ‘low’ values for marginal public subsidy s , and detrimental otherwise. Proof of proposition 5. From assumption 1a, one may easily find that W1** s 0 for any
value for f 2 and s . As such, we show that the introduction of public policies leads to decrease levels for welfare when the market for education is fully-served. When the market for education is partially-served, our analysis leads to mixed results. Indeed, we find that
W2** s 0 for values for s that are set out by public authorities so that s t t 1 r f 2 and that W2** s 0 for values for s that are defined so that s t t 1 r f 2 . ■
From proposition 5, we see that the effects of public subsidies on welfare are likely to differ, depending on the market structure for education (i.e., duopoly or ‘local’ monopolies) which is considered. Moreover, we find that public subsidies deteriorate the level of welfare when the market for education is fully-served (case 1), whereas they may improve such a level when they are ‘low’ (i.e., s t t 1 r f 2 ) and the market is partially-served. As a consequence, public authorities should wisely analyze market structures before setting out public subsidies. In a framework in which the market for education is partially-served, we find that public subsidies may be relevant to reach out welfare-improving states provided that the level of marginal subsidy does not exceed a maximal value. The providing of public subsidies thus appears to be inappropriate for areas in which access to (higher) educational services is wide so that no-adoption patterns do not apply. Rather, upper-bounded public support is likely to be welfare-improving for areas in which access to learning programs is limited.
26
The optimal decision-making (i.e., optimal value for s ) of public authorities can be seen as the result of a welfare-maximizing program of which s* t t 1 r f 2 is the result. 2 Let us note that such an optimal level for s is higher (resp. lower) than marginal cost f 2 if f 2 t 2t 1 r (resp. f 2 t 2t 1 r ). Thus, in a – realistic – framework in which public
authorities define levels for public subsidies so that 0 s f 2 , s* is set out at a level which is equal to t t 1 r f 2 if values for f 2 and r are so that f 2 t 2t 1 r , and s* f 2 if values for f 2 and r are so that f 2 t 2t 1 r . The setting out of public subsidies whose marginal amount is whether s* t t 1 r f 2 or
s* f 2 aims at dealing with the ‘learning divides’ one may observe when individuals have too ‘low’ levels of valuation for educational programs. In particular, it is needed to see if the setting out of such a public policy eventually leads to the disappearing of ‘learning divides’ or if they only attenuate them.
Proposition 6. Although public subsidies eventually foster the adoption of educational
services, they may not lead to the disappearing of the ‘learning gap’. Proof of proposition 6. See Appendix 3. ■
Proposition 6 suggests that short-term oriented public policies (i.e., public subsidies) may not be sufficient enough for ‘learning divides’ to disappear. Indeed, one can see that a – yet narrower – ‘learning gap’ may apply, depending on the values of both r and f 2 . As a consequence, when short-run public policies are found not to efficient enough to deter nonadoption patterns, it seems that longer-run ones should be set out to eventually deal with the ‘learning gap’. For example, complementary to the provision of public subsidies, the setting up of information campaigns aiming at developing the level of intrinsic valuation for educational programs (i.e., r ) would lead to the disappearing of ‘learning divides’. However, as we previously underlined, the mixing of both short-run and long-run policies is likely to generate coordination failures in a context in which public decision-making is not found to be carried out in a stable environment. As such, ‘learning divides’ public concerns may have to
2
As W2 2
**
s 1 2t 1 1 t 0 , the value s for s which is defined so that W2 2
2
*
**
s 0 depicts a
maximum state.
27
be dealt within a wider time-horizon scope and both short-term and long-term objectives have be conciliated for efficient – here learning access-related – outcomes to be reached out. To some extent, proposition 6 highlights that the providing of public subsidies does not always lead to a ‘cultural’ convergence according to which access constraints to learning services are likely to be overcome. Thus, short-termed public support to e-learning organizations cannot be seen as a great ‘equalizer’ which would lead to the developing of universal access to educational services.
