Efficiency in employment-based health insurance: the potential for supra-marginal cost pricing.

Bradford, W. David

I. INTRODUCTION

This paper explores several theoretical models of employment-based health insurance which indicate that price may be set above marginal costs even when the market for insurance appears competitive by traditional measures (such as concentration ratios and entry/exit rates). A great deal of attention has been paid in recent years to health insurance and its role in the escalating resource drain that the health services sector places on the U.S. economy. Concerns over rapidly increasing prices, the lack of access to health care experienced by millions of Americans and other issues have prompted increasingly urgent calls for reform.

One of the few industries in the health services sector that is perceived as reasonably competitive is the private health insurance industry. The Clinton Administration's health care reforms relied heavily upon mandated employment-based health insurance to assure universal coverage. This plan, if re-introduced during the next Congress, would require all firms to provide private health insurance to their employees. This paper argues that this point warrants further consideration; our current understanding of competition in the insurance market does not recognize the severe barriers that exist between actual buyers and sellers of employment-based health insurance. Several theoretical models presented below will demonstrate that since an employee is not generally free to purchase insurance from any insurer, common indicators of competition are of little value.

Much of the previous research into the level of competition in the health insurance (henceforth "insurance") industry has utilized traditional measures of competition, familiar to any student of industrial organization. For example, historically the number of firms selling insurance in an area is seen as positively related to the level of competition. Frech and Ginsburg [1978], and their follow-up study, Frech and Ginsburg [1988], are two widely cited, and typical, investigations. They present a high rate of entry and exit and very low levels of concentration as evidence that the market for private insurance is reasonably competitive, despite the large market shares of the Blue Cross/Blue Shield plans. A more recent review by Frech [1993] reiterates this position, noting that no private insurer has a market share in excess of 1 or 2 percent.(1) This work presumes that the large number of insurers in an area actually compete, in the sense that they share a common customer pool at all times. This assumption is disputed in greater detail below.

Several researchers have noted the limited options which most consumers of health insurance face; however, their primary interest has been in explaining how agents make such constrained choice. Ellis [1989] examines the choices made by employees for health insurance coverage when they are presented with a limited set of complex alternatives. He finds that agents are sensitive to such factors as premiums and deductibles, but often behave in ways that appear to be less than fully informed. Feldman et al. [1989] is another paper that analyses how employers decide upon which health insurance plan to purchase. They also find sensitivity to premiums, deductibles and other non-monetary factors (such as age). Enthoven [1990] argues that the kinds of choices analyzed by Ellis and Feldman et al. do not represent competition since employees are often sheltered from price by their employers. He notes that when employers contribute toward the purchase of insurance in a way that reduces the employees' sensitivity to price (for example by paying the entire premium or some fixed percent of the premium for the employee) competition is severely hampered.(2) While these researchers have recognized the limitations placed on employee choice with respect to the purchase of health insurance, they have not attempted to evaluate the impact of such constraints on the potential for competition in the insurance market.

This paper argues that past research into the competitive nature of the health insurance market has ignored one of the most important characteristics of employment-based health insurance, and so has focused on inappropriate measures of competition. The evaluation of concentration ratios and Herfindahl indexes is only appropriate when customers have the opportunity to buy from any seller. If this freedom of choice does exist, then the usual economic stories assure that a large number of firms will drive price close to marginal cost, and so achieve efficiency. However, with employment-based insurance, the customer (employee) is not free to buy from any seller, but rather is typically restricted to a small number of insurers selected by the employer.(3) In other words, there are two steps to the market process when health insurance is provided through employment. First, the employer selects one insurance carrier (or a few carriers) to supply health insurance to its employees.(4) This choice is clearly made based upon some objective function. Once the menu has been set, employees can select the plan which they find most attractive (if any choice is in fact possible). Therefore, once an insurer has been selected, it may possess significant market power irrespective of the number of "competitors" that are in the area but were not selected by the employer. This will be particularly true when there are costs to the employer of switching carriers, or when (as discussed below) there are no perceptible benefits to the employer of switching.(5) Therefore, it is possible that the market may appear, on the surface, to be quite competitive and still exhibit equilibrium prices that are in excess of marginal costs. This is the question that this paper will attempt to address: "Does a 'competitive' market (identified by traditional measures of concentration and entry/exit) for private employment-based insurance guarantee prices which approximate marginal costs, and therefore efficiently allocate resources?" The models presented below imply that the answer to this question is "no."

