Price competition with network effects in the Dutch health insurance market

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Price Competition with Network Effects in

the Dutch Health Insurance Market

Msc Thesis

Author: Fieke Snijders

Department: Faculty of Economics and Business

Master Econometrics

Track: Mathematical Economics

Supervisors of the Master thesis: Prof. Marco van der Leij and Prof. Jan Tuinstra

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Abstract

I study the effects of the health insurance companies’ bargaining power in the Dutch health care insurance sector. For this study a two-sided market approach is used. Health insurance companies act as intermediates between the policyholders and the health care providers. Policyholders join one health insurance company and are sensitive for premium changes. Health care providers contract multiple health insurance companies in order to have access to a wider population of pol-icyholders. When health insurance companies have bargaining power, they can apply pressure on the health care providers by enforcing discounts on the contract deals. Health insurance companies’ market shares play an important role in this contracting process. This is called the inter-group network externalities. I find that including network effects in the price competition lowers the premium com-pared to a price competition without network effects. However, the degree of this cost pass-through rate depends on the symmetry of the market, the bargaining power of the health insurance companies and the probability of need of health care.

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Verklaring eigen werk

Hierbij verklaar ik, Fieke Snijders, dat ik deze scriptie zelf geschreven heb en dat ik de volledige verantwoordelijkheid op me neem voor de inhoud ervan. Ik bevestig dat de tekst en het werk dat in deze scriptie gepresenteerd wordt origineel is en dat ik geen gebruik heb gemaakt van andere bronnen dan die welke in de tekst en in de referenties worden genoemd. De Faculteit Economie en Bedrijfskunde is alleen verantwoordelijk voor de begeleiding tot het inleveren van de scriptie, niet voor de inhoud.

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Introduction

The Dutch health insurance system can be described as regulated competi-tion. This implies competition between insurers and providers; nevertheless this competition is restricted within the boundaries of a legal and regulatory frame-work. The goal of this semi-free market system is to generate an efficient health care market wherein health care insurers compete with each other on the basis of prices. However in recent years health care and cure has been a growing item of expense within the Dutch society. For years these costs have increased faster than the Dutch gross domestic product (OECD, 2015).

In 2014 the Dutch government announced a new financial structure in order to tackle the rising health care expenditure. Less funds were available for long-term nursing and care. Instead these costs were partly transferred to the basic health insurances. This would lead to an extra financial burden on the basic health in-surance funds (The Ministry of Health, Welfare and Sport, 2014, hereafter HWS). This started a public discussion in the Netherlands about a possible premium in-crease in 2015.

Health insurance company VGZ reacted upon this discussion and suggested that it would be premature at this stage to say premiums will increase in 2015. The premiums will depend on last year results and on the on-going negotiation with the health care suppliers. VGZ explained that it expects to save money with a stricter procurement policy (Volkskrant, 2014).

This raises the question: why did the health insurance companies not imple-ment this stricter bargaining policy earlier? Particular concerns with regarding the ineffective health insurance market exist. High market shares, big profits and excessive reserves in the health insurance market could indicate an imperfect competition between health insurance companies (Metze et al., 2014). I therefore study the impact of this new policy.

This thesis tries to answer the question: ”What will be the impact of a stricter procurement policy of the Dutch health insurance companies? Will financial ben-efits of this procurement policy be passed on to the policyholders in the form of lower premiums?” In order to answer the research questions I compare two price competition models: a standard Bertrand competition model and a two-sided market model.

Two-sided markets are defined as markets in which one or several platforms en-able interaction between end-users, and try to get the two sides “on board” by

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appropriately charging each side. That is, platforms court each side while at-tempting to make, or at least not lose, money overall (Rochet and Tirole, 2003).

One can view the Dutch health insurance system as a two-sided market. On one side of the health insurance companies are the policyholders and on the other side are the health care providers. The health insurance companies are the intermediaries between the policyholders and health care suppliers. They facil-itate the interaction between these two groups while competing with one another.

These two-sided market models enable studying affects of market shares and concentration on the health insurance companies’ bargaining process. This study concerns the basic health insurance and not the additional insurances. The model takes into account that in the Netherlands it is mandatory for all citizen to take out a basic insurance policy.

In the two-sided market model with network effects the health insurance compa-nies benefit a cost reduction. In what extent this is passed on to the policyholders (the cost pass-through rate) depends on factors as the symmetry of the market, expected costs and bargaining power of the health insurance companies.

In a symmetric market this cost benefit is passed on in larger extent to the policyholders. The cost pass-through rate decreases when the market becomes less symmetric. However it strongly depends on the height of the health insurance companies’ expected costs. The lower the expected costs, the less of the benefit is passed on to the policyholder. A higher bargaining power leads to larger cost reduction and higher cost pass-through rate.

The remainder of the paper is organized in the following way. In Chapter 1 more information on the Dutch health insurance market is provided. The second chapter describes the two-sided market approach of the health insurance mar-ket and a literature review on this approach is provided. I set up the standard Bertrand and two-sided market model in Chapter 3. Chapter 4 provides the re-sults in a symmetric market and Chapter 5 the rere-sults of the the asymmetric market. Concluding remarks follow.

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Chapter 1 The Dutch Health Insurance

Market

This chapter starts with describing the Dutch health insurance system. Sec-ondly, it explains how Dutch health care is funded. Finally, it describes the recent developments in the health care market.

1.1 The Dutch health insurance system

The Dutch health insurance system has gone through a long development, with a history that dates back to the eighteenth century. For many decades the Netherlands had a fragmented system of health insurance for normal medical care. It was a two-tier system of private health insurance for those who could afford it and state coverage for the rest. In 2005 the government decided that the health care system as a whole should be liberalized in order to ensure that all Dutch citizens have equal access to basic medical care. It was believed that market forces itself will stimulate an efficient health care system. On January 2006 the Health Insurance Act (Zorgverzekeringswet (Zvw)) was introduced. The Zvw obliged all Dutch citizens to buy, from a private insurance company of their choice, a basic health insurance whose benefits are specified by law. The health insurers must accept all citizens who apply for this basic health insurance. This current health care system is based on a “semi-free market system” and consists of three statutory forms of insurance:

1. The basic health insurance’ covers common medical care.

2. Algemene Wet Bijzondere Ziektekosten (AWBZ) covers long-term nursing and care.

3. Forms of care deemed less essential, covered by supplementary private in-surance.

The aim of this semi-free market system is to reduce the costs made by the health care providers and to provide affordable basic health insurance for all Dutch citizens. This all without sacrificing the quality and transparency of the health care market. The Ministry of Health, Welfare and Sport, (het ministerie

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Chapter 1 The Dutch health insurance market Page 6 van Volksgezondheid, Welzijn en Sport hereafter VWS) determines health care laws nationally in consultation with patient rights groups, health care providers and health insurers. The Health Care Authority (de Nederlandse Zorgautoriteit (NZa)) supervises the system and the Health Inspection supervises the health care providers. This must make the system efficient, consistent and in line with the needs of society.

