Health Insurance as a Two-Part Pricing Contract

Abstract

Monopolies appear throughout health care. We show that health insurance operates like a conventional two-part pricing contract that allows monopolists to extract profits without inefficiently constraining quantity. When insurers are free to offer a range of insurance contracts to different consumer types, health insurance markets perfectly eliminate deadweight losses from upstream health care monopolies. Frictions limiting the sorting of different consumer types into different insurance contracts restore some of these upstream monopoly losses, which manifest as higher rates of uninsurance, rather than as restrictions in quantity utilized by insured consumers. Empirical analysis of pharmaceutical patent expiration supports the prediction that heavily insured markets experience little or no efficiency loss under monopoly, while less insured markets exhibit behavior more consistent with the standard theory of monopoly.

A. Introduction

Fully insured patients face health care that is free at the margin. This leads to over-consumption of costly health care resources. As a result of this “moral hazard,” optimal health insurance contracts balance the need for insurance against the need for more efficient utilization incentives (Arrow 1963; Pauly 1968; Zeckhauser 1970). This balance explains why health insurance contracts often charge an ex post unit price or co-payment, in addition to an upfront premium. Co-payments reduce the degree of insurance, but in return limit the extent of over-consumption, because the consumer faces an out-of-pocket price that partially reflects social cost.

Much attention has been paid to the optimal design of these “two-part” health insurance contracts that charge a premium and an ex post co-payment. The emphasis has been on how to manage moral hazard and other insurance market failures like adverse selection. However, two-part health insurance contracts might have another function that is less appreciated: the reduction of deadweight loss from market power among health care providers.

Our central hypothesis is that health insurance resembles a two-part pricing contract in the sense that consumers pay an upfront fee (premiums) in exchange for lower unit prices (co-payment) in the event of illness. Outside the health insurance context, standard theory implies that two-part pricing contracts allow a monopolist to sell goods at marginal cost, but to extract consumer surplus in the form of an upfront payment (see the seminal paper by Oi 1971). The standard normative prediction is that two part pricing contracts provide a monopolist the same incentives to minimize deadweight loss as a competitive market. Intuitively, deadweight loss-minimization by the monopolist maximizes the total consumer surplus available for the firm to extract in the form of an upfront payment.

An example illustrates the hypothetical analogy between health insurance and a two-part pricing contract. Imagine a monopolist that produces health care and provides health insurance. By setting its co-payment equal to marginal cost, this monopolist can ensure that consumers use care efficiently and thus derive the greatest possible gross consumer surplus from its use. The monopolist can then profit from this strategy by charging an upfront premium equal to this gross consumer surplus. Under this arrangement, consumers remain willing to participate in the health insurance market, utilization occurs at the efficient level where marginal cost equals marginal benefit to consumers, and the firm earns profits equal to gross consumer surplus. This is the usual logic through which two-part pricing generates maximum profits and first-best utilization.

Of course, it is not immediately obvious whether the logic in this simple example extends to the realities of the health care marketplace, which involves the interaction of disintegrated insurers and providers, heterogeneous consumers, and a wide range of information asymmetries. In this paper, we study the applicability of the two-part pricing hypothesis to health care and reach two primary conclusions:

• When different types of consumers can sort into different types of insurance contracts, health insurance markets perfectly eliminate deadweight loss from market power in health care provision. This logic is robust to moral hazard, adverse selection, the disintegration of providers and insurers, and two-sided market power for providers and insurers.

• When perfect sorting of consumers is not possible, deadweight loss from powerful health care providers creates uninsurance, but does not generate under-utilization of medical care by insured consumers.¹ Insurers forced to charge “pooled” uniform premiums to a diverse set of consumers may decide to sell to the highest-demand consumers only, and to price marginal consumers out of the insurance market entirely. However, even under this scenario, insurers still have incentives to encourage efficient utilization among the consumers who remain insured.

