Working paper No: 23/2011 May 2011 LSE Health. Sotiris Vandoros, Katherine Grace Carman. Demand and Pricing of Preventative Health Care

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1 Working aer o: 3/0 May 0 LSE Health Sotiris Vandoros, Katherine Grace Carman Demand and Pricing of Preventative Health Care

2 Demand and Pricing of Preventative Healthcare Sotiris Vandoros, Katherine Grace Carman LSE Health, London School of Economics, UK Deartment of Economics, CentER and etsar, Tilburg University, the etherlands Working Paer o. 3/0 First ublished in May 0 by: LSE Health The London School of Economics and Political Science Houghton Street London WC E Sotiris Vandoros, Katherine Grace Carman. ll rights reserved. o art of this aer may be rerinted or reroduced or utilised in any form or by any electronic, mechanical or other means, now known or hereafter invented, including hotocoying and recording, or in any information storage or retrieve system, without ermission in writing from the ublishers. ritish Library Cataloguing in Publication Data. catalogue record for this ublication is available from the ritish Library IS [ ] Corresonding uthor Sotiris Vandoros LSE Health London School of Economics and Political Science Houghton Street London WC E United Kingdom s.vandoros@lse.ac.uk Tel: +44(0) cknowledgements: We would like to thank Panos Kanavos, Marco Haan, Miguel Carvalho and Chris Muris for comments and suggestions on earlier versions of the aer. ll errors are our own.

3 bstract This study introduces a theoretical framework for the economics of reventative healthcare. Mathematical models are used to exlain how the rice and utilization of revention change deending on demand, as well as factors such as the rice of a cure, the robability of illness, the efficacy of treatment, the robability of illness and cost functions. Different models are develoed deending on the resence and level of health insurance and cometition in reventative healthcare markets. Findings show the effect of various factors on the rice of reventative healthcare, reveal the marginal effects of a change in the arameters on rices and suggest that under certain circumstances revention is not the otimal choice. JEL Classification: I, L Keywords: Preventative healthcare; ricing.

4 Contents. ackground The Model One roducer - Monooly Multile cometitors roviding reventative healthcare Cournot Cometition Seuential Entry Stackelberg Cometition Concluding Remarks... 6 endix... 7 References

5 . ackground In an environment of rising healthcare costs and governments efforts for cost containment, disease revention can lay an increasingly imortant role. Prevention does not necessarily reduce medical care costs, because often the intervention is delivered to a large grou, only a very small fraction of which would get the disease without the intervention and thus incur treatment costs. However, even in the cases when revention costs more than cure, it imroves eole s health, which imlies higher levels of an individual s utility. It has been suggested that the rising value of life has made the US oulation move u the marginal cost schedule of life extension (Hall and Jones 007), in which reventative case can lay a significant role. The uestion for olicy makers is, whether to cover the costs of reventative interventions on a case-by-case basis, given that the total burden of disease may be lower than the cost of revention. Previous studies have focused on the economic imlications of articular reventative interventions from a costbenefit ersective (for examle, see Macintyre et al 000, Goldie 00, van aal 006). In order to rovide tools that can hel answer uestions regarding when revention should be referred to cure, we need to examine the market of reventative health care, taking into account demand and suly of reventative interventions and cure, otimal uantities and rices for each agent and how other arameters affect rices. This aer uses a theoretical model to study demand and ricing of reventative health care in the context of different market structures and healthcare insurance environments. Prevention is the only case in which medical care does not afford satisfaction in the event of illness (rrow 963), while rimary revention constitutes of actions that reduce the occurrence or incidence of disease (Kenkel and Russell 986). The multidimensional nature of the cost of reventative care makes it articularly difficult to measure. For examle, revention concerns not only medical roducts, and the cost of revention can be monetary or non-monetary. Exercise or reducing consumtion of excess unhealthy roducts (such as cigarettes) also consists reventive care, which may not necessarily involve any kind of exenditure. Kenkel and Russell (986) exlore market failures that might lead to too little revention from a societal ersective, secifically, moral hazard, externalities Kenkel and Russell also roose the existence of secondary and tertiary revention. Our analysis is limted to rimary revention, since their definition of secondary revention (actions that reduce or eliminate the health conseuences of a disease given its occurrence) makes it difficult to distinguish between this kind of reventive care and cure. 4