1.2 Dutch health insurance sector figures

In 2014 there were 26 health insurance labels in the Netherlands, divided over nine health insurance concerns (NZa, 2015). The four largest health insur-ance concerns are Achmea, VGZ, CZ and Menzis. Since 2006 these four largest concerns capture approximately 90% of the total market market (Vektis, 2015). From 2010 to 2013 the average annual profit made per basic health insurance policyholder increased with more thane80 (NZa, 2015).

Health insurance companies should have a stable financial position. Their busi-ness processes should be organized in a way to assure continuity and enable them to continue to meet their commitments in the future. Every year DNB prescribes the required solvency margin. This solvency margin is a percentage of the average gross damage over the last 3 years, concerning the basic insurance. Before 2010 this solvency margin was 8%, but the last years it increased to 11%. Remark-able is that the solvency ratio (the insurers’ actual solvency margins presented in terms of the required solvency margin) has never been below 200% (NZa, 2015).

Figure 1.1: Source: VWS, 2010, p. 31. Overview of Zvw financing

The health insurance companies receive nominal premiums from their policy-holders to finance health care costs. Besides, the basic health care insurance consists out of a obligatory and voluntary deductible excess. The first one is the part of the costs of medical treatment which you have to pay yourself. Only after this amount is paid, the insurance company will pay the costs of medical

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Chapter 1 The Dutch health insurance market Page 7

treatment. The policyholders can decide by their selves if they want to use the voluntary deductible excess. Besides the premiums and deductible excesses the health insurance companies receive an equalization of the Health Insurance Fund (Zorgverzekeringsfonds (ZVF)). This fund consists of income-related contribu-tions and public funding (see Figure 1.1). One aim of this fund is to compensate insurers for policyholders with predictably high medical expenses (VWS, 2010). Because of this fund health insurance companies no longer find insuring high-risk individuals an unappealing proposition. Besides the public funding covers the health care costs for children aged up to 18.

1.3 Stages of the Dutch health insurance

pro-cess

Every year health insurance companies compete with each other for policy-holders. The timing of the different decisions made in the Dutch health insurance market system can be explained in 3 stages:

1. Every year, health insurance companies and health care providers can ne-gotiate bilaterally about the prices of the health care services.

2. Afterwards health insurers determine the height of their own premium, which does not vary by policyholder, health status, or other risk character-istics.The Zvw contains a prohibition on discrimination in the basic health insurance premium.

3. The Dutch citizen has the possibility to switch (for free) to another health insurance every year.

Figure 1.2: Timeline health insurance market

My focus is on stages 1 and 2. Information on the exact form of the negotiation process between health care providers and health insurance companies is hard to find due to a lack of transparency of the exact price of medical services. These prices are not published for two reasons. The first reason is that the data contains information on the health care provider’s competitive environment. As a result the negotiation position of the health care providers companies will be enhanced. The second reason is that the data contains sensitive confidential information about someone’s state of health (NRC Handelsblad, 2015).

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Chapter 2 The Health Insurance Market As

a Two-Sided Market Model

In this chapter the health insurance market is described as a two-sided market model. First the two-sided market model is introduced in section 2.1. Next I explain how this model is suitable for the Dutch health insurance market. Section 2.3 provides a literature review on the health insurance market approached as a two-sided market model.

2.1 Two-sided markets

two-sided markets are defined as markets in which one or several platforms enable interaction between end-users, and try to get the two sides “on board” by appropriately charging each side. That is, platforms court each side while attempting to make, or at least not lose, money overall (Rochet and Tirole, 2003). Important key-factors of a two-sided market model are inter-group network externalities, the price structure and the possibility to single- or multi-home. I will illuminate these key-factors in the following subsections.

2.1.1 Inter-group network externalities

Network externalities describes the effect of the number of consumers using a particular good or service on the value of that product to other people. In two-sided markets inter-group externalities are involved: one side of the market exerts an externality over the other side of the market. For example health care providers benefit from more policyholders joining the contracted health insurance company. The intensity of these inter-group network externalities varies per two-sided market. Rochet and Tirole (2003) state that the existence of these inter-group network externalities is a characteristic of a two-sided market.

2.1.2 Price structure

In two-sided markets a distinction is made between price level and price struc-ture. Price level is defined as the total sum of prices charged on both sides of the market by the platform. How this price level is distributed on the two sides is called the price structure. The price structure combined with the inter-group

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Chapter 2 The health insurance market as a two-sided market model Page 9

network externalities play an important role on the platform performance. For example lowering the price on one side of the market can attract more end-users on that side. This in its turn can make the platform more valuable for the end-users on the other side. This development gives the platform the opportunity to raise the price on that other side of the market.

2.1.3 Single- and multi-homing

A distinction is made between end-users who connect to one single platform or to several platforms. It is called single-homing when end-users only join one platform in a particular market. End-users will single-home when platforms are viewed as homogeneous. When end-users participate in multiple platform it is said that they multi-home. End-users consider multi-homing if this leads to any extra benefits. For example to gain access to a greater network of end-users on the other side of the market, or when platforms are viewed as heterogeneous. In the case of the Dutch health insurance industry the policyholders take out one basic health insurance, i.e. they single-home. On the other side of the market the health care providers multi-home as they connect with multiple health insurance companies.

2.2 Two-sided health insurance market model

The health insurance companies act as intermediaries between the policyhold-ers and the health care providpolicyhold-ers in order to create an efficient health insurance market (see Figure 2.1). Health insurance companies secure contract deals with health care providers to establish a health care network. The health care providers connect with multiple health insurance companies in order to have access to a wider population.

Figure 2.1: The Dutch health insurance market approached as two-sided market model

The price the providers pay to connect with a health insurance company is the discount given on the contract deals with them. On the other side of the market the different health insurance companies compete for policyholders. The policy-holders have to pay a health insurance contribution, called premium. In turn the policyholder receive health care when needed (and which is covered by the basic

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health insurance). The health insurance companies try to get both health care providers and policyholders on board in order to maximize profit.

2.3 Earlier research on health insurance

mar-kets as two-sided marmar-kets

There are numerous theory papers on two-sided markets. The most influen-tial ones are Rochet and Tirole (2003) and Armstrong (2006). The health care market has been considered as a two-sided market before (Bardey and Rochet, 2009; Ho, 2009; Bardey and Bourgeon, 2011; Boilley, 2013).

Bardey and Rochet (2009) investigate how the inter-group network externali-ties affect the adverse selection problem in the health insurance market. In their model health insurance companies compete for policyholders on one side of the market and for physicians on the other side. The greater the number of physi-cians contracting with the insurance company the more valuable that insurance will be to policyholders. A drawback of this effect is that it could attract riskier policyholders. An interesting finding of this paper is that as a result of this ad-verse selection health insurance companies are able to negotiate higher discounts on the contract deals with health care providers. In this paper I also study the ability of health insurance companies to enforce discounts on the contracts with the health care providers. However it needs to be mentioned that the focus on bargaining in my model is based on market shares and not based on the diversity of the policyholders.