Our results have several implications for policymakers seeking to limit deadweight loss due to market power in health care. First, the extent and even presence of deadweight losses from health care monopoly are determined by the structure of the insurance market. For example, the extent of premium-discrimination in the health insurance market determines the degree of monopoly loss suffered in the hospital market, even when hospitals do not themselves sell insurance. Therefore, the decision to regulate or allow monopoly in health care provision should be informed by the structure of the health insurance market. Moreover, policies that expand insurance coverage or promote efficiency in the insurance market may be viewed as substitutes for regulating monopoly in health care provision.

Second, the price-cost margin for health care goods is an unreliable measure of welfare loss from monopoly power. When insurance is widespread and reasonably complete, providers may be receiving very high monopoly prices and profits, even though consumers are paying prices near or even below marginal cost. The copayment-cost margin is a similarly inconsistent measure of welfare loss from monopolies, as it is driven primarily by the extent of moral hazard and not by the monopoly power of upstream providers.

The two-part pricing view of health insurance leads to two testable empirical implications that differentiate it from alternative theories. First, eliminating health care monopolies in heavily insured markets will lead to little or no change in the quantity of health care consumed, because consumer copayments will be insensitive to market power among providers. In contrast, eliminating health care monopolies in largely uninsured markets will increase the quantity of health care used and reduce deadweight loss as prices fall from monopoly levels to marginal cost levels. Second, the two-part pricing theory uniquely implies that demand elasticities under monopoly may be greater than -1.0.

Empirical analysis of patent expiration in the pharmaceutical market provides evidence consistent with these positive hypotheses. The elimination of pharmaceutical patent monopoly has little to no impact on quantity consumed for molecules that are heavily insured, but substantial quantity impacts for molecules with less widespread insurance. In addition, demand elasticities in less-insured markets follow the predictions of standard monopoly models, while elasticities in heavily insured markets are consistent only with a two-part pricing interpretation.

The paper proceeds as follows. Section B develops the analogy between health insurance and the standard theory of two-part pricing, even when information is incomplete and market power imperfect. Section C presents our empirical analysis. Finally, Section D summarizes our conclusions and implications for the analysis of market power in health care.

B. Two-Part Health Insurance and Efficient Surplus-Extraction

For decades, many health economists cultivated and then relied upon the intuition that health care competition reduces welfare. According to this argument, healthcare monopolies improve welfare by offsetting excessive utilization due to moral hazard (Crew 1969; Frech 1996; Folland, Goodman et al. 2001).

Gaynor, Haas-Wilson, and Vogt (2000) exposed the flaw in this reasoning: if private insurers could make customers better off by raising their out-of-pocket costs, and thus restricting utilization, they would surely do so. In their model a competitive insurance industry responds to higher prices for medical care by weakly increasing coinsurance or copayments, consequently restricting quantity purchased and reducing consumer welfare. Of course, this important insight leads one to ask whether and how profit-maximizing behavior by medical care providers mediates the effects of health insurance on deadweight loss. For purposes of their argument, Gaynor et al treat health care prices, and medical care provider behavior, as exogenous. By incorporating provider behavior into the Gaynor et al approach, we derive new conclusions about the positive and normative implications of market power on the provider side.

In our model just as in Gaynor et al., moral hazard does not transform market power into a boon for consumers. However, it does give rise to insurance contracts that equip profit-maximizing health care providers with a two-part pricing instrument. This leads to a novel implication. Gaynor et al conclude that, “when the medical market is not competitive and already exhibits prices above marginal costs, price increases lead to lower welfare and price decreases lead to higher welfare.” In contrast, we conclude that price increases due to monopoly power are welfare-neutral among the segment of insured consumers, and that they only lead to welfare losses among consumers that are uninsured or become uninsured.

B.1 Economic Environment

Following Gaynor et al, consumers face a risk of illness and an uncertain demand for a medical remedy, produced at constant marginal cost MC. An insurance contract is an offer of an ex post co-payment (m), and an ex ante premium I. There are consumers of measure one, indexed by h ∈ [0,1], and distributed uniformly over this interval. Patients with lower values of h are sicker. The fraction σ of consumers falls sick. Sick consumers place value on the medical remedy, while healthy consumers do not.

