Consumers typically buy health insurance before knowing which medical product they will eventually need. Hence, they may prefer an insurance policy that gives them an option to utilize multiple differentiated providers upon the emergence of a specific medical need. 1 However, the incidence of such option demand depends crucially on the degree of horizontal differentiation of products: in the absence of horizontal differentiation, all products of equal quality are perfect substitutes, and in the case of quality (vertical) differentiation, the product with superior quality dominates all others. However, to my knowledge, the determination of horizontal differentiation in option demand markets has not yet been studied. This work is the first attempt to fill this gap in the literature.
prior work on hospital pricing has been based on an analogy with conventional markets in which individual consumers make their purchase at the time they know their needs. This is inappropriate for hospital services. With the prevalence of managed care, almost all consumers select among alternative bundles of providers not at the ex-post stage, but at the ex-ante stage before they know their diagnoses. (p. 740)
where firms locate on a line, it seems evident that firms will have an incentive to locate as far apart from each other as possible (at the ends of the line), rather than nearby (in the middle). If they locate in the middle, the products are identical… Thus firms will engage in fierce product quality competition… If firms are located at the ends of the line, then each firm will be considerably more attractive to consumers located very close to it. This will dampen quality competition. (p. 575)
I show here that this conjecture does not hold in option demand markets and that product choices in these markets generally differ from those made in spot markets. More specifically, in this work, I present a comparative analysis of two alternative option demand markets. The first market has the simplest possible structure: each medical provider is selling an insurance policy for its own product by setting an option price, i. e., an insurance premium, and consumers can buy insurance from one or both providers.
I refer to this setup as the benchmark option demand market model or a “pure” option demand market because it is not distorted by any of the structural features of real insurance markets. The formal presentation of the benchmark model can be equivalently interpreted as involving perfectly competitive insurers pricing and selling separate insurance policies for each single product. In the second option demand market to be analyzed here, a single public insurer bargains with providers over prices on behalf of consumers before bundling their products under a single insurance policy. Such dominant public insurance plans, as Medicare in the USA, are common in developed economies. This extension aims to demonstrate how more realistic option demand market may perform relative to the benchmark model.
On the demand side, I assume the conventional preferences for which d’Aspremont, Gabszewicz, and Thisse (1979) obtained the maximum differentiation principle in spot market competition, except for introducing consumers’ uncertainty about their future medical needs; that is, when buying insurance, consumers do not know their future location on the medical conditions/products line. For the benchmark model, I find that competition in simultaneous product choices yields efficient quality provision and horizontal differentiation (providers locate at the first and third quartiles of the product line) and quality provision. 4 In previous works, Ma and Burgess (1993) find insufficient investment in quality for spot market spatial competition, Lyon (1999) and Katz (2011) find that under indemnity insurance investment in quality may be excessive or efficient, respectively.
Competition under sequential product choices in the benchmark model yields asymmetric equilibrium, with the leader located in the middle and the follower located close to the market end. Sequential entry yields lower differentiation and higher surplus for the market leader compared with the equilibrium under simultaneous moves. Nevertheless, although sequential entry implies insufficient differentiation and a niche product property for the follower, it still yields higher expected surplus for consumers as a result of more intense price competition. 5 By contrast, Tabuchi and Thisse (1995) showed that for the respective spot market, the maximal differentiation principle holds under sequential entry.
The analysis of the option demand market under a public insurance regime yields similar qualitative results while highlighting the role of bundling medical products through health insurance policies in softening the competition between medical providers. In particular, I find that under public insurance, horizontal differentiation is excessive, prices are higher and quality provision is lower compared with the benchmark model. Consequently, consumers are worse off than in the benchmark model. This outcome occurs despite the market power held by the public insurer in bargaining over prices on consumers behalf, whereas in the benchmark model, prices are set unilaterally by providers.
The current literature on medical insurance and health-care market outcomes emphasizes that under indemnity insurance medical prices are higher than under HMOs (where consumers sort into insurance plans that define exclusive or preferred providers); see, for example, Lyon (1999) and Katz (2011). This occurs because indemnity insurance bundles providers under a single insurance premium; hence, demand is less responsive to unilateral price increases by each of them. The present results show similar implications of bundling medical products under a single insurance policy even when consumers have significant market power through the representation of the public insurer and are offered not only higher prices but also product choices that decrease consumers’ surplus.