6 and limited information. The authors suggest that in many cases, revention is not cheaer than a cure, although it is still a desirable social olicy. They also refer to some olicies that might encourage revention, such as subsidies and imroved access to clinical reventative services. Grossman (97) does not refer directly to reventative care, but talks about investment in health, which could be considered as a reventative activity. ccording to the author, each erson has a negatively inclined demand curve for health caital, which relates the marginal efficiency of caital to the stock, and an infinitely elastic suly curve. In a theoretical study, Hey and Patel (983) suggest that the uantity of reventative care urchased unambiguously increases with a fall in the rice of reventative care, a fall in the rice of curative care, an increase in the efficacy of reventative care, a decrease in the efficacy of curative care, a rise in the utility-whenhealthy function, a fall in the utility when sick function, and an increase in the discount factor (Hey and Patel 983). Zweifel et al (009) theoretically studied the otimal ath of revention and health insurance from an insurance ersective, distinguishing between observable and non-observable revention related to insurance remiums. They suggest that revention cannot be insured due to the absence of uncertainty surrounding this consumer choice. However, according to Ellis and Manning (007), if consumers are not aware of the imact of revention on the insurance remium, it is desirable for insurers to offer at least some coverage for reventative healthcare. The authors also suggest that the coinsurance rates for revention and treatment are not the same. The most obvious examle of an intervention for which utilization reuires monetary units is a vaccine. Peole are vaccinated to revent contracting a certain disease. Vaccination may be chea or exensive, and this greatly deends on the market status of the roduct, meaning the level of cometition (if any) in the market. s long as the intervention is in atent, no other roducer can rovide exactly the same roduct. While the intervention is atent rotected, the roducer acts as a monoolist if there are no other roducts with a high degree of substitutability. However, during the inatent eriod, other firms can develo and sell roducts that serve the same goal (such as other vaccines for the same disease or me-too roducts in the case of drugs), because they are not exactly the same as the first roduct, and therefore do not infringe on atent rights. In this study we consider both the case of a roduct (such as a vaccine) being the only rovider in the market, and the case of the resence of other roducts that serve the same goal of revention. 5

7 Previous studies have shown that there is cometition between different in-atent interventions. Kanavos, Costa-Font and McGuire (007) suggest that in-atent statins (used for the revention of heart disease) comete against each other. The authors suggest that cometition follows a Cournot-model attern. Danzon and Chao (000) found some evidence of within theraeutic class cometition in France, the UK, Italy and Germany. Ellison et al. (997) also found evidence of within-class cometition in the market of cehalosorins. Individuals who are insured are not ersonally affected by the cost of revention or treatment. Thus, the rice of revention deends on whether consumers are insured or not. Usually health insurance will cover costs of an intervention. However, the choice to cover reventative care deends on its cost comared to a cure. If these costs are not covered by health insurance, the individual will have to make her own decision about whether her exected utility is higher when urchasing reventative care or not. lthough the utility function of the insurer is based on the rofit function, individuals utility functions also include non-monetary factors, such as health level. This aer is organized as follows: Section resents the model and Sections 3, 4 and 5 discuss the cases of monooly, Cournot cometition and Stackelberg cometition resectively. Subsections discuss the cases of demand originating from consumers with no insurance, consumers with full insurance, and an insurer. Section 6 concludes.. The Model. Variables and definitions There are many factors that affect the rice of reventative care. Cost of roduction influences rices and the er-unit cost of roduction must be covered in order for the roduction rocess to be rofitable for the manufacturer. When the roducer has some degree of market ower, an increase in the marginal cost of roduction leads to an increase in rices. In the case of vaccines or drugs, the er-unit cost of roduction is very small. The most significant cost for vaccines is R&D fixed costs. R&D is considered a sunk cost and therefore does not affect ricing. Generic roducers are not subject to R&D costs, but are not considered in this study as we focus on in-atent markets. roducts effectiveness is also a rice determinant because it is a measure of uality: higher efficacy of revention The behaviour of one atient alone cannot change the rice of the insurance remium due to the large oulation of insured atients. evertheless, if all atients over-consume medicines this will have an effect on the rice of the remium. Each atient searately though is unlikely to restrict consumtion for this reason. 6

