David Crainich présente : Disease Prevention in Adverse Selection Equilibria



okay first of all that to say thank you to Mari Beasley and Phillip for dragging me to this workshop and for giving me the opportunity to present one of my research projects on personalized medicine in the paper I am going to present now I basically analyze prevention disease prevention when there are asymmetry of information in the health insurance market so asymmetry of information between insurance and policy orders I will not talk about moral hazard I will just talk about adverse selection because we are supposing developer that the adverse selection I'd mentioned in the title is the result of two things first the development of predisposition tests which are tests providing individual with better information about the probability of developing disease we provide information about the baseline priority of disease in the model the test will say whether people are Irish or risk and two the second reason for which there is adverse selection but will be due to the legal environment in which insurance operate because we will assume that the use of genetic information for making purposes is prohibited and the question that we will raise is the following are the benefits related to the development of predisposition test exploited in these adverse selection equilibria this there is a switches of information the benefits of predisposition test in the paper take the form of better informed decision so better targeted prevention decision so if the test reveals that you provided to develop a disease si so perhaps a good thing would be to redirect resources in order to fight this disease so the big testing gives an information but the question is do they explode and why could they potentially not exploit this information because we know that insurance and prevention decisions are related on the other hand in adverse selection equilibrium some agents are not the job the coverage insurance coverage that they obtain is not optimum okay they would obtain more coverage in the absence of asymmetry of information the insurance market so since there is a distortion in the insurance decision and since insurance of prevention are related we just question the the extent to which individual use the information provided by attending testing so in the world today when they have the information do they adjust deferential decision to the newly available information that's basically the question I am trying to I think you mentioned a few papers on the similar topic let's say so the paper I am going to mention now are all related to genetic information plus prevention plus in this case we have more of other than adverse selection so these three papers did both with others and moral hazard so 13 Posey so they suppose that I wish people every opportunity to perform self-protection action so sir protection actions are actions reducing the probability of loss and they in the paper they establish the conditions under which information on the baseline quality of disease as a positive private value and the positive social value if you have an information about the baseline probability of loss on the one hand this is beneficial because you can adjust your prevention decision in this case the production decision to do information but when you take a genetic test you are exposed to a classification risk and this is why it's not a given that the private value of information is positive and this is exactly what they do same thing for cooling and ice and 2002 also they analyze the economic inefficiencies in the use of genetic testing so economic inefficiencies poker well socially optimal tests are not taken or when socially not optimal tests are taken and they relate this to the information provided to insurance and also to the type of insurance coverage that people have do they have only a compulsory insurance or do they supplement this compulsory insurance with a voluntary insurance and then we have more recently paper by Richard bitter and restricted and partisan they analyzed the welfare implication of different information regime any health insurance market as I said earlier we just talked about the strict prohibition in people when insurance cannot use the information but were other ways to manage the information in the insurance market and what they find that another regime which is the disclosure duty regime dominates the the other available regimes any disclosure beauty regime basically insurers can ask policy order to disclose the genetic test result but they cannot reach wire policy orders to take additional tests and this is what they do I hope that you to other papers for also from people mostly present in the room so we have didn't you read it so they also talked about self protection and they define the again they talk about the value of the genetic test in relation to the efficiency of self protection and the cost of self protection okay so they do talk about self protection but another let's say prevention action this servant so surveillance activities increasing the probability of early detection of potential diseases and I think you work you are going to talk about this paper later but in two words they analyzed welfare implications of genetic test and in the paper there isn't more other because patients are covered by compressor and system so they do not internalize the cost of the cost of surveillance and the cost of treatment and so that what they show is genetic testing even when they are costless might decrease welfare and I finished with two papers dealing only with adverse selection we have multiple zero here until a decision to perform genetic tests there lowing informed self-insurance decision so second shot is the second category of prevention actions and it refers to the action that reduced the extent of the loss okay so self insurance actions do not modify the property of laws but the the the damage in his in his office and the sabbatical 0 here also compare different information regimes in the health insurance market and as and sister shows they find that the discontinuity regime dominates the owners and then I finish with a paper that I published recently close to what basically and again did also self insurance efforts also with no moral utter on the adverse selection but instead of considering different information regimes in the terrace insurance market I take the strict