These models are built around a two-period framework of employee utility maximization, employer choice of insurer based upon a group welfare function, and profit maximization on the part of the providers of insurance. Section II describes this multi-period framework and derives the competitive equilibrium for the bid price in the first period. Section III then explores one possible model of insurer decision making during the second period, where only one insurer is selected by the employer, and offers a base of full coverage and a selection of optional ancillary coverages. Section IV explores a model of the second period in which the employer selects only one insurer who then offers two packages with different deductibles. Lastly, section V concludes with a discussion of the results and their policy implications.

II. THE FIRST-PERIOD COMPETITIVE PROCESS

For most firms purchasing health insurance plans for their employees, there are two phases to any contract.(6) Insurers typically issue the initial insurance contract on a community-rated basis (often on a line-of-business community rate). That is, a new insurance contract is generally priced based upon the historical medical usage of other firms in that industry (where medical usage varies significantly from firm to firm). Thereafter, practices take one of two courses. Either the insurance company continues to price at the community rate, or the insurer prices the contract in future years based upon past experience with the individual firms (experience rating - much like automobile insurance is frequently adjusted based upon an individual driver's ticket and accident record). This latter approach is the most common, so that for the majority of firms contracting for health insurance from a commercial carrier, premiums rise as their medical usage goes up.

The models explored in this paper are two-period in nature. Specifically, there is period 1 in which the employer searches for an insurer with which to contract. Assume that there are exogenous factors which lead firms to periodically enter this first period of bid-taking (change of management, union negotiations, plant expansions, etc). Competitive bids are taken and an insurer selected. Once the insurer has been selected, it sets prices in period 2 as the sole contracted agent.(7) As long as the prices set in period 2 do not yield a value of group welfare that is inferior to the value which resulted in the insurer being selected, the employer will have no incentive (or signal) to return to period 1 in which competitive bids are again sought. As seen below, this will permit the insurer to maintain a price in excess of realized marginal costs in period 2 in most circumstances. The goal of this section is to explore the pricing behavior of the (many) insurers seeking the contract with the employer in period 1.

Employers accept pricing bids from insurers in period 1 in order to select one insurer with which to contract. The bid which results in the highest value to the employer's objective function is selected. As will be explained in more detail below, employers seek to maximize the value of a Bergson-Samuelson group welfare function for their employees. For modeling the first-period market interactions it is sufficient to note that this group welfare is strictly decreasing in price. Therefore, the insurer that makes the lowest price bid will receive the contract. For simplicity and generality, we assume in this section that all insurers are offering homogeneous packages of full coverage and charge a single price (i.e., no deductibles or copayments). This assumption is relaxed below, though the implications for pricing in period 1 are not affected.

Several key assumptions must be made prior to describing insurers' behavior in the first period. First, we assume that insurers offering competitive bids in the first period are doing so in an environment of uncertainty. This is, all insurers have an incomplete information set with respect to some significant characteristics of the employee population they seek to cover. There are many facets of an employee population on which a nonincumbent firm would not have information. For example, a nonincumbent might not have the experience necessary to evaluate the health of the population with as much confidence as an incumbent.(8) A non-incumbent would be unlikely to know firm culture with respect to the propensity of its employees to file claims, or the employer's propensity to request screens on procedures. These and many other factors combine to create uncertainty with respect to the firm's employees' medical costs. Ultimately, insurers must make bids on expected, rather then actual medical costs.

To illustrate the effect of this uncertainty in period 1, assume that firms' per employee (constant) marginal medical costs range across a known distribution with a mean [C.sup.M]. Let insurers in the period 1 market behave as Bertrand competitors. However, since they do not know the marginal medical cost, insurers submit bids based upon expected marginal cost, EC. Since we are assuming that each homogeneous insurer only knows the distribution, Bertrand competition will assure that P = EC for every bid the firm receives, such that every insurer's bid produces the same value for the Bergson-Samuelson group welfare function. Call this competitive level of group welfare, [W.sup.c]. In this market, we can assume that a bid is ultimately granted by lottery. The primary question for this first period is "what relationship is there between [C.sup.M] and EC?" To answer this, consider the following thought experiment.

Assume that the firm has granted the contract to some insurer. This insurer then enters period 2 and begins to cover the firm's employees (the specifics of this Period 2 process appear below). However, in this second period the insurer discovers the actual per employee constant marginal cost, C. Three outcomes are possible. First, C = EC = P and the insurer gets what it anticipated. In this case, the insurer earns no rents, but will continue the contract; similarly, the firm continues to receive a value of [W.sup.c] for its group welfare function and also maintains the contract. There is no return to period 1. Secondly, the insurer finds that C [less than] EC = P. Either the insurer continues to charge the bid price and earns rents, or competitive forces are such that the insurer finds it profit maximizing to lower price to realized marginal cost. In either case, the firm is earning at least [W.sup.c] and does not return to period 1 by seeking new bids.