Additionally, Ho (2009) investigates the bargaining process between health in-surance companies and health care providers. In her model the policyholders choose their health insurance and their health care providers. Where my focus will be on the health insurance companies’ network, Ho (2009) studies the deter-minants and the welfare impacts of observed hospitals’ networks. Ho (2009) finds that hospitals may have incentives to differentiate and selectively contract health insurance plan. This creates exclusiveness which makes it possible for hospitals to increase their profit. However, this paper does not consider a concentrated health insurance market, where only a few health insurance companies dominate the market as in the Netherlands. I suspect that if there are only a few health insurance companies dominating the market it could be crucial for health care providers to contract those health insurance companies.

Bardey and Bourgeon (2011) compare two different competitions between health insurance companies: Managed Care Organizations (MCOs) and “Conventional Insurers.” At MCOs policyholders have to visit the health care providers affili-ated to their insurer, while policyholders from conventional insurers may freely choose their health care providers. The ’Convential Insurance’ framework is close in spirit to my model as the insurers affiliate all possible health care providers, however I do not model the price competition between health care providers. Bardey and Bourgeon (2011) state that in the ’Conventional Insurers’ frame-work horizontal differentiation between health care providers benefits the health

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insurance companies. This is because the health care providers’ differentiation is transferred from the providers’ side to the policyholders’ side. In the MCOs framework Bardey and Bourgeon (2011) show that due to the lower prices paid to the health care providers, policyholders get a higher utility under competition between MCOs.

This paper can be considered in the context of the broader literature on two-sided markets where on one side of the platform the end-users single-home (the policyholders). On the other side of the platform the end-users prefer to multi-home to gain access to a greater network (the health care providers). Armstrong (2006) calls this the ’competitive bottlenecks’ model.

Caillaud and Jullien (2003) report that in this kind of ’competitive bottleneck’ markets the single-home side is treated favorably, while the multi-homing side has all its surplus extracted. Armstrong (2006) explains that within this ’competitive bottleneck’ model the market on the single-homing side is to some extent com-petitive. Platforms have to compete for the single-homing end-users to join them.

On the multi-homing’s side, the platforms can experience monopoly power over providing access to the end-users on the other side. This makes it possible for platforms to charge higher price on the multi-homing side. However due to the competitive environment on the single-homing side these revenues will be trans-ferred to single-homing end-users.

A crucial aspect of the Dutch health insurance market is the fact that Dutch citizens are obliged to take out a basic health insurance. This creates an inelas-tic total demand for basic health insurances. This inelasinelas-ticity is not included in Armstrong’s Competitive Bottleneck. I suspect that this inelastic total demand causes stable market shares which in its turn plays an important role in the health insurer’s bargaining process and premium determination. Therefore I will focus on the health insurance companies’ network benefits. The model characteris-tics for the Dutch health insurance market will be explained in the subsequent chapter.

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Chapter 3 Two Models of the Dutch Health

Insurance Market

In order to study the effect of the procurement policy of the Dutch health insurance companies on the premium for policyholders I compare two price com-petition models: the standard Bertrand model and the two-sided market model. Section 3.1 provides the characteristics for the standard Bertrand competition. In section 3.2 I explain how the standard Bertrand model is adapted into a two-sided market model. Section 3.3 provides information on how an asymmetric market scenarios is created. For this asymmetric market a numerical example is studied which is provided in section 3.4. In section 3.5 I provide my conjecture on how the network effects in the two-sided market model affect the premium.

3.1 Bertrand competition characteristics

As explained in chapter 2 in the Dutch health insurance market health in-surance companies compete on premiums. Suppose there are N health inin-surance companies, indexed by i = 1, ..., N . The assumptions made on the health insur-ance companies are:

1. Total demand for health insurance policies is inelastic.

2. The demand function for each individual health insurance company is linear 3. The health insurance companies are profit maximizing firms.

4. Health insurance companies set premiums simultaneously.

5. The basic health insurance policies provided by the insurers are homoge-neous products.

All Dutch citizens are obliged to take out a basic health insurance. Therefore it is assumed that the total demand is inelastic. I set this continuum of mass of policyholders equal to ’A’. The second assumption, a linear demand function for each individual health insurance companies, is a strong assumption. This is chosen to make the model analytically tractable. The demand function for health

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Chapter 3 Two models of the Dutch health insurance market Page 13

insurance company i is assumed to be

Qi(pi, p−i) = Ai− Bpi+ B N N X j=1 pj = Ai− N − 1 N Bpi+ B N X j6=i pj (3.1)

where pi is the health insurance company i’s premium for i ∈ [1, N ]. The constant

“Ai” embodies the effects of all factors other than premium that affect demand.

I will call this the market position parameter. The necessary condition for a to-tal inelastic demand to exist is:

N

P

i=1

Qi = A. Then the total demand for health

insurance policies in equilibrium will be in total A (see Appendix A).

The parameter ”B” is the price sensitivity parameter, which is assumed to be positive, B > 0. If the price of one health insurance company increases, ceteris paribus, the demand for the other (N − 1) health insurance companies will in-crease. This assumption is made as the requirements of a basic health insurance coverage is legally defined by the Zvw.

Dutch health insurance companies are private firms, therefore it is assumed that the insurers are concerned with maximising profit. Health insurance company i’s profit function can be described as

πi = piQi(pi, p−i) − λKiQi(pi, p−i), (3.2)

where piQi(pi, p−i) is health insurance company i’s received premium from its

policyholders. The model excludes the health insurance company’s income from the Health Insurance Fund. This is because this fund compensates for high risk policyholders and covers the health care costs for the children. It does not play a role in the competition for policyholders.

The expected costs of health insurance company i are described as λKiQi(pi, p−i).

Here λ is the exogenous probability that a policyholder needs health care. Ki

represents the average price per treatment. I will call this the secured contract deal with the health care providers. In this standard Bertrand competition model (without network effects) I assume that the health insurance companies take these contract deals as given: the secured contract deal for all N health insurance com-panies will be equal to an upper bound of the costs: Ku. In the two-sided market

model network effects are included, which could lead to a cost reduction. This is described in the following section.

3.2 Two-sided market model characteristics

In this section I consider the Dutch health insurance market as a two-sided market model where the policyholders and the health care providers are the end-users of the market. The health insurance companies facilitate relations between those two end-users in order to make profit. The health insurance company’s

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expected costs depend on the contract deals with the health care providers. The following assumptions are made on the health care providers side of the market

1. Health insurance companies bargain with health care providers on the se-cured contract deals: Ki.

2. The health care providers are considered as one homogeneous group. No distinction is made between the providers. Ki is the same for all health care

providers.