prohibition case an industry prohibition case I considered different equilibria that may arise because but because you consider that in case of strict prohibition we have the rod silence niblets equilibrium I will be find this very soon but actually what you have adverse selection you might you might have different equilibrium okay and this is what I do this previous paper another will present today is an extension of this previous paper it was actually when I before I published it I try to I submitted my paper to economic jewelers and they didn't like this there is a perfect of course and this is why I said ok they I was told that there is now a tendency for insurance companies to ask for all kind of genetic testing out there even though it's not yet correlated to a particular disease whether or not it's feasible and the extent of the treatment that can be provided and they have that in their database and then the onus is on the patient to let their insurance know if the genetic test that is in their database has finally shown negative effect and I know they do that for viruses or any contaminants and things like that they'd like to know everything that was measured for a particular individual they want them to have them in their database have you were so everything are you talking about the results of genetic tests are you talking about other information genetic tests we won and all the rest I know they apply this when I understand about genetic test to one thing but I will consider here that they cannot using this information is forbidden and this is the regulation that apply in many countries just in Europe us so this is the this is why I take this assumption now the fact that they use other information for instance family history is this valuable information when you try to define the potential risk of of a patient I do not consider it okay even though I should the next extension but what I will instead is that you slug from no information at all and then you have the information okay it simplifies a lot the bottom so as I said I will consider that self insurance actions reduce both financial and the ass consequences of disease and this is why I will work with high dimensional utility function depending on wells and ask the difficulty when we introduce such an assumption is not that self insurance besides its effect on the curve on the financial it's a the big concern beside this financial effect the difficulty is not to assume that self insurance person as an effect on us because this is just an additional incentive to perform self insurance action the difficulty comes from the fact that the researcher in nurse economics has shown that the marginal utility of wealth depends on else and some papers the first I mention here show that the marginal utility of well as Rises with as with the end stages so it means that the explanation might be you better enjoy an extra dollar that you have while you are in good shape because for instance you can travel you you can do anything because you are good at straight and then you can enjoy the money that you have and then you have all the papers assuming it's not the issue they analyze the question and they found out the opposite saying the marginal utility of words Rises when your L status okay so because now okay I will there's one other one will get longer speaks Russian oh that's fun but okay if you have specifically this it's not just shocked in February these other papers you don't really only solve problems yeah yeah because in theory what I said is the marginal utility of else prizes of course with us but you have the opposite also not the income and model utility of s may rise or fall with with whispers it's exactly the same the same a problem okay but if you if you like these these papers one last thing this model will be I guess something you guess but it would be it's modern ok let me start with the assumptions that that I make so first individuals maximize expected utility utility depends as I said on wealth and as the value and age and you have a utility function which is by language okay let me introduce the notation here you have u 1 so u 1 is the marginal utility of words it's the first derivative of the utility function with respect to the first argument which is worse it's positive u2 is the marginal utility of wealth of no else so the first derivative with respect to the second argument of the utility function ok the boosts positive and the second derivatives u 1 1 u 2 2 a negative because we assume that people are alert risk-averse towards financial risk and risk okay the definition of risk aversion and ethics okay so this was just risk emotional impact correlation aversion I guess you have to respect to the same argument yeah no yes so with respect to X and with respect to X okay so for instance people like when they okay okay so no the assumption aspect is just the diver okay and it reminds me that I forgot to mention something you won two is the cross derivative of the utility function and so I said okay no assumption about this side because of all derivative says all the marginal utility of first changes with with us okay okay with the probability P individuals develop a disease financial as consequences which are denoted capital L and M and in order to deal with diseases who were supposed agents at two instruments let me start with self insurance so self insurance is one way to mitigate the consequences of disease so that the capital L and capital and are written as a function of n okay and the assumption is that L Prime and s negative so it simply means that when you increase your self insurance effort you reduce the financial consequence of of the disease and the say for n prime and when you increase the second chance approach to reduce the health consequence of the disease the second derivative of this function about these two functions are positives I mean the returns of self insurance are decreasing so I mean that your first self insurance efforts are very efficient they reduce what a lot the the Aston financial consequences of the disease but the the following actions have less impact and and so is the intensity of self insurance action and the cost of self insurance is supposed to be constant okay self insurance actions include programs allowing early detection of diseases onset and this more effective treatments such as the use of mobile grams of cookies so it's one form of