Finally, the insurer may find that C [greater than] EC = P. In this case the insurer will earn economic losses on the contract and be forced to either raise price above the initial bid or cancel the contract. If the insurer cancels the contract after its initial period, then the firm is forced to seek bids and returns to period 1. However, if the insurer raises price, then the firm is receiving a level of group welfare that falls short of [W.sup.c], and itself cancels the contract and returns to the first-period competitive bidding process. In either instance, the firm is thrown into the competitive bidding process again, because the actual marginal cost of providing medical coverage to its employees is higher than expected, say [C.sup.H].(9)

With this information, we can see that the first-period expected costs are going to be higher than the mean cost for all firms. An insurer who submits a bid to a firm not only does not know the firm's actual marginal medical cost, but is also unable to know (because of this cost uncertainty) why the firm is seeking competitive bids. The firm may be randomly in the market due to some exogenous factors, or the firm may be in the market because its costs are above the expected level. The best the insurer can do is form some estimate of the probability that the firm is in period 1 because of some exogenous factor, [Rho], or because the firm has higher than expected marginal cost, with probability (1-[Rho]). Continuing the example from above, expected marginal cost in period 1 will be EC = [Rho] [C.sup.M] + (1 - [Rho])[C.sup.H] [greater than] [C.sup.M].(10) It is this expected cost which each Bertrand competitive insurer will bid, and upon which the competitive level of group welfare, [W.sup.c], will be based. In short, the period 1 market is characterized by some level of adverse selection.

The question now becomes, "What is the insurer's behavior in period 2?" Can the "competitive" market overcome this adverse selection? For those insurers contracting with firms whose realized marginal cost is below the expected level, will price necessarily fall to realized marginal costs, or will price remain above marginal cost even though the "market" appears competitive? To determine the answer to these questions, two models of period 2 behavior follow.

III. A MODEL OF ONE INSURER WITH BASE AND ANCILLARY COVERAGES

The first order of business is to characterize the employees buying the insurance. We assume that the representative employee is risk averse and possesses a utility function. The agent will therefore demand insurance in order to avoid the risk associated with a loss in income incurred from treating an uncertain illness. We may assume, for simplicity, that the employees of any given firm are completely homogeneous with respect to health status, illness risk, and initial income ([Y.sub.O]). Every agent will then face the gamble presented in Figure 1, where there is a set (and constant across agents) risk of an illness which would cost C [equivalent to] [Y.sup.O]-[Y.sup.L] to treat, resulting in an expected income of [Y.sub.E]. In Figure 1, an agent's utility function U supports a risk premium of [[Pi].sup.i] = [Y.sub.E] - [Y.sub.C] (the amount that this agent would pay in excess of the expected loss, C, to completely avoid the uncertainty). This agent would clearly buy any complete insurance package if the price were less than [[Pi].sup.i] + C.

With the assumptions of homogeneous income and health status, employees will differ only in the shape of their utility functions. We can further assume that every agent has an unique utility function, and so has an unique risk premium.(11) If there are sufficient numbers of employees, then these risk premia can be considered randomly and independently distributed according to the density function f([Pi]) defined over the range [Mathematical Expression Omitted]. The population of employees can be represented as a distribution of risk premia corresponding to a constant expected monetary loss from illness treatment for each agent, C.

This first model assumes that an employee is faced with one insurance provider who sells a package of basic medical coverage and offers a selection of additional packages, each providing one ancillary coverage (such as dental care or eye care). Further, each employee is required by the employer to purchase the base coverage (and bear the full cost of this purchase) and may buy as many ancillary coverages as desired.(12) Following Mussa and Rosen [1978] and Locay and Rodriguez [1992] each agent is assumed to attempt to maximize a separable utility function:

(1) U = a(X) X + [Gamma](I) I + [Sigma](S,A) A.

Here X is a composite commodity, I is the base insurance package, and A are the ancillary coverages. The terms a(X), [Gamma](I) and [Sigma](S,A) represent the agent's strength of preference. Note that this modeling implies that the employee not only gets utility from the consumption of the insurance itself (one unit of I and her choice of A), but also from a function

(2) S = [Pi] + C - [P.sub.A],

where [P.sub.A] is the price of the ancillary coverages.(13) This function represents the surplus risk premium retained by the agent. Clearly no full insurance package will be sold at a price less than C, and the agent will not pay more than [Pi] + C. The agent's utility will be higher, ceteris paribus, the lower [P.sub.A] is below the reservation price (that is, the more of the risk premium the employee gets to keep).