The (more general) literature on common agency showed that selling competing products through a common retailer may alleviate the extend of competition between producers and facilitate collusion; see Bernheim and Winston (1985) and Gal-Or (1991). 6 In the context of the present work, the public insurer may be considered as a common agent that distributes medical products to consumers. However, in contrast to the common agency literature that studied distribution of competing products in spot markets, the current analysis focuses on option market sales where the two products are perceived as complements by consumers, and as such they are bundled under single insurance policy. Hence, the exact role of medical insurers as a common agent in health-care markets deserves further investigation that exceeds the scope of this study.
The current analysis of option demand markets yields distinctive results compared with the respective spot market outcomes because option demand sales and spot demand sales induce different types of competition between medical providers. In spot markets, providers compete over the exclusive purchase of the marginal consumer, as each consumer buys from only one provider. In the option market, providers compete over marginal inclusion under insurance coverage, where the marginal consumer is buying the option to gain access to both of them.
Hence, providers that are perceived as substitutes in the spot market may be perceived as complements in the option market, if product differentiation justifies the additional insurance premium payment. In spot market competition, providers aim to “steal” the marginal consumer from one another by making their products attractive for treating the consumers’ specific medical need. When they sell insurance, they aim to maximize the option value of their products in treating all possible conditions of the marginal consumer, who eventually buys insurance for both products. In the benchmark model, under symmetric equilibrium, providers’ incentive to maximize the option value of their products coincides with market welfare maximization.
More formally, the different market outcomes for competition in option demand and spot markets can be related to the different response functions that prevail in their location sub-game stage. In the current analysis, these response functions are downward sloping, whereas in the corresponding spot market, the best response functions in the location stage imply maximal differentiation regardless of the opponent choice. Gal-Or (1985) showed that whether the sequential moves of identical players yield a first-mover advantage or disadvantage depends on the slope of the response function: a downward-sloping response function implies a first-mover advantage, as in the current analysis, and a flat response function (as in the spot market case) implies profit neutrality with respect to providers’ order of moves. 7
The remainder of the paper is organized as follows: Section 2 presents the detailed setup of the study. Section 3 studies competition and product choices in the benchmark model of option demand markets. Section 4 examines competition and product choices in option demand markets under public insurance, and Section 5 concludes the paper.
2 The Benchmark Model
I study Hotelling’s linear market for differentiated medical products. The market is populated with a unit mass of consumers indexed i who are ex ante identical with respect to their medical needs: each consumer faces the probability
There are two medical providers indexed:
The healthy consumer enjoys a reservation utility
The analysis proceeds in four stages: (1) Each provider chooses variety in the product interval. (2) Providers set prices for their products. (3) Consumers decide whether to buy insurance for only one (preferred) product or for both. (4) Medical conditions are realized, consumers utilize the preferred medical products (under insurance coverage) and providers are reimbursed.
3.1 Simultaneous Entry
I start by studying variety–price choices in simultaneous moves. Narrowing my attention to symmetric equilibria, I assume
To build an intuitive argument for the formal analysis that follows, consider a case in which both varieties are equally priced and symmetrically located on the product line. Consumers would want to buy insurance for both varieties only if the additional premium payment justifies the increase in expected therapeutic effectiveness. If the products are only slightly differentiated, then only a correspondingly low price would justify buying insurance for both. However, if prices are not that low, then the two providers are engaged in fierce price competition, a la Bertrand. This occurs because they have the same stand-alone option value: symmetrically located and equally priced, the two products are perceived as perfect substitutes by the ex ante identical consumers.
Hence, the demand faced by each provider is extremely elastic for high prices: each provider can “steal” the entire market by marginally reducing its rival’s price. Eventually, demand becomes perfectly inelastic once both products are included under insurance coverage. Then, demand cannot increase with further price reductions as the market is saturated. As all consumers in the insurance market are identical, this implies that in equilibrium, they all buy insurance for both products. This equilibrium condition is formally presented in the following lemma.