Consumers do not know their value of h ex ante, but learn it ex post. Insurers, however, cannot observe this value and thus cannot make indemnity payments conditional on the underlying health state. Payments can only be contingent on the consumer's observed decision to purchase the medical good or not. The necessity of tying payments to utilization, rather than the underlying source of risk, results in moral hazard, or over-utilization relative to the first-best, full information case. When insurance payments are tied to medical care use, patients are rewarded for consuming medical care. We will demonstrate that this stimulates excessive use.

B.2 The Typical Competitive Problem

We begin by characterizing the standard competitive equilibrium allocation in the presence of moral hazard. Consider a representative competitive insurer purchasing medical care from a competitive goods market, and providing insurance within the informational structure outlined above.

The firm chooses a co-payment (m) and premium (I) that maximizes consumer utility, subject to a break-even constraint and incentive compatibility for the consumer. The demand for medical care, which is known by the insurer, depends on the consumer's health h, the co-payment m, and income (W), according to q(W, m, h).Following Gaynor et al, we assume that the demand for health care is only determined by health status, income, and copayment, and not by the insurance premium. In other words changes in the insurance premium result in negligible income effects.²

The firm's optimization problem can be written as:

$$\begin{array}{c}{\text{max}}_{I,m}{\int }_0^{1}u(W-I-m{q}^{\ast },q^{\ast },h)dh\\ s.t.I+(m-MC)E(q^{\ast })\ge 0\\ \mathit{\text{and}}{q}^{\ast }=q(W,m,h)\end{array}$$ (1)

Using the break-even constraint to substitute for I in the objective function, we obtain:

$${\text{max}}_m{\int }_0^{1}u(W-MC\ast E(q(W,m,h)+m(E(q(W,m,h))-q(W,m,h)),q(W,m,h),h)dh$$ (2)

Appendix A confirms that the usual moral hazard results obtain in this model, namely: (1) Over-utilization relative to the first-best as m* < MC, and (2) Higher marginal utility of wealth in the “sick” state due to incomplete insurance.

B.3 One-sided Market Power

We now compare this benchmark competitive solution to the case of one-sided monopoly, where an upstream monopolist goods-producer interacts with a perfectly competitive insurance industry. To close the economy, suppose that shares in the monopolist are evenly distributed across consumers. Define total producer surplus as π̅, which accrues to shareholders in the form of a dividend.

In a standard model where a monopolist sells directly to consumers, the firm maximizes profits subject to the consumer's inverse demand curve, P(Q), as in:

$$\begin{array}{c}{\text{max}}_{p,Q}pQ-MC\ast Q\\ s.t.p\le P(Q)\end{array}$$ (3)

In our case, when the monopolist instead sells to a competitive insurance industry, it maximizes profits subject to the representative insurer's break-even constraint. Accordingly, define the total gross surplus to the insurer as G(Q); this is the insurer's profits prior to any payments made to the monopolist. The monopolist now solves:

$$\begin{array}{c}{\text{Max}}_{p,Q}pQ-MC\ast Q\\ s.t.pQ\le G(Q)\end{array}$$ (4)

The monopolist cannot price above the average surplus of the insurer, $\frac{G(Q)}{Q}$.

For its part, the insurer will maximize gross surplus at any given level of quantity. From the insurer's point of view, gross surplus can be characterized as the maximum amount the insurer can extract before driving consumers out of the market. The gross surplus-maximization problem can be written as:

$$\begin{array}{l}G(Q)={max}_{I,m}I+mE(q(W,m,h)\hfill \\ s.t.{\int }_0^{1}u(W-I-mq(W,m,h)+\overline{\pi },q(W,m,h),h)dh\ge \overline{U}\hfill \\ \mathit{\text{and}}E(q(W,m,h)\le Q\hfill \end{array}$$ (5)

Defining η as the Lagrange multiplier on the second constraint, the problem can be rewritten as:

$$\begin{array}{l}G(Q)={max}_{I,m}I+mE(q(W,m,h))+\eta (Q-E(q(W,m,h))\hfill \\ s.t.{\int }_0^{1}u(W-I-mq(W,m,h)+\overline{\pi },q(W,m,h),h)dh\ge \overline{U}\hfill \end{array}$$ (6)