5. Conclusion
The aim of this article has been to analyze the adoption patterns which are likely to apply in the market for education by considering two types of cultural landscapes (i.e., fully-served and partially-served markets). Notably, the main concern of our work has been to study to what extent the setting out of public subsiding may – positively or negatively – affect the bridging of ‘learning divides’ while stimulating the providing of high levels of quality for educational programs. Following the increasing popularity of e-learning services for both business and public purposes, we have considered a theoretical framework in which traditional learning providers and virtual ones simultaneously evolve. Indeed, we have studied competition patterns between these two types of – here commercial – organizations to measure the relevancy of ‘pro’ e-learning support policies from a social point of view. One of our major research directions has been to identify how public policies should be designed to eventually facilitating access to learning services while not levelling down overall educational quality. In particular, we have built a duopoly model in which two learning organizations (namely, the brick’n mortar learning provider and the e-learning provider) compete while having to deal with differing cost structures. Two cases have thus been taken into account inasmuch as we have suggested that the value of intrinsic valuation for educational services (i.e., r ) may be high (resp. low) so that the market for education is fully-served (resp. partially-served). Optimal pricing and quality strategies, as well as ensuing optimal profits have been identified. 28
The impact of public subsidies has been analyzed, notably to measure to what extent they are likely to reduce the ‘learning divides’ one may observe in areas in which intrinsic valuation for educational services is low. To do so, a welfare analysis has been carried out and has evidenced that the providing of public subsidies that level is too high is detrimental from a social point of view. It has also revealed that – under some specific circumstances – public subsidies may not be efficient enough to fully-cover the ‘learning gap’. This last result can lead to several interpretations. A somehow pessimistic interpretation is that it may not be possible to provide universal access to educational services through the designing of short-termed public policies. Although the setting out of public policies is found to ‘equalize’ the competitive game between the two types of learning organizations from both a pricing and quality-based point of view, detrimental effects to welfare levels may appear. We suggest that the mixing of short-term (e.g., public subsidies) and long-term (e.g., educational campaigns) public policies may be appropriate to lead to the disappearing of ‘learning divides’. Yet, such a practice is likely to generate coordination failures and seems to provide efficient results only when the political context is found to be stable. Nevertheless, we would like to address another – rather optimistic – interpretation. Indeed, our findings pinpoint that it may be possible for public authorities to widen access to educational services while preserving their ‘cultural’ learning-provision model. Put it differently, they may allow a larger scope of people to get access to educational services while avoiding the emerging of a mass-consumption model for such (higher) services. Our study has been introduced in a somehow atypical market-based framework to identify adoption patterns for educational services as well as suitable public policies to break the socalled ‘learning divides. From a general way, our results have revealed that the introduction of the e-learning activity in the market for education and the providing of public support to virtual organizations does not negatively affect the level of quality which is provided by both types of organizations. Besides, asymmetric public subsidies for virtual organizations are welfare-improving when the market for education is partially-served, provided that their level is sufficiently low. However, they are found to be detrimental when the market is fully-served. The findings of the model thus address practical implications. Indeed, although the appearing of virtual providers is likely to lead to the increasing of the overall quality within the market, public subsiding policies have to clearly be designed to avoid any welfare-related detrimental effect. 29
Some extensions may be considered for further research. First, we may extent our model to another one in which both organizations are able to share their assets. Indeed, by ‘assets’, we here refer to the educational staff (e.g., teachers) that may be contractually affiliated to both types organizations. To some extent, we could introduce blended learning as an alternative way for potential students to acquire knowledge when participating to various learning environments. Such hybrid adoption patterns are all the more relevant to analyze since they enable students to rapidly assimilate new types of competences which are valuable for jobseeking purposes. Nevertheless, they are also likely to make ‘learning gaps’ deeper between those who have a high ability to pay for educational services and those who have a much lower one. Second, we could also extend our analysis to the case in which at least one of the learning organizations goes public. We would therefore be able to analyze adoption patterns in a framework in which the pricing strategy of at least one of the provider is set to be null. Consequently, we would more precisely introduce cultural differences between countries that intend to develop a mass-consumption way of providing (higher) educational programs and those that prefer restricting such an access. Finally, one may find relevant to switch from a duopoly to an oligopoly framework since the number of learning organizations located in a given area is likely to be higher than that considered in our theoretical model. The analysis of adoption patterns for educational services raises major concerns from both market-based and public viewpoints. Although e-learning activities have been widely analyzed according to an empirical approach to see how these may attenuate ‘learning divides’, we believe that industrial organization modelling may also provide relevant insights to better understand adoption dynamics and to identify efficient public policies. As such, learning providers could be apprehended as commercial players whose activities are driven by for-profit behaviors. We strongly believe that both empirical and model-based further contributions will lead to the better understanding of adoption dynamics within the market for education and to the shaping of suitable public policies.