Equilibrium prices must satisfy
Lemma 1 states that in equilibrium, consumers are indifferent between having either or both products under insurance coverage (I assume that they buy insurance for both). The equilibrium is solved backward, starting with the price competition sub-game. According to Lemma 1, as long as
This condition can be written explicitly as
The simultaneous game has a unique equilibrium symmetric with efficient horizontal differentiation:
Imposing symmetry in eq.  yields
In equilibrium, the option price and profit for each provider are
3.2 Sequential Entry
Suppose now that provider 2 has the opportunity to choose variety first. Next, provider 1 enters the market by choosing variety, and then they both compete in prices, as in Section 3.1 (still assuming that
Sequential entry results in asymmetric equilibrium: the leader locates at the market center, and the follower is close to the market end.
Maximizing eq. [4a] with respect to y1 yields the quadratic equation
Note that horizontal differentiation here is inefficient: it is lower than that under simultaneous moves and asymmetric. However, the equilibrium option prices (and profits) are
Recall that the best response function in the location sub-game defined by eq.  is downward sloping in the opponent’s market share choice, and thus, the first-mover advantage presented in Proposition 2 is consistent with Gal-Or’s (1985) results. In the respective spot market competition, maximal differentiation is always optimal, implying flat (zero-slope) response functions. In this case, consistent with Gal-Or’s (1985) study, providers’ product choice and profits are neutral to entry timing, as noted by Tabuchi and Thisse (1995).
3.3 Quality Choice
In this section, I add to the analysis of vertical differentiation through costly product quality choices. With product quality denoted as
There exists a unique symmetric equilibrium with efficient horizontal differentiation and quality provision.
Differentiating eq. [8a] for
The Appendix shows that in the respective spot market, the principle of maximum differentiation still holds, and the quality provided is
4 Public Insurance
This section extends the benchmark setup by elaborating a more realistic insurance market structure: a single public insurer that bargains over prices with both providers before bundling their services under a single insurance policy that is offered to consumers. Such dominant public insurance plans, such as Medicare in the USA, are common in developed economies. This preliminary extension aims to demonstrate how a more realistic option demand market performs relative to the benchmark model of “pure” option demand markets presented thus far.
4.1 Simultaneous Entry
Consider the simultaneous entry game described in Section 3.1 and assume that in the second stage of the game, prices are set through simultaneous Nash bargaining between both providers and the public insurer. 13 Then, the bargaining solution prices are translated by the public insurer into an actuarially fair insurance premium, denoted pr.
If, for example, only provider 2 is eventually under insurance coverage, the insurance premium is
In the market with a public insurer that bundles medical providers under a single insurance policy, the result of simultaneous moves is excessive horizontal differentiation and higher medical prices relative to the benchmark model with separate insurance sales.
Compare eq.  with the results summarized in Proposition 1 for the benchmark model. ■
Proposition 4 presents an extensive implication of the effect of bundling provider services under a single insurance policy. It shows that when medical products are bundled under a single insurance policy, even a public monopolistic insurer that negotiates over prices on behalf of consumers cannot give consumers the utility level that they would obtain when medical products are sold under separate insurance policies and all market power is obtained by providers. This outcome is due to both higher prices and excessive product differentiation. The consumer’s exact expected utility in this market is
4.2 Sequential Entry
In the market with a public insurer that bundles medical providers under a single insurance policy, sequential entry results in asymmetric equilibrium with the market leader located near the market center and the follower located near the market end.
It is difficult to derive a closed-form solution for the product choice that maximizes eq. [18a]. However, Figure 1 presents the shape of eq. [17a], showing that it is maximized at
The corresponding equilibrium prices are
Furthermore, under the public insurance regime, the timing of entry does not affect prices that much, whereas in the benchmark model, the price of the leader is four times greater than the price of the follower. However, under the public insurance regime, the market leader still has significant first-mover gains by capturing more than two-thirds of the market through central product positioning. Finally, consumers’ expected utility here is
4.3 Quality Choice
Adding quality choice to the analysis of public insurance regime, I still follow the preferences and quality cost specifications presented in eqs  and . Repeating the calculations in eqs – for the utility function  yields the following price equation for provider 1:
In the market with a public insurer that bundles medical providers under a single insurance policy, horizontal differentiation is excessive, quality provision is lower and prices are higher compared with the benchmark model.