8 means lower future exected cost of cure. Purchasers of the roduct are willing to ay more if the exected increase in utility due the urchase increases. This will allow roducers to charge a higher rice if the roduct is exected to revent a reduction in utility (illness) with a higher robability. Price of cure also affects rice of revention. If an individual does not urchase reventative care, she has higher robabilities of becoming ill, thus urchasing curative care and exeriencing the disutility of being ill. The higher the rice of the cure, the more willing the individual is to buy reventative care. Finally, market structure also affects rices. monoolist rovider of reventative care has more market ower than when cometitors are resent. Deending on which case alies, a model for each market structure is considered. Prices differ deending on the resence of cometitors as well as the resence of insurance. For each case a different market structure alies. n individual suffers from additional disutility (aart from the monetary cost) from a state of illness. We develo a theoretical framework that we use to study under which circumstances the urchase of reventative care may lead to an increase of the utility of agents. We study how rices change with changes in effectiveness, cost of roduction, rice of cure, market structure and insurance coverage.. The baseline euations ssume there are individuals in an economy, all with health level h. ll are vulnerable to a articular disease. The disease occurs with robability i to each individual (i is the same for all individuals), with i(0,]. In case they become ill, their health level decreases by x n, (where n denotes the individual), so the new health level is h-x n. x n is not the same for all individuals. It is uniformly distributed across the oulation. In case the individual contracts the disease, the cost of cure is. Individuals can reduce the robability of becoming ill by utilising reventative care. Preventative care is rovided by a firm at rice. Consumers can choose to urchase zero or one unit of revention. Preventative care is urchased once. Purchasing an extra unit offers no extra utility. Consumers that choose revention reduce the robability of becoming ill by s (which is universal); s is a measure of effectiveness of the reventative good. The new robability of becoming ill is i-s. Therefore, even after taking reventative care, the individual might have to ay for cure ( ) with robability i-s. Effectiveness, s, ranges from zero to i, with s=0 indicating erfect ineffectiveness of reventative care and s 7

9 = i indicating erfect effectiveness. In cases that the outcome is different, we will also consider the case in which s varies among individuals, while x is assumed to be common for all. We consider a two-eriod model 3. In the first eriod the individual makes her decisions about urchasing reventative care or not, and faces the robability of getting ill in eriod. Demand for reventative care is = F( x) () where is uantity of reventative care demanded, is the oulation and F(x) is the cumulative distribution function of the worsening of health level due to illness amongst the oulation. Only eole in the uer levels of x (eole whose health worsens more when having the secific disease) will urchase reventative care. Peole with x below the reference value x* will not choose revention, since their disutility of being ill is lower. We assume that x is uniformly distributed across the oulation. For simlicity, we also make the assumtion that consumers are risk-neutral. These assumtions hel simlifying the algebra when deriving the results, without affecting the direction of the changes as a result of a change in a determinant of rice. F(x) has a minimum value of 0 and a maximum value of. For any value of x higher than, F(x) will be and for any value of x lower than 0, F(x) will be 0. The rovider of reventative care is a rofit maximizing harmaceutical firm. The firm rovides its roduct in a market, where individuals are the rimary urchasers. 4 Costs are assumed to be linear, since this simlifies the analysis without affecting the results. Thus, the rofit function of the firm is: π = ( ) ( )α () where is the rice of reventative care and α is the er unit cost of roduction, which is constant (linear cost or constant marginal cost assumtion). The first order condition for maximizing rofits is: = ( ) + ( ) - α ( ) = 0 (3) Throughout the aer we assume that rices are strictly ositive: 3 dynamic model with more than eriods could be introduced, but this would not add any insight to the model. The reason is that the goal is to see how rice adats to demand and this simlification does not affect the direction of results. 4 Costs may be covered by health insurance (deending on the model discussed below). 8

10 >0, >0 The methodology used to determine demand for reventative health care is based on the vertical differentiation model by Tirole (988). In that model, a demand function is constructed deending on how imortant higher uality is for each consumer. The main assumtion is that consumers agree over the reference ordering, but some consumers are willing to ay a higher rice than others for the same uality. In this study, consumers refer a better-exected level of health to a worse one, but they have a different level of disutility for a given disease. We now roceed to see how ricing takes lace under different circumstances. 3. One roducer - Monooly The rovider of the only roduct in a new theraeutic class acts as a monoolist in order to maximize rofits. There is no cometition from other substitutes that serve the same goal. The ricing decision is subject to consumer s demand function. 3. Demand by Consumers without health insurance If the consumer chooses the reventative care her utility is: U = h i sh x i sh i s (4) y urchasing reventative care in eriod, the healthy erson (with level of health h) reduces her utility by the rice of the roduct,. In eriod, discounted by β, her utility is the sum of the robability of becoming ill, (i-s), multilied by the health level of an ill erson (h-x) and the cost of cure ( ), lus the robability of remaining healthy, (-(i-s)), multilied by the health level of a healthy erson. h, s, i and x are constrained between 0 and. If she does not choose the reventative care, her utility is: U = h ih x ih i (5) In this case, the utility in the first eriod is the health level of a healthy erson, without any other costs, since the individual has not urchased any reventative care. Her utility in eriod, discounted by discount factor β, is the health level of a sick erson (h-x) lus the urchase or reventative care, multilied by the robability of getting ill, i, and the health level of a healthy erson, h, multilied by the robability of not becoming ill, -i. The robability of getting ill in euation (5) is reduced by s comared to euation (4), which is the reduction of the robability of getting ill due to the use of reventive care. We assume that the health level h enters the utility function linearly. This is a simlifying assumtion, 9