surveillance except that in the paper about surveillance increasing surveillance increases the probability that you detect early but in this case once you perform selfie trance actually it detects the disease okay increasing in its intensity make different stats increasing the frequency with which you perform this surveillance actions the first instrument and then we have another instrument which is insurance because insurance contracts are sold by perfectly competitive insurance companies okay so it will just mean in the model insurance companies do not make profit and a critical assumption is that self insurance actions can be observed by insurance companies so that the contracts are contingent on the intensity of self insurance that's a critical assumption because of course all the prevention actions cannot be observed by insurance but if you consider surveillance for instance you can show to your insurer to perform certain insurance actions to meet because in fact most of the time insurance to the customs no no the insurers do not pay the prevention insurance just pay something which is random if the mother they do not play something which is not you decide but okay this is something this is something I could I could assume what that what they do what they do is if you perform the self insurance action then your insurance premium force okay but they don't pay the action at the cost of the action itself okay yeah and also the timing of the model is that you choose the intensity of insurance before the risk is resolved right yeah so what you're thinking is something that you do if you can sing so you know this secondary prevention because here the financial cost so it means that what ensures sell the policy hundred is a contract that defines of course the coverage but also the self insurance action but the contract specifies the self insurance action since they know the self in transaction they know the extent of the loss and then you have sovereign sensitive insurance and immunity is equal to the cost of the treatment something that they can observe times a and a is the insurance coverage a being would be zero and one okay so the contract that you that you buy specifies the self insurance action that you will have to perform the insurance premium capital R is equal to the insurance in them DT times R small R which is the insurance price or the cost per Europe covered okay when R is equal to P the property of disease we say that the contracts are actuarial a choreography okay that's all then you have a genetic test which is perfect and cross last this is a predisposition test and we will assume that insurers do not know the individuals information not stages so it means that as an individual you can prove to your insurer that you didn't take the test okay so that and this is a paper by a routine this turn the test is taken in the seat and the test swords the population to two groups the arms group and the lower is group so PhD theses of the high risk group people in the lowest group is a probability of disease DL and the first group represented proportion of the population although the interest and observe their will let's produce we are not going to present dialog because you told me from the Titans the papers would be okay inevitability of disease is p.m. which is simply one minus lambda x times the pianist and intensity page okay last piece of information about last assumption the adverse selection equilibrium because we will consider three type of a tree equilibrium that will depend on two things so we will have four situations and three equilibrium so the kind of equilibrium looking depends on our interest make profit and the proportion of iowa's in the population if we suppose that interest make non- profits on each contract each time then sell the contract the constraint is that they make more losses on each contract and if the proportion of I risk is sufficiently I we have roots island Stiglitz equilibrium otherwise if some non- profit on each contract and the proportion of iris is low or below this threshold we have another contract which is Wilson pooling equilibria and then we have the other way to make profit the instead of making profit on each contract teachers may make negative profits losses on some contract as long as they are called balanced by the profit that they made on other contracts okay so that in the second case we are those of the cross is a decision between the field contracts okay and in that case we have again the road silence eaglets equilibrium if lambda is sufficiently I and another equilibrium which is amazing in Spence equilibrium if lambda is sufficiently low now let me explain what are the consequences of these four situation because this is crucial because we'll analyse self-insurance decision in these four cases you see that the root challenge stiglitz is something that you find as long as the proportion of is is sufficiently high let me start with non- profits on each contract this is the Wilson pooling equilibrium pooling in the sense that everybody buys the same contract if I were to devise the same contract and if insurers have to make non- profits and if there is comfort since there is competition the profit that they make is equal to zero so it means that the price of the contract will depend on p.m. which is the average probability of these so everybody buy the contract based on the average probability of disease that's the Wilson equilibrium now and this is something that you can reach if the proportion of high risk is sufficiently know if the proportion of virus is iron a dress shop you have the recession stability separating equilibrium this is a cigarette ik equilibrium because in procedures do not by the same control and actually you have to contract a contract design for the I with people and a project designed alors people of course if you offer these contracts and if you offer the full coverage nobody will buy the expensive contract again the Irish people will say ok I'm the lowest person I planted Laurie's contract and so insurance making losses so that in order to give incentives to Irish people to buy their contract the contract that this design for them what insurers is that they for the low-risk people so those who are buying the less expensive contract they say ok if you want to buy the less expensive contract I have to reduce your insurance coverage and this is why we have a directional