Maximizing eq.  with respect to y1 and q1 and imposing symmetry yields
Proposition 6 follows Proposition 4 in demonstrating the negative effect of bundling medical providers under a single insurance policy on consumers. This occurs because of excessive product differentiation, lower quality and higher prices. The consumers expected utility is
Product choice and prices – results summary.
This work presents the first analysis of competition through horizontal and vertical differentiation in option demand markets, which are common in the health-care sector. This study shows that product choices in option demand markets may differ greatly from those in spot markets, and the results highlight the role of bundling medical products under a single insurance policy in softening competition between medical providers. The analysis focuses on two alternative market structures: (a) a “pure” option demand market abstracting various structural characteristics of real insurance markets and (b) a public insurance regime with the public insurer bargaining over price with providers on behalf of consumers before bundling both products under a single insurance policy.
For the benchmark model, I showed that simultaneous entry results in efficient horizontal differentiation and quality provision. Both the quality and variety choices made by providers aim to maximize the option value of their products to consumers, accounting for the cost of quality provision. Hence, in this market, under symmetric equilibrium, providers’ private incentives coincide with the objective of welfare maximization.
Then, I showed that under public insurance, horizontal differentiation is excessive, prices are higher, and quality provision is lower compared with the benchmark model. Hence, under the public insurance regime, consumers are worse off, although the public insurer has significant market power and the ability to negotiate prices; by contrast, in the benchmark model, all market power is held by providers. These results call for subsequent research on the motivations for bundling medical products under insurance policies and their implications for market outcomes. In particular, it seems highly relevant to explore this issue in an extended framework with multiple for-profit insurers and providers (as in Gal-Or  and Douven et al. ) under alternative degrees of vertical integration.
The analysis of sequential entry that may be of special relevance to the debate on “me-too” drugs yielded asymmetric equilibrium with the leader located at the market center and the follower located close to the market end, therefore, capturing a smaller market share. Nonetheless, despite the inefficient horizontal differentiation and the niche properties of the followers’ products, consumers are better off than they are under the efficient equilibrium obtained under simultaneous moves because of lower equilibrium prices.
A strong assumption employed in this work is that consumers are ex ante identical with respect to expected medical needs and preferred medical providers. This assumption sharpens the analysis by imposing fierce (Bertrand) competition in option prices. Gal-Or (1997) and Douven et al. (2014) employed the same assumption but allowed consumers to differ in their preferences for differentiated insurers, with prices set through multilateral negotiations. In a subsequent paper (Sorek 2015), I let consumers be ex ante identical with respect to their expected medical needs but differentiated with respect to their geographic address, and providers choose both the geographic location and horizontal product differentiation. I find that equilibrium with efficient differentiation in the product space can still be present in this elaborated setup.
The author would like to thank Randy Beard, Esther Gal-Or and Aditi Sengupta for their helpful comments, anonymous referee of this journal for insightful comments and suggestions, and Adeet Handel for the thought-provoking discussions. I also benefited from participants’ comments on presentations at Auburn University, the spring 2014 Midwest-Theory Conference at UIPUI, the ASHE 2014 conference at USC, the IIOC-2015 in Boston as well as from discussion comments by Guy Arie and Ted Frech.
Here, I present the outcomes of duopolistic competition in the spot market, in which providers sell their products to sick consumers, and all other specifications and notations presented in Sections 2–4 are the same. The demand faced by provider 1, D1, in spot market competition is
Bardey, D., and J. -M. Bourgeon. 2011. “Health Care Network Formation and Policyholders’ Welfare.” The B.E. Journal of Economic Analysis & Policy (Contributions) 11:1935–1682.
Bardey, D., C. Cantac, and J.-M. Lozachmeur. 2012. “The Regulation of Health Care Providers’ Payments When Horizontal and Vertical Differentiation Matter.” Journal of Health Economics 31:691–704.
Barros, P. P., and X. Martinez-Giralt. 2002. “Public and Private Provision of Health Care.” Journal of Economics and Management Strategy 11:109–33.