This employee's utility is maximized by choosing X and A,(14) subject to the budget constraint

(3) [Y.sub.0] = X + [P.sub.I] + [P.sub.A] A,

where the price of the composite commodity has been normalized to one. The constrained maximization yields the expected demand system. Of primary interest here is the employee's demand for ancillary coverages:

[A.sup.*] = A([P.sub.A], [P.sub.I], [Pi], C).

With employee demand established, we must establish how the insurer is selected by the employer. The employer acts as an agent for the employees, sifting through information on alternative carriers, and selecting (in this model) one from which the employees are allowed to purchase. There are several reasons an employer might be willing to accept this responsibility. One is altruism. A second, and more compelling, reason is that the employer will be able to offer a lower real income if she is able to get all of her employees enrolled in a group health insurance plan. This follows since employees, if purchasing their insurance separately, would pay significantly more for a individual package than for a group package with comparable coverages.

If we accept that the employers will act as purchasing agents for their employees, some objective function must be followed. Following Locay and Rodriguez [1992] we assume the employer picks the insurer which maximizes the value of a Bergson-Samuelson group welfare function.(15) This function can be expressed as

[Mathematical Expression Omitted].

This function is concave, and in the relevant range [Delta]G/[Delta]U([center dot]) [greater than] 0. The implications of this selection process will be discussed in greater detail below.

Before we evaluate the insurer's behavior, it is important to recall the timing of the employer's and insurer's decisions. In period 1, the employer searches across all (Bertrand) competitive insurers to select one with which to contract. This search involves taking competitive price bids from the prospective carriers and evaluating the level of group welfare, as defined in (4), associated with each. In this first period, each insurer is preparing bids based upon the same incomplete information, yielding a competitive price [P.sub.i] = EC. Once the selection is made, the process moves into period 2. In the second period, the insurer begins to cover the firm's employees as the sole insurance carrier. When this occurs, the uncertainty with respect to cost is reduced through actual claims experience; however, at least some of this information will be the sole property of the incumbent insurer. From the employer's side in this second period, as long as the level of group welfare does not drop below the competitive level, [W.sup.c], which caused the insurer to be selected in the first period, there will be no signal or incentive to undergo a new search. This is particularly true if there are any costs associated with the search or with changing insurers.

With the dynamic setting and the employee and employer objective functions in hand, we can define the insurer's objective function. The insurer picks the price of [P.sub.I] and [P.sub.A] to maximize profits in period 2 such that this level of group welfare is at least not inferior to [W.sup.c] (in order to assure that the employer has nothing to gain by instituting a new search). Combining (4) with this competitive group welfare "standard" imposes a constraint on insurer behavior. The insurer's objective function is

[Mathematical Expression Omitted]

where the [[Delta].sup.i] - terms reflect the per policy administrative overhead and n is the number of employees. The first term in the Lagrangian is the per unit profit multiplied by the expected demand for ancillary coverage, whereas the second term is the per unit profit multiplied by the certain number of base coverages sold.(16) Equation (5) is maximized with respect to [P.sub.P], [P.sub.A], and [Lambda].

The first-order conditions from the maximization process are

[Mathematical Expression Omitted],

[Mathematical Expression Omitted],

[Mathematical Expression Omitted],

where subscripts denote partial derivatives.

Note that while [Pi] [greater than] 0 is not implied directly, such an assumption is reasonable. Specifically, by the Envelope Theorem profit is a strictly decreasing function of [Lambda] (where -[Lambda] is the marginal profitability of group welfare), and so no profit-maximizing firm would choose to supply greater levels of group welfare than its competitors. We therefore assume that the first equation in (6.c) reduces to a strict equality and that the insurer will not provide any level of group welfare in excess of the competitive level [W.sup.c]. However apparent this argument might appear, it is important for the results below, since this guarantees that the employer will have no incentive to switch insurers as long as prices are set in Period 2 according to (6.a) - (6.c).

What then can be said about the relationship between price and marginal cost? Concentrating on the ancillary services, this can be found by combining (6.a) and (6.b) such that

[Mathematical Expression Omitted],

where

[Mathematical Expression Omitted]

is the marginal interpersonal substitution between the ancillary and base coverage. Further manipulation of (7) results in

[Mathematical Expression Omitted].