According to the envelope theorem, G′(Q) = η. Moreover, the first-order condition for the monopolist implies that G′(Q) = MC. Since this implies η = MC in equilibrium, we can use this expression to eliminate η from the problem, as in:

$$\begin{array}{l}G(Q)={\text{max}}_{I,m}I+(m-MC)E(q(W,m,h)+MC\ast Q\hfill \\ s.t.{\int }_0^{1}u(W-I-mq(W,m,h)+\overline{\pi },q(W,m,h),h)dh\ge \overline{U}\hfill \end{array}$$ (7)

The equilibrium values of I and m are unaffected by the constant term MC *Q. As a result, we can eliminate it from the objective function, as in:

$$\begin{array}{l}{max}_{I,m}I+(m-MC)E(q(W,m,h))\hfill \\ s.t.{\int }_0^{1}u(W-I-mq(W,m,h)+\overline{\pi },q(W,m,h),h)dh\ge \overline{U}\hfill \end{array}$$ (8)

We now demonstrate that the optimal copayment set by the insurer here is equivalent to what a competitive insurer facing a fully competitive medical care market would charge. The first step is to note that, since π̅ is the optimal profit of the monopolist, the above problem is equivalent to:

$$\begin{array}{c}\underset{I,m}{max}\int u(W-I-mq(W,m,h)+\overline{\pi },q(W,m,h),h)dh\\ \text{s}.\text{t}.\text{I}+(\text{m}-\text{MC})\text{E}(\text{q}(\text{W},\text{m},\text{h}))\ge \overline{\Pi }\end{array}$$ (9)

Since the firm's participation constraint binds in equilibrium, we can substitute it into the objective function to obtain:

$$\underset{m}{\text{max}}{\int }_0^{1}u(W-m(q(W,m,h)-E(q(W,m,h)))-MC\ast (E(q(W,m,h))),q(W,m,h),h)dh$$ (10)

Note that this is exactly equivalent to the fully competitive problem in 2. Therefore, the presence of two-part health insurance contracts produces the same equilibrium copayment levels as competition. Of course, the premium will be higher under monopoly than under competition, since the premium becomes the source of the provider's monopoly profits. However, since copayments are the same under monopoly and competition, both cases will generate identical health care utilization levels. Moreover, the monopolist with a two-part pricing instrument is able to earn the maximum amount of profit possible – i.e., G(Q) – MC * Q – unlike the standard monopolist that fails to extract deadweight loss.

These results have two important implications for measuring monopoly loss. First, the price-cost margin, or $\frac{p}{MC}$, provides little insight into the extent of deadweight loss. p may be much higher than marginal cost even when quantity is set efficiently, and when deadweight loss is zero. Even the copayment-cost margin, or $\frac{m}{MC}$ is an inconsistent measure of monopoly loss per se, since the optimal copayment is determined by information asymmetries rather than provider market power. Upstream monopolists with market power have no incentive to request or promote high copayments downstream.

B.4 Two-sided market power

The results above generalize to the case of two-sided market power, in which health care providers bargain individually with powerful health insurers. This is a common situation in health care, where powerful providers (drug manufacturers, hospital networks, physician practice groups) bargain with large health insurers.

Two-sided market power continues to lead to the same optimal quantity as full competition. To understand why, observe that the non-competitive insurer continues to set copayments so as to maximize the total amount of consumer surplus available for extraction from its insureds. The insurer and health care provider then bargain over how this surplus is divided, but this bargaining step does not affect the optimal copayment, or the amount of health care quantity demanded by consumers at that copayment level.