Appendix 1. Proof of Proposition 1
30
The optimal level of profit of the e-learning provider can be rewritten as
2**
9t 1 18 9t 2
2**
2
3 f 22 9t 2 9t 2 6 f 2
9t 1 18 9t 2
2
3 f 22 9t 2 6t 6 f 2 3t 2
From assumptions 1a and 1b, it is straightforward to find that 2** 0 for any value of f 2 ( 0 f 2 t ). ■
Appendix 2. Positive welfare levels
The level of welfare that applies in case 1 can be rewritten as follows: W1** F1
f s 1 36r 8 9t 18 f 2 2 45t 4 f 2 s 3s 36 2(9t 2)
f s From assumptions 1a and 1b, 2 45t 4 f 2 s 3s 0 . Besides, we find that 2(9t 2) 36r 8 9t 18 f 2 0 if and only if values for r are defined so that r
1 1 4 f 2 t . As 2 4 9
values for r are supposed to be sufficiently large for the market for education to be fullyserved,
1 36r 8 9t 18 f 2 0 . Thus, W1** 0 when fixed costs F1 are sufficiently small. 36
In a similar fashion, the level of welfare that applies when the market for education is partially-served is given by 2
1 1 2t 1 2r r f 2 ( f 2 s )( f 2 s ) t (r 2 (r f 2 s ) 2 ) W F1 2 2t 1 ** 2
From assumptions 1a and 2, it is straightforward to find that W2** 0 for sufficiently small values of F1 . ■
31
Appendix 3. Proof of Proposition 2
As we previously pointed out, two cases have to be taken into account: (i)
s
*
f 2 ; f 2 tr 2t 1 and (ii) s* t t 1 r f 2 ; f 2 tr 2t 1 .
Let us first focus on the s* f 2 ; f 2 tr 2t 1 case. We show that n** 0 if the following conditions are simultaneously met: r 1 2 2t 1 f 2 tr 2t 1 0 f 2 r 1 2 (2t 1 f 2 ) 2t 1 2t 1 f 2
Such conditions can be summarized as follows: 0 f 2 2t 1 f 2 t r 1 2 2t 1 1 2 (2t 1 f 2 ) 2t 1 2t 1 f 2
In a similar fashion, we show that n** 0 if the following conditions are simultaneously met: r 1 2 2t 1 f 2 tr 2t 1 0 f 2 r 1 2 (2t 1 f 2 ) 2t 1 2t 1 f 2
Such conditions can be summarized as follows: 0 max 1 2 2t 1 ; f 2 r 1 2 (2t 1 f 2 ) 2t 1 2t 1 f 2
We thus identify possible conditions under which public subsidies are found to fully bridge the ‘learning gap’ and other conditions under which such policies are not found to be efficient enough to fully cover this gap. Similar results are found when the s* t t 1 r f 2 ; f 2 tr 2t 1 case is dealt. ■
References
Alberto, B. & Dumont, B. (2002). Les technologies de l’information et de la communication dans l’enseignement supérieur : Pratiques et besoins des enseignants. Rapport ITEM SUP pour le ministère de la Recherche, Direction de la Technologie, Sous-direction des technologies éducatives et des technologies de l’information et de la communication (SDTETIC), Bureau de l’Enseignement supérieur (B3), Paris, France. Allen, R.F., & Shen, J. (1999). Some new evidence of the character of competition among higher education institutions. Economics of Education Review, 18(4), 465–470.
32
Becker, W.E. & Watts, M. (2001). Teaching methods in U.S. undergraduate economics courses. Journal of Economic Education, 32(3), 269–279. Belfield, C., & Levin, H.M. (2002). The effects of competition on educational outcomes. Review of Educational Research, 72(2), 279–341. Belleflamme, P. & Peitz, M. (2010). Industrial Organization: Markets and Strategies. Cambridge University Press, Cambridge, UK. Ben Youssef, A. & Ragni, L. (2008). Uses of educational information and communication technologies: From digital divides to digital trajectories. University and Knowledge Society Journal (RUSC), 5(1), 70–82. Blair, J.P. & Staley, S. (1995). Quality competition and public schools: Further evidence. Economics of Education Review, 14(2), 193–198. Borland, M.W. & Howsen, R.M. (1992). Student achievement and the degree of market concentration in education. Economics of Education Review, 11(1), 31–39. Bradley, S. & Taylor, J. (1998). The effect of school size on exam performance in secondary schools. Oxford Bulletin of Economics and Statistics, 60(3), 291–325. Brasington, D.M. (2003). The supply of public school quality. Economics of Education Review, 22(4), 367–377. Brown, W.B. & Liedholm, C.E. (2000). Teaching microeconomic principles – Can web courses replace the classroom in principles of microeconomics? American Economic Review, 92(2), 444–448. Cukusic, M., Alfirevic, N., Granic, A. & Garaca, Z. (2010). e-Learning process management and the e-learning performance: Results of a European empirical study. Computers & Education, 55(2), 554–565. Dee, T.S. (1998). Competition and the quality of public schools. Economics of Education Review, 17(4), 419– 427. Dixit, A. (1979). A model of duopoly suggesting a theory of entry barriers. Bell Journal of Economics, 10(2), 20–32. Durden, G.C. & Ellis, L.V. (1995). The effects of attendance on student learning in principles of economics. American Economic Review, 85(2), 343–346. Dustmann, C. (2005). The class size debate and educational mechanisms: Editorial. Economic Journal, 113(485), F1–F2. Dutton, J.D., Dutton, M. & Perry, J. (2002). How do online students differ from lecture students? Journal of Asynchronous Learning Networks, 6(1). http://www.sloan-c.org/publications/jaln/v6n1/v6n1_dutton.asp Epple, D. & Romano, R.E. (1998). Competition between private and public schools, vouchers, and peer group effects. American Economic Review, 88(1), 33–62. Friedman, M. (1962). Capitalism and Freedom. University of Chicago Press, Chicago, IL. Goldfarb, A. (2006). The teaching role of universities in the diffusion of Internet. International Journal of Industrial Organization, 24(2), 203–225. Hanushek, E.A. (1986). The economics of schooling: Production and efficiency in public schools. Journal of Economic Literature, 24(3), 1141–1177. Hoskins, S.L. & van Hooff, J.C. (2005). Motivation and ability: Which students use online learning and what influence does it have on their achievement? British Journal of Education Technology, 36(2), 177–192. Hotelling, H. (1929). Stability in competition. The Economic Journal, 39(153), 41–57. Hoxby, C.M. (1994). Do private schools provide competition from public schools? NBER working paper no. 4978, Cambridge, MA.