In (8), [[Tau].sub.AI] is the expected rate of interpersonal tradeoff between the ancillary and base coverage and [[Epsilon].sub.A] is the expected elasticity of demand for the ancillary coverage facing the insurer. It is clear that no profit maximizing insurer will set price such that (8) is negative.(17)

Since the negativity of (8) is ruled out by rationality of the firm, the relevant question is under what circumstances will (8) be a strict equality, resulting in price equal to marginal cost. There are three possible situations in which this could occur. First, [Theta]([Pi]) = [infinity] would cause marginal-cost pricing; however, this is ruled out for any relevant price (that is any price within the range of expected demand). Secondly,

[Mathematical Expression Omitted]

(which would also imply that, [[Epsilon].sub.A] = [infinity], or that the demand for ancillary coverages is perfectly elastic) would lead to marginal-cost pricing. However, such perfectly elastic demand curves are not permissible in this model. To see why, assume the insurer raises price.(18) Since agents are not able to go to another insurer, the only possible responses to the price change are to reduce the quantity of ancillary coverages purchased or to stop buying ancillary coverage completely. Though any price increase would raise price above some marginal employee's reservation price, there must remain a pool of employees for whom the higher price is still below their reservation price.(19) Therefore, given that employees have a restricted choice of insurers, their demand elasticity will not be infinite and this case is ruled out. Lastly, if the rate of interpersonal substitution, [[Tau].sub.AI], equals one, then marginal-cost pricing will result. Since there is no a priori expectation on the magnitude of this interpersonal substitutability term and since there are infinitely more possible values for [[Tau].sub.AI] other than one in the appropriate range, it seems very likely that (8) will be a strict inequality.

This first model implies that where firms offer a base package with choices across ancillary coverages, in all but one special case, the incentives facing the insurers in period 2 will be to maintain the price of ancillary packages above marginal cost. Now one may ask, would not the competitive pressure from other insurers (who would want to get a contract with this firm) force this insurer to set P = MC? The answer to this question is clearly "no."

As we have seen above, for insurers whose first-period bids were above realized marginal cost, these insurers can still provide the competitive level of group welfare, [W.sup.c], simultaneous with making this decision to maintain price above realized marginal cost. It is simply not possible for the employer to increases group welfare (which is the employer's objective function in the selection process) by selecting another insurer.(20) The implication of (8) above is that in most circumstances the insurer will be able to maintain price above marginal cost, and that there will be no penalty for such action, within the bounds set by (6.a) - (6.c).(21) That is, the system can remain in period 2 even with price set above marginal cost. According to this model, a competitive market for insurance (as "competition" has been generally understood in the literature on this topic) is not sufficient to assure efficient marginal cost pricing.(22)

IV. MODEL OF ONE INSURER OFFERING MULTIPLE PLANS WITH DEDUCTIBLES

Given the setup in the last section, we see that it is quite unlikely that an insurer offering a package of basic coverage and a menu of ancillary coverages will follow marginal-cost pricing, even in a competitive market. Other models of employment-based insurance are possible. One common situation facing employees is the option to buy insurance from a single insurer (which has contracted with the employer) who offers a menu of packages that differ only in the magnitudes of their deductibles and required coinsurance payments. If an insurer does choose to offer a homogeneous (in terms of the covered treatments) package to all employees of the contracted employer, then it will clearly be in the interests of the insurer to provide packages with different deductibles and prices.(23)

To see why, let us assume that an employer has selected one insurer to offer a package of medical coverage that is uniform in terms of the covered treatments. As above, we assume that the employees are homogeneous in every way except for their utility functions and that each possesses an unique risk premium. In addition, we will assume for this section that the employees may opt not to purchase insurance. Figure 2 illustrates the situation faced by the insurer. Note that if the insurer offers a policy which covers illness with an expected annual payout of C = [Y.sub.O] - [Y.sub.E], and a per policy administrative overhead of [Delta] = [Y.sub.E] - a, then it could profitably set the price as low as [P.sub.A] = [Y.sub.O] - a. At this price, the employee defined by the utility function [U.sub.B]([center dot]) would purchase the policy. The employee defined by the utility function [U.sub.A]([center dot]), would not, since [P.sub.A] is above her reservation price.

However, this employee may be captured if the insurer could offer a package of coverage for a sufficiently low price. This can be accomplished by instituting a deductible (of say, [Mu]C). The deductible serves several purposes. First, it would not completely insure the employee from risk. Secondly, it reduces the amount the insurer would have to pay (on average) in medical expenses for the employee. Clearly, if appropriately selected, the deductible can (a) reduce the price of the policy below the reservation price of the less risk averse employees (encouraging employee "B" to purchase coverage) and (b) encourage the more risk averse employees (for example employee "A" in Figure 2) to purchase the nondeductible policy, in order to avoid the risk inherent in the deductible. In this manner, the insurer can select an appropriate schedule of prices and deductibles to segment the employee population and capture all employees.

We can therefore consider the following model. Assuming a selection process in period 1, as discussed above, in period 2 the selected insurer is constrained by the competitive level of the Bergson-Samuelson group welfare function defined in (4). The insurer then offers two packages of insurance, both of which cover the same range of medical treatments for illness. The packages differ according to their prices ([P.sub.A] and [P.sub.B]) and deductibles ([[Mu].sub.A] and [[Mu].sub.B], respectively).(24) The employees are maximizing their individual utility functions:

(9) U = a(X)X + [Sigma](S, I)I.