3. The network effects are included in the contract deals.

I incorporate the network effects in the contract deals the health insurance com-panies make with the health care providers: Ki. The more policyholders join a

specific health insurance company the more attractive this insurer will be for the health care providers, as it has the accessibility to a larger network of possible patients. A larger market share improves the bargaining position of the health insurance company. A better bargaining position leads to cheaper contract deals with the health care providers. The discount on these contracts secured by the insurers can be interpreted as the price the health care providers have to pay to connect with the health insurance companies. Suppose the contract deals of a health insurance company is determined in the following way: if the insurer attracts Qi policyholders, the contract deal is

Ki = Ku− βδK

Qi

A (3.3)

where δK=Ku− Kl: Ku and Kl are respectively the upper-bound and the

lower-bound for the health care costs. The upper-lower-bound captures the bargaining posi-tion of the health care providers. The higher the upper bound of the costs, the better the bargaining position of the health care providers. The lower-bound can be explained as the health care sold at cost. β is the bargaining power of the health insurance companies towards the health care providers. In this model I consider homogeneous bargaining power over all health insurance companies. The higher β, the more the cost depends on the market share. Combining Equation 3.3 and Equation 3.2 then the profit function of the health insurance companies in the two-sided market is

πi = piQi(pi, p−i) − λKuQi(pi, p−i) +

λβδK

A Q

2

i(pi, p−i) (3.4)

This expression is quadratic in platform i’s demand. The condition that guar-antee the concavity of the profit function is δ2π1

δp2 i

≤ 0. This satisfaction of this concavity constraint is described in the following lemma:

Lemma 1 The concavity constraint on equation (3.4) is satisfied when

0 ≤ B ≤ 4A 3λβδK

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The optimum premium, demand and costs for all health insurers are obtained by simultaneous optimization of Equation (3.4).

Varying bargaining power variable

In the two-sided market model I implement the variable β in order to study the effects of the bargaining power of the health insurance companies. I model the negotiation process by which health insurance companies choose their equi-librium networks and which determines the division of the profits generated by each contract. When β=0 the two-sided market model is equal to the standard Bertrand model, where Ki = Ku. When β > 0 then the insurance companies can

enforce discounts with a higher market share. When β = 1 the discount is pro-portional to the market share of the company. When β > 1 the health insurance companies can enforce larger discounts disproportionate to their market share. For example, in the symmetric case in which health insurance companies have equal market share, Qi

A = 1

N, with a bargaining power of β = N , they enforce

a discount of δK and secure contract deals at wholesale price (Kl). The upper

bound of the β depends on the number of health insurances of the market. The restriction on β is that is must satisfy Lemma 1 in order to satisfy the concavity condition of the profit function.

3.3 Symmetric and asymmetric market

In order to create an asymmetric market I model asymmetric demand func-tions by varying the market position parameter (Ai) for i = 1, ..., N health

in-surance companies. Equation (3.5) describes the market position vector of the N health insurance companies.

     A1 A2 .. . AN      =     αA 1−α N −1A · · · 1−α N −1A     (3.5)

The variable α lies in the interval [_N1, 1]. It measures the “strength” of the first platform’s market position. An increase in α improves the market position of the first health insurance company, while the position of the other N − 1 firms will deteriorate. The assumption of total inelastic demand is satisfied by this market position distribution, namelyPN

i Ai = αA+ N −1

N −1(1−α)A = A (see Appendix A).

Before analyzing the model in an asymmetric health insurance market, I examine the case if platforms were completely symmetric. This is when α is equal _N1 then it holds that (A1 = A2.... = AN). In a completely symmetric market all N

health insurance companies have the same demand function (Equation 3.1). Thus the N health insurance companies will obtain the same market share (Qi

A = 1 N)

if they charge the same premium. Combining this result with Equation (3.3) then it follows that in the two-sided market model the secured contract deal in a

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symmetric equilibrium is

Ki = Ku−

βδK

N for i ∈ [1, N ]. (3.6) The secured contract deals in the standard Bertrand models are taken as given: Ki = Ku.

In the asymmetric situation I consider asymmetric demand functions. For the asymmetric setting I set out a numerical example in order to conveniently study the model of the Dutch health insurance market. This numerical example is outlined in the next section.

3.4 Numerical example asymmetric situation

When α > _N1 an asymmetric market is created where the health insurance company have different demand functions (see Equation 3.5 and Equation 3.1). These different demand fucntions will cause different market shares. This will lead to different secured contract deals in the two-sided market model. The pa-rameters’ values for the numerical example are shown in Table 3.1

Parameter Value Explanation ($)

N 4 Number of Health Insurance Companies α (0.25, 1] Asymmetric market parameter

A 100 Total Population

Ku 100 Upper bound health care providers contract deal

Kl 75 Lower bound health care providers contract deal

δK 25 Ku− Kl

λ 1₅ Probability of need of health care B 1 Price sensitivity

Table 3.1: Parameter values used in the asymmetric scenario

Based on the Dutch Market, where four corporations capture 90% of the market, I set the number of health insurance companies equal to four. I will vary α on the interval (0.25, 1]. An increase in α leads to a stronger demand function for the first health insurance company with market position Ai = αA. I will call

this the advantaged health insurance company. The other 3 health insurance companies will have market position 1−α₃ A and are called the disadvantaged com-panies. The advantaged and disadvantaged companies are respectively indexed with i = {a, d}.

The four health insurance companies compete for policyholders, which I set on a total number, A, of 100. The upper and lower bound of the contract deals with the health care providers are respectively 100 and 75. The probability of need of health care is set on ₂₀1.

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The parameter B reflects the sensitivity of demand between the health insur-ance companies. I set this parameter on B = 1. If a health insurinsur-ance com-pany increases its premium, ceteris paribus, it decreases its demand while other firms’ demand will increase. For this numerical example the concavity condition (Lemma 1) is satisfied for β < 80₃ .

As a result of this parameter choice the demand for the advantaged and dis-advantaged companies can be written as:

Qa= α100 − 3 4pi+ 1 4 X j6=i pj Qd= 1 − α 3 100 − 3 4pi+ 1 4 X j=6=i pj (3.7)

The profit function for the four health insurance companies in the asymmetric function is πi = (pi− 20)Qi(pi, p−i) + β 20Q 2 i(pi, p−i) (3.8)

3.5 Conjecture

In the two-sided health insurance market, the health insurance companies ask premium of the citizens and set contract deals with the health care providers. If I assume that health insurance companies have enough bargaining power to de-termine prices on both sides of the market, the price structure matters because it can choose to set high or low prices on either side. For example, insurers can set a low premium to attract more policyholders and then compensate with discounts on the contract deals with health care providers. In this two-sided market model it is quite clear that when β > 0 health insurance companies enforce discounts on the contract deals. The question is to what extent this benefit will be passed on to the policyholder in terms of lower premium.

To be able to enforce higher discounts of the health care providers, a health insurance company needs to gain more market share. This creates a downward pressure on the prices offered to the policyholders compared to the models where no externalities are involved. This effect will be magnified by an increase of bar-gaining power. In the case of symmetric scenario the health insurance companies will have equal market share. The more concentrated the market is the higher the market share will be, which will decrease the contract costs.