stability equilibrium the contract that insurance premium up based on the true probability of disease th for the lower input for the iris p.m. for the low-risk and iris people obtain the full insurance coverage while lowest people obtain on the departure of insurance coverage that's the relief and will do now if we suppose that insurance may not make at the profits do not on each control but on the average contract but they might do they could say to the fat start from the red Chinese civil it's equilibrium they could say to the low-risk people okay for the moment what you have is a contract which is not expensive because it is based on your probability of disease which is low but you'll take only a partial coverage what if I propose I offer you a higher coverage but of course if I offer aisle coverage you will have to pay more because otherwise you will attract Angus people and this is why at the Miyazaki spends equilibrium I wish people obtain full insurance lowest people obtain partial insurance but they don't pay a premium which is based on the true probability of disease and typically Lord's people pay a little bit more than an insurance premium based on the local disease and Irish people pay a little bit less than premium based on the royalties okay so I'm not sure that I will have the time to analyze their self insurance actually all this contract of at least it shows what what I try to get your last name and I will say that I would like if you have a small or very small fraction of very high-risk types yeah everybody else is much more of this yeah which i think is quite typical of many smaller too many yes yeah then I would just change your glass descriptor a little bit by saying low risk types babe a little bit tighter than their true risk and I was supposed to pay a lot less okay so the reason I say that is because you get a more effective more effective targeting of implicitly in distribution from the good Vista the bad risks in that scenario that's not true okay yeah and this is at this specificity you have this very small fraction of people so from a utilitarian suspect that they like perspective yeah yeah here I just said that Louis people of a partial coverage but I didn't say that what they obtained is if the percent of it might be very iron very close to other percentage positions yeah okay but yes if you have a very acutely you still have single yeah okay individual make insurance and self insurance decision so genetic tests are not available now I am going to try to explain how people make self insurance decision and I start when they have they don't have the information okay there is not really looking for me and when there is no genetic information it means that everybody is in the same starts from the same position so as I said when you have no information you do not consider other variables everybody thinks that is or her property of disease is P and laboratory activities and then you have the equilibrium which is defined by the values of a the insurance coverage and self insurance action and R which is the price of insurance that maximizes this expected utility so you have with the probability 1 minus P M people are healthy if they are LC this is their wealth level and this is there as stages the wealth level is W initial words – what they pay for the self insurance action – the insurance premium under else State is H they are sick with the probability P M okay in that case the best level is W – what they pay for themself in transaction – the insurance premium – for those who do not buy the full insurance contracts of module whose a is lower than one – the out-of-pocket payment okay and in this case we have the S States is equal to H – and which is 5 the health consequence of the disease okay and we have two constraints they must be people must be included between 0 & 1 and this constraint says that insurers cannot make negative profits but this will be easily so because since I wish you perfect competition R is equal to 2 p.m. so that we have the following the following problem so this is the expected utility this is the constraint and you see here that the only thing I've changed is that now I consider that the price of insurance is depends on p.m. via red probability and this is module and then you have three first-order conditions I'm going and we're trying not to be too too too technical simply first consider that what an integer solution so that you don't have a corner solution so in this case it means that a is lower or equal to one but when a is equal to one it's not a constraint because of the constraint that's not the choice and then I will explain when this this occurs okay why do you have an interest solution that is equal to zero and what this first-order condition simply says is that the marginal utility of words in the no disease case must be equal to the marginal utility of words in the disease case okay and then you have the second order condition with respect to n intensity of self insurance actually what does self insurance changes so first you pay for it so it reduces your wealth in both in both cases okay that's the cost and then you have the first advantage because when you increase your self insurance action your insurance premium force okay so you pay a lower insurance premium in both cases and then we have two additional advantage the first is that and these two additional advantage occur in the disease case because you reduce the extent of the financial loss this matters if your a is not equal to 1 and then you reduce the extent of your of the eldest consequence okay and what I have explained is exactly what you have here in the first-order condition you have all these effects something that is important is that I said ok to the two last advantages are that you reduce the financial consequences and you reduce the X consequences but you wait these two advantage by the probability that you are that you are that you are sick okay you wait these two advantage by people okay and something interesting is that when you use these two equations together we have this actually everything simplifies and here I just look at the self insurance decision so this is what I will call the self-insured decision rule and you see that the self insurance decision rule is the same when you have an inferior solution okay when you have a cola solution it is slightly different I will explain what but first look at the self