However, now the excess risk premium function would be defined as

(10) s([Pi]) = {[Pi] + [[Mu].sub.A]C-[P.sub.A]

{[Pi] + [[Mu].sub.B]C-[P.sub.B]

if [Pi] [greater than or equal to] [[Pi].sup.C]

if [Pi] [less than] [[Pi].sup.C]

where [[Pi].sup.c] is some critical level of the employee's risk premium which separates the group which would choose to purchase the lower deductible package from those who would choose to purchase the higher deductible package.(25) An employee's budget constraint will then be defined according to which package is chosen.

Given the model outlined above, the insurer will face an expected demand for insurance which is the sum of the expected demand from the population with risk premia below the critical level and the expected demand from the population with risk premia above the critical level. Therefore, the insurer will attempt to maximize profits constrained by the requirement that it provide at least the competitive level of group welfare, [W.sup.c], as above. The insurer's objective function is

[Mathematical Expression Omitted]

where I ([P.sub.i], [Pi], [[Mu].sub.i]) are the employees' state-dependent demand functions and [Delta] is the per unit administrative cost. This function is maximized with respect to [P.sub.A], [[Mu].sub.A], [P.sub.B], and [Lambda].

The first-order conditions of this model are

(12.a) [Mathematical Expression Omitted],

(12.b) [Mathematical Expression Omitted],

(12.c) [Mathematical Expression Omitted],

(12.d) [Mathematical Expression Omitted],

(12.e) [Mathematical Expression Omitted], [Lambda] [greater than or equal to] 0, [L.sub.[Lambda]] [Lambda] = 0.

where subscripts denote partial derivatives. As with the section above, the primary goal is to evaluate what incentives exist which may or may not drive this insurer to offer coverage at prices which equal marginal cost.

Recall that this insurer must provide (according to (12.e)) a level of group welfare that is at least not inferior to that provided by other insurers in the market. Therefore, any pricing incentive imbedded in (12.a) - (12.e) can be implemented by this insurer without causing the employer to search for another carrier. The employer's objective function cannot be enhanced by such action as long as (12.e) is not violated. To evaluate the relationship between price and the marginal cost of supplying one of the packages, say package A (where identical arguments will hold for package B), conditions (12.a) and (12.b) can be combined such that

(13) [Mathematical Expression Omitted],

where

(14) [Mathematical Expression Omitted].

Again, no profit-maximizing insurer would operate with a negative value to (13). Clearly, (13) will generally reduce to a strict inequality and the insurer will keep price above marginal cost (to the insurer) for insurance bundle "A." If [Mathematical Expression Omitted] then a strict equality results. As in section III, since there is no a priori expected relationship between the two, this condition cannot be generally counted on to assure marginal-cost pricing. Additionally, if the employees' demand for the insurance package is completely elastic with respect to the price and/or deductible (such there is an infinite change in the demand for the insurance for an infinitesimal change in the price, for example) then the denominator could equal infinity (if [[Theta].sub.A[Mu]] [less than] 1). In this circumstance, price would be set equal to marginal cost.

Such perfectly elastic demand curves might exist if all employees perceived plan A and plan B to be perfect substitutes and if the insurer set the price of both plans equal to the reservation price of the employee with the largest risk premium and sold only one unit. In this case a small increase in [P.sub.A] would cause the sole consumer to switch to plan B or to no coverage. For any other pricing strategy, there will always be at least some consumers who would remain with plan A after a small increase in price. Alternately, (13) could revert to a strict equality if the employees were able to costlessly obtain a perfect substitute to this plan from another insurer. According to the setup of the model, and for many employees in the work force, such freedom is not admissible, since the employer selects only one insurer from which the employees can purchase health insurance. It seems, as in the previous section, that a group decision-making structure will allow an insurer to maintain the price of health insurance purchased by employees above the marginal costs of providing the service without prompting a new search by the employer (i.e. without returning to period 1).

V. CONCLUSIONS AND POLICY IMPLICATIONS

The extant literature on the health insurance industry has focused its attention on such indicators as concentration ratios, Herfindahl Indexes, and entry and exit rates to evaluate the competitiveness of the industry. The results of these studies generally indicate that the industry is competitive. This paper points out that the nature of the market for employment-based health insurance drives a wedge between the seller of insurance and the ultimate consumer of insurance, making traditional measures of competition less relevant. This wedge rises from the fact that employers act as an intermediary between insurers and employees by selecting the insurer (or small set of insurers) from which the employee may purchase medical coverage.