In the case where health insurance companies have high market shares and high bargaining power health insurance companies will be able to pursue a stricter procurement policy. However, in this two-sided market the health insurance companies do have to compete for the policyholders. According to Armstrong’s (2006) competitive bottleneck model these financial benefits generated from the multi-homing side will be passed on in larger extent to the policyholders. However I suspect this effect could be small due to the stable market shares of the Dutch health insurance companies caused by the total inelastic demand assumption.

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Chapter 4 Results and Analysis of the

Symmetric Market Situation

In this chapter I present the results of the analysis of the symmetric health insurance market. In this symmetric scenario there are no differences between insurers and in equilibrium they all enter the same contract deals with the health care providers. Section 4.1 provide the optimum results of the two-sided market model and the standard Bertrand model. In section 4.2 the cost pass-through rate of the two-sided market model is evaluated. Then I characterise the cost and network effects. In the last section I compare the welfare distribution of the two models.

4.1 Standard Bertrand market model versus

two-sided market model

In both models (standard Bertrand and two-sided market model) I will as-sume that the N health insurance companies have the same demand function (see Equation 3.1) and the same market position Ai = _NA (see Equation 3.5).

Standard Bertrand model

The optimum premium in the standard Bertrand model is the solution of max

pi

πi(p) = piQi(pi, p−i) − λKiQi(pi, p−i). (4.1)

The negotiated costs in the standard Bertrand Model are taken as given and equal to the upper bound of the cost, Ki = Ku. This holds for all N health insurance

companies and each health insurance company is aware of each other’s costs before deciding their optimum premium. Firms also understand the demand structure, and know the value of λ. I assume that health insurance companies make a decision based on best-responses, which means that each firm best-responds to the prices set by the other health insurance companies. The decision problem is the same for each health insurance company by symmetry. Therefore I assume that every insurer sets the same premium. The solution of this symmetric Nash equilibrium is summarized in proposition 1.

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Chapter 4 Results and Analysis of the Symmetric Market Situation Page 19

Proposition 1 In a symmetric standard Bertrand market model with N health insurance companies the symmetric Nash equilibrium as function of N , A, B, λ and Ku is

pB_i = A

(N − 1)B + λKu (4.2) Proof. See Appendix C

Two-sided market model

In the two-sided market the costs depend on the bargaining power and the market share. In a market which consist of N symmetric firms the optimum premium is solution of max pi πi(p) = piQi(pi, p−i) − λKuQi(pi, p−i) + λβδK A Q 2 i(pi, p−i) (4.3)

All N health insurance companies maximize this profit function simultaneously. In the symmetric situation they enforce the same discount on the contract deals with the health care providers. As in the standard Bertrand model all health insurers are aware of each other’s costs. As a result the decision problem for all N health insurance companies is the same. The corresponding demand for health insurance company i = 1..N is calculated with Equation (3.1). The step-by-step derivation of the F.O.C. can be found in the appendix. The symmetric Nash equilibrium premium in the two-sided market is stated in the following proposi-tion.

Proposition 2 In a symmetric two-sided market with N health insurance com-panies the Nash equilibrium premium, demand and profit of company i is charac-terised by pT_i = A (N − 1)B + λ N(N Ku− 2βδk), (4.4) and QT_i = A N K_iT = Ku− βδk N πT_i = (1 − N )(βBλδk) + N A B(N − 1)N2 A (4.5)

Proof. See Appendix D

Subtracting the standard Bertrand optimum from the two-sided market optimum:

pT_i − pB i = −

2βλδk

N ≤ 0 (4.6)

which is smaller than 0 as it is assumed that β ≥ 0, λ ∈ [0, 1], δk ≥ 0 and N ≥ 1.

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smaller than the Nash equilibrium premium of the standard Bertrand model. The intuition behind this difference is that in the two-sided market model a higher market share leads to a cost reduction if β > 0. In a price competition a firm can increase its market share by lowering its price. This difference between opti-mum premiums decreases as N increases. The more number of health insurance companies in the market the lower the market shares. This leads to the following proposition

Proposition 3 When β > 0 and δk> 0 the health insurance companies’ premium

in the symmetric two-sided market model are lower than in the symmetric stan-dard Bertrand model. This difference between premium depends on the number of health insurance companies in the market (N ) and the upper and lower-bound of the health care costs

Note that if Ku = Kl, i.e. δk = 0 the standard Bertrand and the two-sided

market optima are the same. The cost in the two-sided market model decreases with the bargaining power: i.e. the first derivative of the cost function is negative

dK_it dβ =

−δk

N (4.7)

The bigger the difference between the upper (Ku) and lower bound (Kl) of the

costs the faster the cost decrease in β. And, as expected, the more concentrated the market is the lower the enforced discounts on the contract deals are. This as a result of a lower market share of the health insurance companies (in a symmetric market the policyholders are equally distributed over the N firm).

4.2 Cost pass-through two-sided market model

In this section, I calculate the cost pass-through of the two-sided market model. So to which extent a reduction in costs is passed on to the policyholder. The derivative of the optimum premium function pT_i with respect to variable β is

dpT i

dβ =

−2λδK

N (4.8)

The policyholders benefit from the increasing bargaining power as the premium decreases. Combining this Equation (4.8) with equation (4.7) shows that a health insurance company’s optimal pass-through of linear cost is given by

dpT i

dKT i

= 2λ (4.9)

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Proposition 4 In a completely symmetric health insurance market and where health insurance companies set their premium by maximizing simultaneously their profit, an increase in the bargaining power, β, leads to a reduction in the health insurance costs and the premium decreases twice as fast as the probability of ill-ness (2λ).

The intuition for this proposition is as follows: a higher β means a greater bar-gaining power for the health insurance companies, which would lead to lower costs. A cost reduction gives the health insurance company the possibility to decrease the premium. Besides when β > 0 a higher market share leads to bigger cost reductions. This gives the health insurance companies an extra impulse to decrease the premium more to gain more market share.

In choosing their optimal premium, health insurance companies take the probabil-ity of illness λ into account. The higher this probabilprobabil-ity is the more cost-benefit is passed on to the policyholder. When λ > 1₂ the cost pass-through rate is higher than one. In this case the cost benefit is passed in larger extent to the policyholder.