insurance decision would simply what it says that when you make yourself each one decision you consider the cost of self insurance you consider that the the the financial benefit of self insurance it reduces don't forget that this is negative it reduces the financial consequence of the disease and you wait this reduction but the probability of this is p.m. so that's the financial effect of self insurance and here you have the else effect of self insurance with a probability P R you reduce the else consequence of the disease so you have a financial effect and the else effect and these two effect and this is what makes the analysis complicated compared to the first paper these two effects are weighted for the first and Jill talking about financial consequences they this effect is weighted by the modularity of wealth and says since this second effect is I'm talking about as consequences this is weighted by the marginal utility of and okay what's interesting is that well of course when I computed first my self order from first to the condition you see that it depended on a in this case you see that combining the two first order condition you see a third piece it doesn't disappears to 30 because a will have an impact on the M okay and so it will have an impact on the marginal utility of wealth and other marginal utility of words but at least you should in the decision rule when you wait the benefits and the benefits re and the cost of self-assurance a does not appeal anymore in the second decision let me now try to explain intuitively why we do obtain this self insurance decision and to do it I will consider the simplest program and the simplest program is the one I dealt with in the previous paper is when you have uni-dimensional utility function so no else consequences and then we will progress towards the resultant of just in this way so no else consequences insurance so you have insurance and self-assurance insurance is available at fair odds okay so insurance available at fair odds relocates worse from the novice estate to the disease state and it does no cost I know cause I mean no extra additional cost because the premium is based on the probability of disease okay so it means that the redistribution through insurance leaves unchanged expected worth so this is a pure redistribution effect and this is why risk-averse people like insurance and they purchase full insurance contract this is the old wizard bye music okay that's for insurance now let me consider self insurance actually self insurance plays the same role as interstellar disputes wealth from the no disease state to the disease state okay but the difference it does it's not this does this redistribution is not modified the expected ones and this is due to the decreasing returns of self insurance okay because as I said the first unit of self insurance are very official okay while the when you I don't know you perform your tenth or eleventh insurance insurance action the effect on the loss is is less strong okay so it means that the first units of self insurance redistribute wealth to the new disease from the notice it will be this case while increasing expected utility and from this point so beyond that point self insurance redistribute wealth but it reduce the expected they expect that worth so that the best thing to do is to use self insurance if you are risk averse the best thing to do is to use self insurance as long as it released redistributes wealth between the two states and increase the expected works once you reach that point then you use insurance because insurance distribute wealth but does not modify expected expected wealth okay and this is why in this in the first-order condition for self insurance but I put the self-insured decision rule if you can serve this term because you just consider a wealth and no hat you have this so this must be equal to zero in three places and this is exactly what I have you okay so the decision when as us when there is no health diseases have no effect comment on else okay and graphically simply it means that you start from this point so in the x-axis wealth wealth in the Norris case and here you have wealth in velocities okay you start from this point you would like to go there okay you would like I have worked in the Norris case and in the Ross case but self insurance and insurance offer the opportunity to go in this direction okay and when you use insurance along this straight line it means that the marginal paddy expect that worse remains unchanged so first best thing to do is just to start with self insurance and from this point instead of continuing with self insurance you choose insurance and if you are risk averse to go to that point which is the diagonal because you're risk averse insurance is available at fair odds and you fully the okay now that's the simplest case now let's take another case which is by by dimensional utility function this time but with assuming that self insurance has no impact does not reduce the Earth's consequence of the disease and prime is equal to zero okay self insurance just which uses the financial consequence of this is not the else consequences okay and in this case we have the following insurance demand they trans demand depends on my you want to term the sign of you want to it depends on how the marginal utility of words changes with else specifically if the marginal utility of words does not change with else okay in this case you demand for insurance but if let's suppose that imaginative utility of West rises with and so it means that you prefer an additional dollar when you are in good state in good and state rather than one you are in the paddle state side means that you will not fully etrem you will prefer to keep this extra dollar you will prefer not to pay the premium tank okay perhaps your reimbursement your intensity will be lower but this is my my main trait of I'm prefer keeping my words when I am in the good end state so this is less than full coverage of the Martin utility of course prices whistle and you have the opposite of course well the marginal utility of furnace force with the end state people would like to buy more than full insurance if they can and my parents it's not alone but if they can they would buy more than full insurance they would offer insure because they would like to have more money when they are investing so now what you have in this case back to my three self-insurance