Using several theoretical models of the market for employment-based insurance, this paper finds that even if the market for insurance appears "competitive" by traditional measures, it is highly unlikely that price will equal marginal cost. Whether the employer picks one insurer who offers base and optional ancillary coverages, or chooses one insurer who offers packages differing only with respect to the deductible and coinsurance levels, the result is unchanged. In each case, the profit-maximizing insurer is likely to face incentives to set price above marginal cost. Further, there need be no penalty associated with such action, since in each case price in excess of marginal cost is not sufficient to cause the employer to search for a new insurance carrier. Competition in the market for employment-based insurance is clearly more complex than previously treated. While concentration ratios may be important, this paper suggests that less easily observable factors such as the degree of employee choice, the level of employee information, and the presence of heterogeneous filing systems and preexisting condition clauses are critically important factors which affect the competitive performance of the market.

One key barrier to competition in these models of employment-based insurance is the inability of the employees to select among competing insurers. Without choice at this level, price will not generally equal marginal costs. Therefore, offering employees a menu of insurers is one mechanism to improve the competitive outcome of insurance markets. However, this in and of itself need not ensure marginal cost pricing if employee information is incomplete. For example, when insurers offer very diverse packages of coverage, enforce different and complex filing systems, or are varied with respect to form (i.e. traditional indemnity versus HMO) then they may retain market power even if several are selected by the employer.

These results have several specific policy implications. As American society debates how to reform its health delivery system, these models indicate that care should be taken in relying too heavily on employment-based health insurance to achieve the goal of universal coverage. However, this is the approach the Clinton Administration pursued in its advocation of mandated employer-sponsored health insurance. While larger companies often self-insure (and so are not captured in the preceding models), the Clinton plan would have forced all smaller companies that find it difficult to self-insure (and make up the majority of businesses in the United States) to offer health insurance to their employees. If the next Congress reconsiders health care reform, implementation of plans similar to that recently presented by the Clinton Administration should be preceded by, or coincident with, other reforms in the health insurance industry itself.

Several specific reforms are suggested by these results. Attempts to increase employee information and decrease uncertainty should encourage competitive switching of insurers in response to price increases when multiple insurers are available. Uniform filing requirements could not only save resources (the most common justification for this policy) but would also reduce insurer-specific human capital and increase an employer's and employees' willingness to "shop around." Mandating a base package of health care which would be homogeneous across insurers who choose to offer basic coverage is another reform which would decrease the market power of insurers over employee consumers. Lastly, and perhaps most importantly, defining risk pools which are not based on employment could truly introduce competition into this market. With such risk pools, an employer would no longer have to act as a group decision maker, restricting its employees' choice and circumventing the competitive process. Health benefits could become somewhat akin to direct deposit, where the employee selects an insurer from any in the area, and the employer forwards the benefits, as employers currently forward pay checks. Key to this reform would be a requirement that these risk pools select a reasonably large number of insurers, of comparable structure, to certify and give all employees the option to purchase from any of the insurers. This would eliminate one of the most serious barriers to competition extant in our current system and pave the way for reform of the other industries in the health care sector.

1. See Frech [1993, 308].

2. Further, if a firm is passing the cost of the insurance along to its employees, either by requiring that they pay the full price, or offering commensurately lower net wages, then the firm may be less price sensitive. However, this still begs the question of what is the employer's objective function with respect to insurance purchase. One possible answer to this question is discussed below.

3. Pauly [1986] notes that "[in the] great majority of groups there is no choice by the individual employee." While this figure has undoubtedly changed since the early 1980s, Feldman et al. [1989] find that the average firm in their sample offers a menu of only four insurers from which its employees can choose. Finally, preliminary examination of the raw data from the 1987 National Medical Expenditure Survey indicates that 63 percent of those firms that offered some health insurance to their employees offer only one plan (from conversations with researchers at the Agency for Health Care Policy and Research).

4. Note that this paper does not consider the growing incidence of self-insurance. Very large employers are finding it increasingly profitable to pay employees' medical costs out-of-pocket (often in conjunction with purchased stop-loss policies); however, the majority of people employed in the U.S. work at firms which are too small to self-insure, and so must rely upon traditional insurers to obtain coverage.

5. One would expect there to always be significant costs to switching. Few employers have the expertise or understanding of underwriting or the medical market to easily evaluate new insurers. In addition to the lack of information, switching insurers would involve costly paperwork and create an environment of uncertainty for employees and employers alike, who must contend with such issues as preexisting condition clauses and learning a new set of rules for processing claims.

6. Institutional information with respect to the structuring of typical employer-benefit health insurance contracts is taken from Williams and Torrens [1993, 332-60] and from conversations with executives at several major New England insurers.