Formally, consider Nash-bargaining between a powerful health care provider and a powerful insurer. The two sides bargain over a price, p, and a quantity, Q. The relative market power of the provider is given by γ, and that of the insurer is given by 1 − γ. Nash-bargaining solves the product of the two sides' respective profits, exponentiated by their relative market power:

$${max}_{p,Q}{(pQ-MC\ast Q)}^{\gamma }{(G(Q)-pQ)}^{1-\gamma }$$ (11)

The first-order conditions for this problem can be written as:

$$\begin{array}{c}[Q]:\gamma \ast \frac{G(Q)-pQ}{Q}+(1-\gamma )(G\prime (Q)-p)=0\\ [p]:\gamma \frac{G(Q)-pQ}{Q}-(1-\gamma )(p-MC)=0\end{array}$$

Subtracting these two expressions yields:

$$(1-\gamma )(G\prime (Q)-MC)=0$$

Since G′(Q) = MC in this case as well, we can use exactly the same argument we developed in Section B.3, beginning with equation 7. The result of repeating this procedure is a proof that the insurer under two-sided market power sets the optimal copayment in exactly the same way as an insurer under one-sided market power, and under competition. This demonstrates that copayments and utilization are the same under two-sided market power as under competition. When market power shifts from one side to the other, the distribution of rents may change, but there are no changes in copayments, utilization or efficiency.

It is important to note, however, that two-sided market power can sometimes create complex incentives that are not well-approximated by a Nash-bargaining model. For example, in a dynamic setting with multiple players, there may be incentives for one side to “walk away” from the negotiation. The result might be exclusive dealing, which is sometimes observed in pharmaceutical and hospital markets (Ellison and Snyder 2003; Ho 2006). Such exclusive dealing would lower consumer welfare by restricting consumer choices to certain sets of hospitals or drugs. Generally speaking, health insurance as a two-part tariff mitigates deadweight loss in cases where providers and insurers find it optimal to come to terms. Market power on the insurer side might create additional deadweight loss if it leads insurers into exclusive dealing arrangements. We leave this as an issue for future research.

B.5 Adverse Selection

The analysis above allowed for moral hazard, or incomplete ex post information. The basic logic of health insurance as two-part pricing holds up under another common failing of insurance markets — adverse selection, or incomplete ex ante information.³ In this case, the insurer can observe neither the severity of illness ex post, nor ex ante differences in the propensity of consumers to fall ill. Appendix B demonstrates that, in a Rothschild-Stiglitz type model of adverse selection, two-part pricing continues to remove the deadweight loss associated with monopoly.

B.6 Pooling Equilibrium

Notably, the logic alluded to in Section B.5 breaks down outside the Rothschild-Stiglitz context of adverse selection. Within the Rothschild-Stiglitz separating equlibrium, insurers are able to offer different insurance contracts that attract different types of consumers. This ability to sort different consumer types into different contracts proves to be a key factor in limiting deadweight loss from market power in health care.

Within the Rothschild-Stiglitz context, it is not possible for different types of consumers to be pooled in a single insurance contract – the so-called “pooling equilibrium” solution. However, frictions in the labor market (cf, Crocker and Moran 2003; Bhattacharya and Vogt 2006; Fang and Gavazza 2007), market power among insurers (Stiglitz 1977), community-rating laws (cf, Adams 2007), or restrictions on premium-differentiation (cf, Bhattacharya and Bundorf 2005) can generate distortions that lead to stable pooling equilibria. In a pooling equilibrium, the premium is a less efficient instrument for surplus-extraction, because insurers cannot effectively offer different contracts to different consumer types. This can lead to inefficiency and deadweight loss from market power in the provision of medical care, but not of the typical form. Deadweight loss (and attendant reductions in the quantity of health care) occurs for individuals who are uninsured or are priced out of the insurance market, but there is no deadweight loss for those individuals who remain insured.

Below we use a stylized model to illustrate this result. Consider two types of consumers — C and N -- the chronically ill and not chronically ill. The C types are sicker, demand more health care and derive more consumer surplus from any given health insurance offer. Assume, that through some combination of legal, informational, and labor market constraints, firms either choose or are compelled to offer a single premium and copayment schedule.⁴ Insurers cannot differentiate between the two types ex ante (adverse selection), nor can they distinguish ex post between patients with different levels of illness severity (moral hazard).