conditions but if M fried n is equal to zero this disappears this disappears disappears can you have actually done your left is only this term okay equal to zero so it means you have exactly the same self insurance decision rule which is this one okay so it means that when else sorry when diseases have an impact on else okay but when the self insurance action does not reduce this else consequence the self in front decision rule is simply the same okay if I go back my figure simply because the choice that you make between insurance and self insurance remains unchanged again you would like to go there you will have the opportunity to go to go there okay you choose self insurance that part and then insurance but if you want to is deeper to zero you stop here if you want to is positive you stop here if you want to is negative and if you can buy all the returns you you go there okay but it doesn't change where you should stop where you should stop it's exactly at the same point which is as long as I make as long as self insurance increases by expected words I take self insurance and then I choose I choose insurance okay last case which is the case that I discuss in the paper like I mentioned that utility function and self insurance as an impact on else it reduces the as consequence of the disease then we have something more complicated but what you do actually is because in this case you have self insurance as a financial effect and the else effect and so the financial effect is the one I've just mentioned and then the else had practiced this one and what you do simply is to wait the financial effect and the answer fact by the marginal utility of worth and and this is why we end up with this with this condition one last day why do we have three different conditions but these are not actually I don't have two different conditions but this one looks slightly different it's simply because when you want to expose it if you would like to buy full insurance okay but you cannot you cannot buy full insurance so it means that in your insurance decision here you cannot make this and this equal because of the constraint so if this and this is not people the marginal utility of wealth in the disease case and the marginal utility of course in the dodaf escape I'm not the same and this is why here the financial consequences of self insurance are weighted by unexpected marginal utility of words okay this is because we have a corner solution why in these two cases because the optimal insurance decision is is taken then the marginal utility of words in the two states are the same and so that this simplified okay if a you won a is equal to u1 b then you can write this as being equal to p1 b as i write here or okay fifty fifteen and before the questions or before the element for yeah I'm sorry too long because I now I must talk about ownership adverse selection to do the following there are two ways to present the paper I defined the optimum here and then try to find whether the optimum is reach in all these adverse selection equilibrium I'm not going to do this okay and just I will just say okay do do we use the door I present my paper at the beginning of the top and say okay do we use the information before talking about the selection one word about the residual case if the insurance companies are allowed to ask policy orders to disclose the test results when you compute the equilibrium you have for self insurance you have these two combinations and as you can see around this is not clear but the I here is equal to L and so in this case people have the information okay people who are tourists know that they are the risk people who have iris know that there are times okay and what occurs the Lisa fair in receiver cases when for instance when you if you want to is higher or equal to zero you see here that they wait the financial effect of self insurance by if you are lori's by PL and the past effect of self insurance is weighted by P and purse also administer you use the receiver the receiver you use the genetic information because you wake these financial and as consequences of self-interest by your true mobility of disease now and I start with adverse selection consider the pooling equilibria so in the put in equilibrium I remind you that the people by the same contract which is based on the average probability of disease so and in this case the insurance choice is made by lowest people okay so lorries and all these people will simply by the same so this is the expected utility of low-risk people knowing that they know that they are at low risk okay but they pay the average insurance premium okay they transform depends on p.m. they would like to say to the to the insurer I am a low risk insurance cannot take with this information okay and then I compute the equilibrium and now you will have to believe me but so you have a new insurance decision and what you have is the following this is the self insurance decision rule financial effect of self insurance has effect of self insurance but you see now that the financial effect of self insurance is weighted not by P and this is a decision taken by the low risk agent and the low risk agent knows that is a low risk agent despite this the way he or she waits the financial benefit of self insurance and the way he or she waits the ass benefit of self insurance is by p.m. the average probability of disease which is quite surprising they have the information they know that they are I guess but the decision is search the insurance decision is such that it modifies the marginal utility of wealth in the disease case in the scale and you have and you'll have this okay so here typically we have a situation where people do not use the genetic information when making such instrument decision okay now quickly the separating equilibrium related siblings I explained earlier this market equilibrium so everybody pays an insurance premium depending on his or her true risk lowest people obtain a partial insurance contract and his people obtain the full insurance country okay and the contraint constraint is that when you offer contract to lorries and i most people you must be sure that Irish people prefer to come their contract so this is the contract and their expected utility at the lessee for equilibrium okay they say to the insurer pacquiao iris will give me that I will contract full insurance but I pay more but I infringement okay the culture