11 since if the health level would enter exonentially with 0<h< the analysis would become more comlicated and the changes would be towards the same direction, with only the magnitude changing. The consumer seeks to maximize her utility. Thus, she will choose revention if her utility is higher in this case rather than in the case in which she does not take revention, or when: h i sh x i sh i s h ih x ih i x (6) s (x reflects the worsening of health due to illness). So the fraction of the oulation with an x larger than will choose to take reventative care, since this is the fraction of the s oulation whose health level worsens most if affected by the disease. Peole with x below the reference value x * will not choose revention because the disutility of being affected is lower. y substituting (6) into the demand function () we can rewrite as: = F s (8) x is assumed to be distributed uniformly among the oulation so we can rewrite (8) as: = s (9) Quantity of the reventative roduct is an increasing function of the total oulation, the rice of cure, the discount factor and the effectiveness of the roduct, and a decreasing function of the rice of reventative care. From euations (8) and (9) it follows that if - F s 0 => s 0 => bs, nobody would urchase reventative care and that if - F s => s => bs( ), everybody would urchase reventative care. We roceed to see what would haen when bs bs( ). The demand function for reventative care is 0

12 = (0) s s which is euivalent to s s () The first derivative of uantity with resect to rice is: ( ) = < 0 () s y inserting (0) and () into the monoolist rofit maximization function (3) we get: s s = s s a a = 0 s (3) The rice of reventative care is an increasing function of the discount factor, the effectiveness of the roduct, the rice of cure and the er-unit cost of roduction. The artial derivatives of with resect to s, α and are: ( ) = > 0 s = > 0 a s = > 0 The more effective the good is, the lower the exected disutility originating from illness, so there is sace for higher disutility from increased exenses for urchasing revention. rise in the er-unit cost of roduction of the good will also lead to an increase in its rice, as a result of the rofit function maximization of the monoolist. Poulation size (), the initial robability of getting ill in the absence of reventative care (i) and the disutility of illness (x) have no effect on the rice of reventive care in this setting. 3. Demand by Consumers with full insurance We now consider the case of a consumer who is fully insured and exresses demand for reventative health care herself. This is not a realistic case because health insurance exresses demand as a third arty ayer and is the arty who negotiates rices with the rovider. evertheless this examle is of theoretical interest. If the consumer chooses to take reventative care, her utility is: U = h i sh x i sh (4)

13 In eriod, the consumer has the utility of a healthy erson with no health exenses because any urchase of reventative health care is fully covered. In eriod, discounted by β, her utility is the sum of the robability of becoming ill, (i-s), multilied by the health level of an ill erson (h-x), and the robability of remaining healthy, (-(i-s)), multilied by the health level of a healthy erson (h). Cost of reventative care or cure does not enter her utility, since the consumer has full health insurance and exenses for urchasing reventative care or exenses due to otential illness are fully covered by the insurer. If she chooses not to take reventive care, her utility is: U = h i( h x) ih (5) In this case, the utility in the first eriod is the health level of a healthy erson, without any other costs, as before. Her utility in eriod, discounted by discount factor β, is the health level of a sick erson (h-x) lus the urchase or reventative care, multilied by the robability of getting ill, i, and the health level of a healthy erson, h, multilied by the robability of not becoming ill, -i. The consumer will choose to urchase reventative care if the utility when taking revention is higher than the utility when not making the urchase: i sh x i sh > h i( h x) ih h sx > 0 (6) which holds for every x > 0 and s > 0. This means that the consumer will take reventative care if it has even the slightest ositive effect on her health (s > 0) and the ossible illness causes even the slightest disutility to the consumer. In this case, demand is (given that x [0, ]). Hence, demand euals the total oulation and is erfectly inelastic. Consumers do not ay for reventative care (as they are fully insured) so they demand the same amount of revention at any rice level. This can be considered as moral hazard because consumers consume more reventative care than what they would have if they were not insured and they exress demand for reventative care even if the cost is higher then the total exected cost of illness. This, of course, has some limit, as the funds of insurers are finite. Therefore, there is some maximum oint for rice. Changes in the level of effectiveness of revention (s) will not affect the rice or uantity demanded. ll consumers are strictly better off by ursuing reventative care because they do not ay for it (or because their individual urchasing behaviour does not affect health insurance contributions). The only case in which there would be a difference would be when s changes from s = 0 to s > 0, since in the first case they would be