33
Hoxby, C.M. (2000). Does competition among public schools benefit students and taxpayers? American Economic Review, 90(5), 1209–1238. Hoyt, W.H. & Lee, K. (1998). Educational vouchers, welfare effects, and voting. Journal of Public Economics, 69(2), 211–228. Jaag, C., (2006). School competition. MPRA working paper no. 339, Munich, Germany. Jepsen, C. (2002). The role of aggregation in estimating the effects of private school competition on student achievement. Journal of Urban Economics, 52(3), 477–500. Johnson, R.D., Hornik, S. & Salas, E. (2008). An empirical examination of factors contributing to the creation of successful e-learning environments. International Journal of Human-Computer Studies, 66(5), 356–369. Knudsen, O.K., & Servelle, P. (1978). The demand for higher education at private institutions of moderate selectivity. American Economist, 22(2), 30–34. Lazear, E.P., 2001. Educational production. Quarterly Journal of Economics, 116(3), 777–803. Lee, J.K. & Lee, W.K. (2008). The relationship of e-Learner’s self-regulatory efficacy and perception of eLearning environmental quality. Computers in Human Behavior, 24(1), 32–47. Levin, H.M. (1974). Measuring efficiency in educational production. Public Finance Quarterly, 2(1), 3–25. McMillan, R. (2004). Competition, incentives, and public school productivity. Journal of Public Economics, 88(9-10), 1871–1892. Musselin, C. (2008). Les Universitaires. La Découverte, Paris, France. Piccoli, G., Ahmad, R. & Ives, B. (2001). Web-based virtual learning environments: A research framework and a preliminary assessment of effectiveness in basic IT skills training. MIS Quarterly, 25(4), 401–426. Rivkin, S.G., Hanushek, E.A. & Kain, J.F. (2005). Teachers, schools and academic achievement. Econometrica, 73(2), 417–458. Romer, P. (1993). Idea gaps and object gaps in economic development. Journal of Monetary Economics, 32(3), 543–573. Shy, O. (1996). Industrial Organization: Theory and Applications. MIT Press, Cambridge, MA. Singh, V. & Vives, X. (1984). Price and quantity competition in a differentiated duopoly. Rand Journal of Economics, 15(4), 546–555. Sosin, K., Blecha, B.J., Agawal, R., Bartlett, R.L. & Daniel, J.I. (2004). Efficiency in the use of technology in economic education: Some preliminary results. American Economic Review, 94(2), 253–258. Tao, Y.H. (2008). Typology of college student perception on institutional e-learning issues – An extension study of a teacher’s typology in Taiwan. Computers & Education, 50(4), 1495–1508. Tirole, J. (1988). The Theory of Industrial Organization. MIT Press, Cambridge, MA. Vaughan, M., & Baxter, S. (1988). Tuition, unemployment and the demand for education: a case study for classroom use. Journal of Economics, 19, 135–140. Vickers, J. (1995). Concepts of competition. Oxford Economic Papers, 47(1), 1–23. Wan, Z., Wang, Y. & Haggerty, N. (2008). Why people benefit from e-learning differently: The effects of psychological processes on e-learning outcomes. Information & Management, 45(8), 513–521. Webster, J. & Hackley, P. (1997). Teaching effectiveness in technology-mediated distance learning. Academy of Management Journal, 40, 1282–1309. West, E.G. (1997). Education vouchers in principle and practice: A survey. World Bank Research Observer, 12(1), 83–103.
34
Wirt, J., Choy, S., Provasnik P., Sen, A. & Tobin, R. (2004). The Condition of Education 2004. NCES 2004-077, U.S. Department of Education: Institute of Education Sciences, Washington, DC
35