4.3 Cost and network effects

The previous section shows that the cost reduction in the two-sided market models leads to lower premiums than in the standard Bertrand model. The difference between the standard Bertrand premium and the two-sided premium is described as ∆premium = pBi − pTi . The question that arises is: how much of

this reduction in the premium is caused by the network effects and how much is caused by a reduction in cost? This question can be described as in the following equation:

∆premium= ∆costs+ ∆network, (4.10)

where ∆costs are the cost effects and ∆network are the network effects. I

calcu-late these different effects with a Bertrand model where the costs for the health insurance companies are reduced exogenously. I will call this the cost Bertrand model. The optimum premium in this Cost Bertrand model is the solution of Equation (4.1). However Ki is replaced by the cost of the two-sided market

model in equation (4.6): Ki = Ku −βδ_Nk. The optimum premium is a solution of

max

pi

πi(p) = piQi(pi, p−i) − λ(Ku−

βδk

N )Qi(pi, p−i). (4.11) Which gives the premium:

pCB_i = λKu+

βλδK

N + A

(N − 1)B (4.12) The cost effect and the network effect are calculated respectively as ∆costs =

pB

i − pCBi and ∆network = pCBi − pTi. For the symmetric market gives this the

solution:

∆costs = ∆network =

βλδK

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Thus half of the premium reduction in the two-sided market model is caused by the cost effects and another half by the network effects.

Proposition 5 The premium reduction caused by a stricter bargaining policy in the symmetric two-sided market model will be twice as much as the premium reduction caused by an exogenous cost reduction of the same size in a symmetric Bertrand model.

The cost reduction in the two-sided market model is correlated with the health insurance company’s market share. With a higher market share the health insur-ance company can enforce a bigger cost reduction on the health care providers side. At the same time lower cost makes it possible to reduce the premiums more on the policyholders’ side. The network effects in this two-sided market creates cross-subsidization from the health providers’ side to the policyholders’ side. This result is in line with the result of Armstrong (2006) in his ”Competitive Bottleneck” model.

4.4 Welfare distribution

The two-sided market with the network effects leads to a cost reduction for the health insurance companies. In other words the insurers are able to buy-in health care cheaper from the health care providers. How does this change the wel-fare distribution among the health insurance companies, policyholders and health care providers compared to the distribution in the standard Bertrand model?

I analyse the difference in welfare between the two-sided market model and the standard Bertrand model calculated per policyholder. The welfare change for the health insurance companies, policyholders and health care providers is described as follows:

• Health insurance companies: The expected profit in the two-sided mar-ket model subtracted by the expected profit in the standard Bertrand model multiplied by N firms and divided by the total number of policyholders: ∆ωprof it = (πiT − πBi )NA

• Policyholders: The difference of the standard Bertrand premium and the premium charged in the two-sided market model: ∆ωpremium= −(pTi − pBi )

• Health care providers: The difference of the expected two-sided market costs and the expected standard Bertrand costs divided by the total number of policyholders: ∆ωcosts =

λA(−βδK)

A

The result in this symmetric market ∆ωprof it= −βλδk N ∆ωpremium= 2βλδk N ∆ωcosts= −βλδk N

∆ωprof it+ ∆ωpremium+ ∆ωcosts = 0

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The profits made in the two-sided market model are lower than in the standard Bertrand model. Besides health care providers receive less money for their service. The cost benefit health insurance companies made on the health care providers side is in larger extent transferred to the policyholder.

Finding 1 Comparing the symmetric two-sided market model with the symmet-ric standard Bertrand model I find that the welfare loss for the health insurance companies is the same as for the health care providers. The sum of those two losses is transferred to the policyholders.

This finding is in line with with the finding in Chapter where is stated that the premium reduction is caused for 50% by network effects and 50% by costs effects. In two-sided markets health care providers might be found to work more efficiently.

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Chapter 5 Results and Analysis of the

Asymmetric Market Situation

In this chapter I analyse the price competition in an asymmetric market. This asymmetry causes unequal market shares among the health insurance companies. Which in turn will lead to different secured contract deals with the hospitals. I will analyse the numerical example explained in Chapter 3.4. Section 5.1 provides the optimum standard Bertrand output and the optimum two-sided market output. In section 5.2 I analyse the market power in the the standard Bertrand and two-sided market model. Section 5.3 provides the effects of the asymmetry on the cost pass-through rate. In section 5.4 the cost and network effects are presented. Section 5.5 provides an overview of the welfare distribution in the asymmetric situation.

5.1 Comparison standard Bertrand and two-sided

market model

In the numerical example I consider a market which consists of four health insurance companies (N = 4) and the total population is set on 100. The prob-ability that a policyholder needs medical services is equal to λ = 1

5. The upper

and the lower-bound of the contract deals with the health care providers are re-spectively 100 and 75. For the comparison between the standard Bertrand and two-sided market output I will evaluate derivatives of the optimum premiums towards α. What will be the effect of this asymmetric market variable on the health insurance premium?

5.1.1 Standard Bertrand model

As in Chapter 4.1 I assume that all four health insurance simultaneously de-termine their premium height. All firms are aware of the asymmetric market situation and know each other’s demand curve and expected costs. The solution of this profit maximization is a solution of Equation (4.1), where in the standard Bertrand model Ki = Ku = 100. This leads to an asymmetric Nash equilibrium

stated in the following proposition

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Chapter 5 Results and analysis of the asymmetric market situation Page 25

Proposition 6 In an asymmetric standard Bertrand model with 4 health in-surance companies and a market described in Chapter 3.4, the asymmetric Nash equilibrium premiums for the advantaged and disadvantaged company are charac-terised respectively by pB_a = 400(1 + 3α) 21 + 20 p B d = 400(2 − α) 21 + 20 (5.1) and the resulting asymmetric equilibrium demands, equal

QB_a = (1 + 3α) 7 A Q B d = (2 − α) 7 A (5.2) Proof. See Appendix C

Equations 16 and 17 show that the mark-ups (defined as premiums minus marginal costs Ku) are proportional to the individual demand. The advantaged

(disad-vantaged) health insurance company’s market share is increasing (decreasing) function of α. The reason for this is straightforward: an increase in α improves (deteriorates) the market position for the advantaged (disadvantaged) company.

5.1.2 Two-sided market model

In the two-sided market model, the secured contract deals between the health insurance companies and health care providers are described as Ki = Ku −

βδKQ_Ni = 100 − 25βQ₄ i for i = 1, .., 4. The deals differ among the N health

in-surance companies as they have different demand functions. Again each firm has perfect knowledge of each other’s expected costs and demand function. Each health insurance company best-responds to the premiums set by the other firms. The asymmetric Nash equilibrium of the two-sided market model is stated in the following proposition.

Proposition 7 In an asymmetric two-sided market model with four health in-surance companies’ the advantaged and disadvantaged health inin-surance optimum premiums for the numerical example in Chapter 3.4 are characterised by respec-tively pT_a = 1 12 h 100(1 + 12α) + H + 3M i pT_d = 1 12 h 100(5 − 4α) + H − M i (5.3) with H = 6 5(200 − 25β) M = 30000(4α − 1) −700 + 30β (5.4)

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with the corresponding demand functions

QT_a∗ =      100, if α ≤ ₄₀1 (80 − 3β) 25 + 750(1−4α)_3β−70 , if ₁₂₀1 (3β − 40) < α < ₄₀1(80 − 3β) 0, if α ≥ ₁₂₀1 (3β − 40) QT_d∗ =      100, if α ≥ ₄₀1 (9β − 200) 25 + 250(4α−1)_3β−70 , if ₄₀1(9β − 200) < α < ₄₀1 (80 − 3β) 0, if α ≥ ₄₀1 (80 − 3β) (5.5)

Proof. See Appendix D.