Bernheim, D. B., and M. D. Winston. 1985. “Common Marketing Agency as a Device for Facilitating Collusion.” The RAND Journal of Economics 16:269–81.
Capps, C., D. Dranove, and M. Satterthwaite. 2003. “Competition and Market Power in Option Demand Markets.” RAND Journal of Economics 34:737–63.
Douven, R., R. Halbersma, K. Katona, and V. Shestalova. 2014. “Vertical Integration and Exclusive Behavior of Insurers and Hospitals.” Journal of Economics & Management Strategy 23:344–68.
DiMasi, J. A., and C. Paquette. 2004. “The Economics of Follow-On Drug Development: Trends in Entry Rates and the Timing of Development.” PharmacoEconomics 22:1–14.
Economides, N. 1989. “Quality Variations and Maximal Variety Differentiation.” Regional Science and Urban Economics 19:21–9.
Gaynor, M., K. Ho, and R. J. Town. 2015. “The Industrial Organization of Health Care Markets.” Journal of Economic Literature 53:235–84.
Gaynor M., and C. A. Ma. 1996. Insurance, vertical restraints and competition. Unpublished manuscript, US: Carnegie Mellon University. Available at: http://www.andrew.cmu.edu/user/mgaynor/Assets/exclusive.pdf.
Gaynor, M., and R. J. Town. 2012. “Competition in Healthcare Markets.” In Handbook of Health Economics, Volume 2, Chapter 9, edited by T. G. McGuire, M. V. Pauly, and P. Pita Barros, 499–639. Amsterdam and London: Elsevier North-Holland.
Katz, M. L. 2011. “Insurance, Consumer Choice, and the Equilibrium Price and Quality of Hospital.” The B.E. Journal of Economic Analysis & Policy (Advances) 11:Article 5.
Lyon, T. P. 1999. “Quality Competition, Insurance, and Consumer Choice in Health Care Markets.” Journal of Economics & Management Strategy 8:545–80.
Sorek, G. 2015. “Location and Product Choice in Option Demand Markets.” Auburn University Economics Working Papers. Available at: http://cla.auburn.edu/econwp/Archives/2015/2015-11.pdf
Tabuchi, T., and J. -F. Thisse. 1995. “Asymmetric Equilibria in Spatial Competition.” International Journal of Industrial Organization 13:213–27.
Town, R., and G. Vistnes. 2001. “Hospital Competition in HMO Networks.” Journal of Health Economics 20 (733):752.
An earlier version of this work titled “Health Insurance and Competition in Health Care Markets” was also circulated.
Horizontal differentiation is commonly interpreted in terms of the geographic distance between providers or differences in product characteristics, e. g., hospitals’ area of specialization or differential effectiveness of alternative pharmaceuticals within therapeutic categories. See Bardey, Cantac, and Lozachmeur (2012) for more detailed examples.
It is well known that alternative modeling of demand could also alter the principle of maximum differentiation, e. g., different transportation costs (Economides 1986) and preference distribution (Anderson, Goeree, and Ramer 1997), or uncertainty with respect to quality (Bester 1998). However, in the present analysis, option demand not only mitigates the incentive for maximal differentiation but also supports efficient location choices.
In the context of health-care markets, the analysis of sequential moves may be of special relevance to the debate on the welfare implications of follow-on drugs, also known as “me-too” drugs. As phrased recently in “Forbes” magazine: “They may have some unique niche in the market, but they are fairly redundant with other therapies that are already available. Many of these you could call me-too drugs.” The full article is available at http://www.forbes.com/sites/johnlamattina/2015/01/19/im.pact-of-me-too-drugs-on-health-care-costs/. For more on follow-on drugs, see DiMasi and Paquette (2004).
I am grateful to the referee of this journal for highlighting this relation to the literature on common agency.
I am grateful to the referee of this journal for pointing out this inference.
Economides (1989) showed that the principle of maximum differentiation holds in a similar model with quality choice and linear transportation costs.
Gal-Or (1997) studied such multilateral bargaining with two (for-profit) competing insurers and two providers.
All corresponding calculations for the respective spot market are presented in the Appendix.