7. The range of possible second-period prices will be constrained by the initial bid. The nature of this second-period "price setting" is discussed in more detail below.

8. Even if the incumbent insurer or the employer made claims data available, nonincumbents would not have sufficient information to evaluate the degree to which moral hazard exists if only claims data is presented. Much more, (almost certainly proprietary) data would be required. As a further example, Thorpe [1992] reports that employee turnover among small employers who offer insurance is 23 percent. For small employers who do not offer insurance the turnover rate approached 40 percent.

9. Executives from major New England insurers report that high medical use firms do tend to respond to the higher premiums associated with experience rating by switching insurers more frequently than low medical use firms.

10. Obviously this is a simplification since we would not expect every "high-cost" firm to have [C.sup.H] as its marginal cost. However, the argument is dependant only on there being two classes of firms in the period 1 market, "normal cost" (read: randomly selected) and "higher than normal cost" (read: self selected). Assuming a fixed high-cost level simplifies the example, without loss of generality.

11. Since the probability that one agent's risk premium exactly equals another's is approximately zero, this is a reasonable assumption.

12. While assuming that the employer requires the employee to purchase a base package may sound unusual it is really no different than an employer providing its employees with a base package and then paying commensurably reduced wages (a fairly common practice according to Enthoven [1990]).

13. Again, to avoid complicating the notation, without any compensating gain in generality, the assumption is made that each ancillary coverage protects the employee against a different potential medical condition, all of which possess the same probability of occurring and require the same expenditure for successful treatment as the base coverage.

14. Recall that the employees have no choice about the purchase of the base coverage, I, nor will an employee be able to purchase more than one unit.

15. This is a reasonable objective function for the employer since the employees' and employer's objectives are overlapping with respect to the price of the coverage. Employee utility is decreasing in price. So whether we assume the employees are paying the full cost of the insurance "out of pocket," or are only receiving pay that is net of the cost of the coverage, employee utility is higher with lower price, while employers profit is unaffected.

16. For compactness, C is dropped from the functional notation here and below.

17. There is another possible outcome of the model that is not discussed above. A firm might find it profitable (depending upon the size of the interpersonal tradeoff between the base and ancillary coverages) to actually set [P.sub.A] below marginal cost, raising the level of group welfare such that [P.sub.I] could be set above marginal cost. As with the circumstances discussed in the body of the text, this outcome is obviously inefficient, even though the market appears competitive. Exempting this behavior, a rational firm would never select price such that (8) is negative. The author would like to thank an anonymous referee for suggesting this point.

18. Obviously the insurer will not be able to raise price without violating (6.c). The assumption is proposed only to demonstrate the inconsistency of perfectly elastic demand curves.

19. This will hold unless the insurer had previously set price such that it equaled the highest reservation price in the employee population and sold only one unit of ancillary coverage. It seems extraordinarily unlikely that this will be a profit-maximizing strategy.

20. In addition, if there are costs to the employer from searching for and switching to another insurance carrier, the insurer with the contract is even further protected.

21. Note that the "excess profit" earned in period 2 as a result of P [greater than] MC should not be considered compensation to the insurer for accepting risk in period 1 (and so potentially socially efficient). In period 2, all costs incurred in period 1 are sunk. Risk-bearing costs in period 1 are not part of the marginal costs of supplying insurance to the employees in period 2.

22. Again, "efficiency" in this context is used solely with respect to the allocation of resources to health insurance, considering the marginal costs of supplying the service, and the marginal benefits the employees receive from the service. These arguments make no reference with regards to the possible inefficiencies introduced by the insurance into other medical markets.

23. Though plans which are identical in coverage breadth may differ in both deductibles and coinsurance amounts, we shall treat these two financial instruments as if they were the same. One can certainly argue that if there is a sufficiently well defined probability of the nature and expense of future medical treatment, then a insurer could devise a coinsurance rate and a deductible that would be actuarially equivalent.

24. Clearly, the insurer could set the price of one policy below that of the least risk averse employee. This reduces the model to one where the insurer is (effectively) offering only one policy. While this is a potentially interesting model, it is beyond the scope of this paper to consider all possible permutations of policy options facing an insurer.

25. For simplicity, assume that there is one critical value that is least costly for the insurer to identify, and so exogenously establishes two groups.

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W. DAVID BRADFORD, Assistant Professor, University of New Hampshire. The author would like to express his appreciation to Karen Smith Conway, Fred Kaen, and Torsten Schmidt for their helpful comments and suggestions. In addition, the contributions of two anonymous referees and the co-editor of this journal, Eleanor Brown, have substantially improved the paper. Sharon Kunz provided valuable research support. All remaining errors are the sole responsibility of the author.