In order to evaluate the difference in optimum premium between the advan-taged and disadvanadvan-taged companies as α changes, I take the first derivatives of the optimum premiums towards α for both the standard Bertrand model and the two-sided market model.

dpB a dα = 3ν and dpB d dα = −ν (5.6) dpT a dα = 3ρ and dpT d dα = −ρ (5.7) With ν = 400 21 ρ = 1 3(100 + 3000 3β − 70)

Comparing these derivatives on the intervals β ∈ [0, 1] it follows that dpBa

dα > dpTa dα and dpBd dα < dpT d

dα, which leads to the following finding.

Finding 2 In the numerical example of Chapter 3.4 where the health insurance market consist of four health insurance companies and a price sensitivity variable of B = 1 the premium of the advantaged (disadvantaged) company increases (de-creases) more in α in the standard Bertrand model than in the two-sided market model.

Proof. See Appendix E

This could be interpreted in a way that the network effects in the two-sided market model mitigate the effects of increasing (decreasing) premiums of the ad-vantaged (disadad-vantaged ) health insurance companies in an asymmetric market.

5.2 Competition

In this section I compare the Lerner index for the standard Bertrand com-petition and the two-sided market model. The Lerner index ranges from 0 to 1, higher numbers implying greater market power. For α ∈ [1₄, 1] the Lerner indices

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for the advantaged and disadvantaged companies in the standard Bertrand model lie respectively on the interval:

LiB_a(α) ∈ [5 8, 80 101] LiB_d(α) ∈ [20 41, 5 8] (5.8) See Appendix F

The Lerner indices of the standard Bertrand model are illustrated in Figure 5.1

Figure 5.1: Interval of the advantaged and disadvantaged company’s Lerner index in the standard Bertrand model

Figure 5.1 illustrates that the Lerner index for the advantaged (disadvantaged) company increases (decreases) in α, which describes an increase (decrease) in degree of monopoly power of the advantaged (disadvantaged) health insurance company. The variable β does not impact the Lerner indices as it is not included in the standard Bertrand model.

The lerner indices of the two-sided market model depend on both the asymmetric market parameter α and the bargaining power β (see Appendix F). Figure 5.2 illustrates the effects of the asymmetric market variable and the bargaining power in the two-sided market model on the advantaged and disadvantaged Lerner in-dices.

The Lerner indices for the advantaged and disadvantaged companies in the two-sided market model lie respectively on the interval:

LiT_a(α, β) ∈ [5 8, 2849 3386] LiT_d(α, β) ∈ [ 629 1346, 37 58] (5.9)

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Figure 5.2: Lerner indices interval of the advantaged and disadvantaged company in the two-sided market model

The maximum (minimum) of the Lerner index for the advantaged (disadvan-taged) company exist when {α = 1, β = 2}. Comparing Figure 5.1 with Figure 5.2 shows that the maximum of the Lerner index for the advantaged company is higher in the two-sided market model than in the standard Bertrand model.

In addition, Figure 5.2 shows that β has a larger effect on the advantaged (dis-advantaged) company’s Lerner index when the market is more asymmetric (sym-metric).

5.3 Cost pass-through rate in the two-sided

mar-ket model

In this section I analyse the effect of the asymmetric market variable α on the average cost pass-through rate. The average cost pass-through rate is d ¯piT

d ¯KiT

where ¯piT and ¯Ki T

are respectively the volume weighted average premium and cost. These are computed by multiplying the health insurance company’s ex-pected cost and premium by the market share of each firm (see Equation 42 in Appendix G).

Previously I have assumed that the probability of need of health care was λ = 1₅. This implies that 20% of the policyholders will need health care. A higher prob-ability means higher expected costs for the health insurance companies. This expectation will be taken into account in the premiums set by the insurers. In order to analyse the impact of these higher expected cost on the average cost pass-through rate I will analyse four different probabilities: λ = {1₅,2₅,3₅,4₅}. The av-erage cost pass-through rate for the different asymmetric scenarios, α = {1₂,3₄, 1}, are summarised in Figure 5.3.

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(a) λ = 1₅ (b) λ = 2₅

(c) λ = 3₅ (d) λ = 4₅

Figure 5.3: The cost pass-through rates on the interval of β ∈ [0, 2]

A general look at the Figure 5.3 shows that the degree in which cost benefits are passed on to the policyholder decreases as β increases. In addition the fig-ures illustrate that the cost pass-through rate curves shifts upwards as λ increases.

In the symmetric market situation it was shown that the cost pass-through rate is smaller than one for λ < 1₂. Figures 5.3a and 5.3b illustrate that when λ ≤ 2₅ all three cost pass-through rate curves (α = {1₂,3₄, 1}) lie underneath one as well. Figures 5.3c and 5.3d illustrate the average cost pass-through rate curves for λ ∈ {3₅,4₅}. In both situations the ’α = 1

2’ curve lies above one and in the

situa-tion where λ = 4₅ the ’α = 3₄’ curve lies above one if β is low enough.

Thus the more symmetric the market the more cost benefits will be passed on to the policyholder. In addition, if health insurance companies gain more bargaining power the cost-pass through rate decreases.

In the meantime it holds that δ ¯KiT

δα ≤ 0 for α ∈ [ 1

4, 1]: the derivative of the

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neg-Chapter 5 Results and analysis of the asymmetric market situation Page 30

ative (see Equation 39 - 40 in Appendix G). This implies that when α increases on average the health insurance companies enforce bigger discounts. This leads us to the following finding

Finding 3 The higher the asymmetry variable α in the interval [1₄, 1], and the higher the bargaining power β the lower weighted average costs of the 4 health insurance companies. However the cost past-through rate decreases in the asym-metry variable α and the bargaining power β.

This result is important for the research question of this paper. It shows that including network effect in the price competition between health insurance com-panies leads to lower health care costs and premiums. However, the degree of the cost pass-through rate depends on the market situation. The more symmetric the health insurance market is, the more of this bargaining benefit is passed-through to the policyholder in the form of lower premium. The cost pass-through rate lies above one when λ is high (higher expected costs) and the variables α and β are low enough.

5.4 Cost and network effects

In the symmetric scenario the difference in the standard Bertrand premium and the two-sided market premium is caused for 50% by the network effects and 50% by the cost effects (see Equation 4.14). What will be the ratio of these effects in an asymmetric market?

The cost Bertrand model of Chapter 4.4 is used to distinguish the different the network effects and cost effects. However, in this asymmetric market situation the volume weighted average premiums are used: ¯piT, ¯piBand ¯piCB (see Appendix

H). I will examine a market with a relative low and a relative high probability of need of health care: λ = {1₅, 4₅}.