14 indifferent between urchasing care or not and in the second case they would all demand this good. ut we have assumed that s > 0, because the roduct is suosed to have at least a marginal ositive effect. The rice of cure, would also not have any effect on demand and conseuently on the rice. Individuals will urchase the good no matter what the rice of cure is as they are always strictly better off. s long as α < max, a change in α will not affect rice or uantity. If α exceeds the maximum ossible rice, the uantity sulied will be zero. The size of oulation (), the initial robability of getting ill (i) and the disutility of illness (x) 5 again have no effect on the rice of reventive care. FIGURE In this articular monooly market, the single rovider will sell at the maximum ossible rice at which there will be demand, as long as rofits are ositive. more realistic case would be the resence of co-ayments on behalf of atients. co-ayment only for revention and no co-ayment for cure would be euivalent to case 3., with = 0 and eual with the amount of the co-ayment. The new rice function would be = s a The artial derivatives of with resect to s, α and would be: 5 Given that x > 0 3

15 = > 0 s = > 0 a If both revention and cure are subject to co-ayments, the solution would be the same as case 3., with and being the amount of co-ayment for revention and cure resectively. Conseuently, co-ayments would change the outcome from a very high rice to a more reasonable finite rice of revention. 3.3 Demand by cost minimizing insurer Demand originating from a fully insured individual is an interesting theoretical case, but in ractice it is health insurance that normally exresses demand as a third-arty ayer. Cost minimization is vital for health insurance given rising health care costs. Preventative care is costly, but may also hel avoid future costs for cure of a disease, since some insured will avoid falling ill if they consume reventative care. The insurer is interested in covering reventative costs because this decreases exected future health costs, as long as the total cost of revention does not exceed the monetary cost of cure. The variable reresenting individuals utility originating from their health level does not enter the insurer s utility function Different disutility from illness across individuals Suose disutility from illness (x) varies across individuals. This is the same assumtion made in revious cases. If the individual takes reventative care, the cost for the insurer are eual to: C ins = i s (7) This is the rice aid in eriod for reventative care, lus the cost of cure, multilied by the (reduced by s) robability of becoming ill in eriod, discounted by β. If the insured individuals choose not to take reventative care, the cost for the insurer is: C ins = i (8) This concerns only costs in eriod, since in eriod no reventative care is urchased. Costs involve the rice of cure,, multilied by the robability i of getting ill, discounted by the discount factor β. The insurer will cover the reventative care costs if 4

16 i s > i < s β (9) If this relation holds, then the insurer covers reventative care. Individuals then take all the reventive care the insurer covers because they are strictly better off by taking it without aying. Thus, demand is for rice < sβ and 0 for rice > sβ. FIGURE Given this demand function, the firm will sell reventative care only if it has nonnegative rofits. Since cost is linear, it will rovide the good only if α < = sβ. If indeed α < = sβ, the firm will suly the roduct at rice = sβ, leading to revenue maximization of * = * sβ. α > is highly unlikely in a harmaceutical market with small er unit costs. If the firm sets a higher rice, her suly and rofits will be zero. y setting a rice lower than sβ, its rofits will be lower than if the rice was sβ, since they will rovide the same uantity () at a lower rice. monoolist would sell at = sβ. This is the only oint at which marginal revenue is not zero (marginal revenue is zero for 0 < < and for > and * for =). The highest ossible difference between total revenue and total cost for the firm would be exactly at the oint where =. Thus the monoolist is willing to sell uantity at rice = sβ Different effectiveness levels across individuals We now consider the case in which effectiveness of reventative care varies across individuals. s is uniformly distributed across individuals, with s [0,], while x is 5