that you offer to the of the lorries people must be such that the iris people prefer their contract rather than the contract offer to those people and so you have to maximize this so you have to constrain etc I do not just give you the finer result you will have to believe me when we have to read the paper that I sent to you to me what you have here is that for the lowest people again the self its insurance decision rule as the same form you always have the financial effect the highest effect of self insurance but if you see that lowest people despite the fact that they do not obtain the full insurance coverage they await the financial loss and they wait the fact it's all the financials they wait the financial effect of self insurance and they will be as effectiveness by P so the Russian secret equilibrium the information is exploited okay and let me finish with the mere existence equilibrium so here people so I wish people have what they they beat with premium they pay a slower than the true Giants premium had to be the sons in the actuarial sense okay they get from coverage low-risk people pay more than the internal premium they would pay at the Miss affair and the obtain partial coverage the problem is the following ok so here we have the constraint and the final with a snap plug this is what lures people do this is not August people do they wait the financial effect of self insurance and they wait the as effect of self insurance party troupe ability of disease so it means that to summarize that will be my last word at the middle a kiss fans equilibrium and this is the same at the Rock Island civility equilibrium the information is exploited people used information when making the decision does it perfectly right and this is why finally I end up with some clear-cut results what are you just just now that is something I try to do if you try to compare what people do because the products that the value of bh4 the new mass of that is people have at the right-sided secret equilibrium at the pudding equilibrium at the listen equilibrium is not the same and so it modifies this it modifies this and there is nothing that you can compare so I'm not saying here that in some cases they do more insurance or more self insurance or or less the only thing I'm able to say in that they used information or not can you do as you did for me symmetric information part where we simplified model particular things and in that case you can get more prevention efforts and then we introduced what happened time as well so yeah okay that's a good suggestion because if so for instance as I did in my explanation if you simplify a little bit and you say okay else I've had diseases as consequences but let's suppose that self-assurance does not modify the the final the end consequences of these okay so this is this case so if you if you suppose that you have this equal to zero so it means that the self insurance decision will be equal so at the pudding equilibrium it will be equal to this is equal to zero Abdulla Safed russian Stieglitz music he spells you will have that the self insurance machine will be the because when you compare what happens at the roadside siblings and me a kiss fans you have things changing on the right hand side but also here so everything changes it's difficult to try to order the immensity of the phone the only thing you can do is okay suppose this is equal to zero this disappears this is always positive so this is equal to zero and things become simple you serve a very nice under coverage doesn't mean that your incentive to the production because the difference between the so I think it nothing there very interesting if you like you simply the health economics journals were complaining about the fact that correlation and preferences is something that matters so instead of trying to compare effort races across which means you could start let you do a comparison within regime where you start with zero effectiveness in the health state and introduce a little effect yes at the margin because that would allow you to say something about population preferences the question I should have asked you very very beginning of your presentation how do you think that would change your model if you introduces if you introduce two types of goods because I'm really for me the this practice preference correlation really depends on the type of food you you you consider it exactly as you to get an example in winning and if you consider traveling were medical expenses then you should expect it varies very much with your have shop and that's to beat up dude so I really in general I don't really understand the cross correlation in our model and so for instance you could really add a model where you have two types of goods and then so what I'm suggesting is repeat several movie it's a et with utility of going traveling utility correlations yeah this is this is something I should you know see how things change right out if I fully mark or the because ya would in the same regime increasing for everything increasing wind so then you just say well because this is an interesting test right there some genetic test Jean really quite a lot secondly before I return some population for a while yeah thank you this is something I should try different is is there empirical evidence across Oh my ideas parents yeah and and there is no consensus this is a failure there is no consensus because the empirical evidence suggests that it might go in the direction I mean it can be positive it can be negative between we disease yeah this is disease specific yeah it depends it is it effectiveness or self insurance mom never changes one but actually and this is related to Philips question my question because Philip said okay can you can you for instance all the self insurance plus it no because there are too many effects going in different directions so that I'm not sure that if that the only question I can provide an answer to is this one now if I if I introduce comparative statics but at least I should try I usually but I am in very pessimistic because they doubt there are too many and here is the insurance decision the prevention decision which depends on the marginal utility of words and add more cases I could assume for instance that you want to expose it deeper but despite this I'm not sure but it doesn't mean that I should not try [Applause]

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