Figure 5.4: Histogram of Network and Cost Effects for λ = 1₅ for different asymmetric scenarios

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Figure 5.4 shows the results of a market with λ = 1₅. The difference in average premium between the two-sided market model and the standard Bertrand model decreases in α. Furthermore it shows that a higher bargaining power of the health insurance companies leads to bigger cost and network effects in all (a)symmetric scenarios α ∈ {1₄,1₂,3₄, 1}. In the extreme case where α = 1 the cost effects are smaller than the network effects.

For λ = 4₅ an increase in α leads to bigger differences in average premium between the two-sided market model and the standard Bertrand model as illustrated in Figure 5.5.

Figure 5.5: Histogram of Network and Cost Effects for λ = 4₅ for different asymmetric scenarios

Remarkable in Figure 5.5 is that when α > 1₄ the ratio of network effects to cost effects departs from 1 to 1: the network effects increase and it appears that the cost effects decrease. These results are summarized in the following finding.

Finding 4 For low (high) values of λ the difference in average premium between the standard Bertrand model and the two-sided market model decreases (increases) as the asymmetry variable α increases on the interval α ∈ [0.25, 1]. In both cases: λ = {1₅,4₅} the cost effects decrease in α.

Proof See Equation (47) - (54) in Appendix H.

For a higher λ the health insurance have higher expected costs. In the previ-ous section it was shown that the average cost pass-through rate curves shift upward when λ increases. In other words the cost benefits made in the two-sided market is passed on to a larger extent to the policyholders. Which is caused by an increase of the network effects.

An intuition of this result is that the higher variable α, the better firm 1’s market position is compared to the other 3 firms: A1 > Aj for j = 2, 3, 4. The

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demand function.

A higher market share makes it possible to enforce bigger discounts on the con-tract deals. This cost reduction makes it possible for the advantaged company to lower the premium (relative high cost pass-through rate) which will attract even more policyholders. In turn, this will entail further cost reductions and so on.

5.5 Welfare distribution

In this section I compare the stakeholders’ expected welfare under asymmetric two-sided market competition and under the standard Bertrand competition. For the numerical example (outlined in Chapter 3.4) and for λ = 1₅. I analyse four different scenarios, namely for α = {1₄,1₂,3₄, 1}. α = 1₄ implies a symmetric health insurance market, with an equally distributed market share. Besides I vary the bargaining power on the interval [0, 1])

The welfare differences between the two-sided market model and standard Bertrand model are calculated as in Chapter 4.4. However for this asymmetric market situ-ation the weighted average profits ( ˆπi), premiums ( ˆpi) and secured contract deals

( ˆKi) are used. This lead to the following expressions:

∆ωprof it = ( ˆπiT − ˆπiB) N A ∆ωpremium = −( ˆpiT − ˆpii B ) ∆ωcosts = −βλ N ˆ δk (5.10)

The welfare changes of for respectively health insurance companies, policy-olders and health care providers (∆ωprof it, ∆ωpremium, ∆ωcosts) are summarized

in Table 5.1. β = 0 β = 0.25 β = 0.5 β = 0.75 β = 1 α =1 4 (0, 0, 0) (-0.31 , 0.62, -0.31) (-0.63 , 1.26, -0.63) (-0.94 , 1.88, -0.94) (-1.25 , 2.50, -1.25) α =1 2 (0, 0, 0) (-0.29 , 0.62, -0.33) (-0.58 , 1.24, -0.66) (-0.86 , 1.86, -1.00) (-1.15 , 2.48, -1.33) α =3 4 (0, 0, 0) (-0.21 , 0.60, -0.39) (-0.42 , 1.21, -0.79) (-0.63 , 1.81, -1.18) (-0.84 , 2.42, -1.58) α = 1 (0, 0, 0) (-0.09 , 0.58, -0.49) (-0.17 , 1.16, -0.99) (-0.25 , 1.74, -1.49) (-0.32 , 2.32, -2.00)

Table 5.1: Average Welfare Difference (∆ωprof it, ∆ωpremium, ∆ωcosts)

For β = 0 the health insurance companies do not have any bargaining power and thus is the two-sided market model output the same as the standard Bertrand output. As a result, the difference between welfare in the two models is 0. In-cluding network effects in the price competition (β > 0) leads to a cost reduction in the health care market and lower premiums for the policyholders. For α = 1₄ the market is completely symmetric and the health insurance companies and providers both hand in the same amount of welfare which is in total transferred to the policyholders (see Finding 1 Chapter 4.4).

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For this numerical example it occurs that the health insurance companies’ av-erage welfare declines in the two-sided market model compared to the standard Bertrand model. The higher the bargaining power β the bigger the loss in the av-erage profits. As it is a price competition, health insurance companies who lower the premium will gain more market share. Therefore including network effects and increasing the bargaining power of health insurance companies stimulates to lower the premium in order to gain more market share. Therefore cost benefits made are passed on to the policyholders. Thus for the policyholder the welfare increases in β.

The table shows us that for a given bargaining power β, the average welfare change for the policyholders does not differ much when varying α. However, when the asymmetric variable increase, welfare shifts from the health care providers to-wards the health insurance companies.

Finding 5 It follows that, in the numerical example of Chapter 3.4, an increase in the asymmetry market parameter leads to a welfare transfer from the health care providers to the health insurance companies

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Chapter 6 Conclusion

In this paper the impact of a stricter procurement policy of the Dutch health insurance companies is studied. I researched how this policy will affect health insurance companies’ costs and premiums. A two-sided Market model is used to study price competition with the network effects.

6.1 Main findings

In the two-sided market model network effects are implemented which leads to cost reductions for the health insurance companies on the health care providers side. These cost benefits are passed on to the policyholders. However, the degree of this cost pass-through rate depends on the symmetry of the market, the bar-gaining power of the health insurance companies and the probability of need of health care.

The higher the probability of illness the higher the cost pass-through rate. In a symmetric market with λ > 1₂ the cost benefits are passed on in larger extent to the policyholders. This is in line with theoretical prediction that the policy-holders’ side is treated favourably, while the health care providers’ side has its entire surplus extracted (Caillaud and Jullien, 2003; Armstrong, 2006)

In the symmetric market the premium reduction is caused 50% by cost effects and 50% by network effects. In other words health care providers and health insurance companies hand in the same amount of welfare and this welfare is dis-tributed among the policyholders.

For the asymmetric situation a market with four health insurance companies is considered. I analyzed the case where one health insurance company (the ad-vantaged company) holds a stronger market position by having a stronger linear demand function than the other firms (disadvantaged companies) in the market.

I find that the difference in premium between the advantaged and disadvantaged companies are greater in the standard Bertrand model than in the two-sided market model as the asymmetric market variable α increases. However the ad-vantaged company reaches a higher degree of monopoly power in the two-sided market model than in the standard Bertrand model.

Price competition with network effects in the Dutch health insurance market