17 common for all consumers. We make this assumtion because this is the case in which the insurer will not urchase reventative care for everyone, but only for the consumers with a high s. In 4. and 4. we did not have to make this distinction because the results would have been the same. s above, the insurer will cover the reventative care costs if i s > i Demand for reventative care is then = F( s) Substituting s into euation () gives us: = s (0) () F which due to the assumtion of uniform distribution of s among the oulation, is euivalent to: = The fraction of the oulation that is covered increases with the cost of cure and the discount factor and decreases with the rice of revention. Euation (3) is euivalent to The first derivative of with resect to is d d () (3) (4) (5) Substituting euations (4) and (5) into the rofit maximizing euation (3) of the monoolist gives us: = 0 (6) (7) = > 0 a 6

18 = > 0 Price of reventative care increases with the rice of cure and the er-unit cost of roduction. The difference comared to the case of universal effectiveness s across individuals is that now only a fraction of the oulation receives reventative care. In the revious case, either all consumers or none received this care. n increase in the effectiveness of revention (s) would lead to an increase in its rice. The same will hold for the rice of cure,. n increase in the rice of cure will lead to an uward shift of, as the monoolist can now take advantage of the fact that revention becomes more rofitable for the insurer, so an increase in can fill in that ga. 4. Multile cometitors roviding reventative healthcare Cournot Cometition ssume only two firms articiate in the reventative care market (duooly case). oth firms, and are identical, roduce similar roducts of the same theraeutic class, have the same roduction function and enter the market simultaneously. Cost of R&D is a sunk cost, so it does not lay a role in this analysis. The ost-r&d cost functions are the same for both firms. This is the case of a Cournot duooly (Cournot 838). 4. Demand by Consumers without insurance s seen in the initial analysis in the monoolistic case (section 3.) and according to euation (6), a consumer without insurance will choose revention if her utility is higher in this case rather than in the case in which she does not take revention, or when x s (6) So the fraction of the oulation with an x larger than will choose to take s reventative care due to the fact that this is the fraction of the oulation whose health level worsens most if affected by the disease. Peole with x below the reference value will not choose revention, since the disutility of being affected is lower. Substituting in the same manner as in the revious section, gives us the following demand function 7

19 = s (8) which is euivalent to = (9) s This is the demand function and is euivalent to s (30) s s With two layers in the market, the function becomes: The rofit function for firm is: First order conditions are: ( ) s s s (3) s ( s s ( )) (3) 0 s (33) y symmetry, s fter substituting and rearranging, the euilibrium uantities are: (34) Total uantity is = * * (35) 3 s (36) Substituting into the demand function gives us rice : s s 6 (37) 3 The artial derivatives of with resect to s, α and are: = > 0 s 3 = > 0 a s = > 0 3 8

20 s exected, an increase in reventative care effectiveness (s) will trigger a rice increase. The more effective the good is, the lower the exected disutility originating from illness, so there is sace for higher disutility from increased exenses for urchasing revention. rise in the er-unit cost of roduction of the good will also lead to an increase in its rice. decrease in the rice of cure is also exected to lead to an increase in the rice of revention. If cure becomes cheaer, a roortion of the oulation will not demand reventative care for that given rice, because their exected utility will be higher than if not urchasing reventative care. This will lead the rovider of revention to decrease the rice of her roduct. The size of oulation (), the initial robability of getting ill (i) and the disutility of illness (x) have no effect on the rice of reventive care. 4. Demand by Consumers with full insurance s discussed in section 3., in this theoretical case, demand euals the whole oulation and is erfectly inelastic. Consumers do not ay for reventative care out-ofocket so they demand the same amount of revention, regardless the rice. s exlained in section 3., this is a case of moral hazard. In a uantity cometition model, such as the Cournot model, the rice would be set at the highest ossible level (theoretically an infinite rice, but in ractice a very high rice). The cometition among the two firms is in the field of uantity. In this case there are multile euilibria. There is an euilibrium if * *. ny nonnegative combination of uantities adding u to is an * * euilibrium. For examle,, 500, 500 is an euilibrium. 4.3 Demand by cost-minimizing insurer 4.3. Different disutility from illness across individuals Suose disutility from illness (x) varies across individuals. This is the same assumtion made in case 4.. The insurer will cover the reventative care costs if i s > i < s β If this holds, then the insurer covers reventative care. Individuals then take all the reventive care the insurer covers (as in section 3.3.) due to the fact that they are strictly better off by consuming it without aying (Figure ). Therefore, demand is for rice < sβ and 0 for rice > sβ. In this case, both firms will sell the roduct in the market at rice = s β, which is the rice that maximizes their rofits. Cometition is in the field 9