B.6.1 Competitive Outcomes

In order to characterize the welfare loss due to monopolies in the presence of pooling equilibria, we must first characterize the competitive pooling equilibrium that serves as a benchmark. Accordingly, suppose that both insurance and medical care are provided by competitive firms. The representative medical care provider sells goods at marginal cost. All consumers have reservation utility levels U̅.⁵ For completeness, we also endow the two types with s^C and s^N shares of the insurer's profits.

The representative insurer maximizes:

$$\begin{array}{l}{max}_{I,m}{\int }_0^1{u}^C(W-I-m{q}^C,q^C,h){\mu }^C(h)dh\hfill \\ s.t.2I+(m-MC)E(q^C(W,m,h))+(m-MC)E(q^N(W,m,h))\ge 0\hfill \\ {\int }_0^1{u}^N(W-I-m{q}^N,q^N,h){\mu }^N(h)dh\ge \overline{U}\hfill \\ {\int }_0^1{u}^C(W-I-m{q}^C,q^C,h){\mu }^C(h)dh\ge \overline{U}\hfill \end{array}$$ (12)

Note that the participation constraint for C types will fail to bind. To prove this, suppose to the contrary that it does bind for the optimal contract(I*,m*). This implies that the N types will exit the market under this contract, because their consumer surplus from a given health insurance contract is always lower than the corresponding surplus enjoyed by a C type. This cannot be an equilibrium chosen by competitive firms. To see why, recall first that we assumed a pooling equilibrium is feasible. This implies there is some nonnegative-profit pooled insurance contract that satisfies all three constraints in this problem. Call this contract (I^f,m^f). Since the C types always derive more utility from a given contract than their N type counterparts, we know their utility from (I^f,m^f)is higher than that received by the N types. Moreover, since (I^f,m^f) satisfies the participation constraint of the N types, it produces utility weakly greater than U̅ for the N types. Therefore, it must produce utility strictly greater than U̅ for the C types. Such a contract is feasible and produces higher utility for the C types than does (I*,m*). Therefore, (I*,m*) cannot be an equilibrium. This proves by contradiction that the participation constraint for C types will fail to bind.

Next, observe that the representative insurer's problem can be equivalently rewritten in terms of maximizing the utility of the N types, according to:

$$\begin{array}{l}{max}_{I,m}{\int }_0^1{u}^N(W-I-m{q}^N,q^N,h){\mu }^N(h)dh\hfill \\ s.t.2I+(m-MC)E(q^C(W,m,h))+(m-MC)E(q^N(W,m,h))\ge 0\hfill \\ {\int }_0^1{u}^C(W-I-m{q}^C,q^C,h){\mu }^C(h)dh\ge \overline{U}\hfill \end{array}$$ (13)

Since the participation constraint of the C types fails to bind, we can eliminate that constraint and then substitute for I using the firm's break-even constraint:

$${max}_m{\int }_0^1{u}^N[W-m(q^N-\frac{E(q^c)-E(q^N)}{2})-MC(\frac{E(q^c)-E(q^N)}{2}),q^N,h]{\mu }^N(h)dh$$ (14)

The solution to this problem yields the optimal copayment set in a competitive pooling equilibrium.

B.6.2 Effects of Market Power on Uninsurance

In the presence of a pooling equilibrium, monopoly will not always produce the same copayment as a competitive marketplace. This can be shown in the simplest case of an integrated monopolist that provides insurance and medical care. The integrated firm offers a single insurance contract to both types of consumers. Each type is endowed with s^H and s^L shares of the firm, which then solves the following profit-maximization problem:

$$\begin{array}{l}{max}_{I,m}2I+(m-MC)E(q^C(W,m,h))+(m-MC)E(q^N(W,m,h))\hfill \\ s.t.{\int }_0^1{u}^C(W-I-m{q}^C+s^C\overline{\pi },q^C,h){\mu }^C(h)dh\ge \overline{U}\hfill \\ {\int }_0^1{u}^N(W-I-m{q}^N+s^N\overline{\pi },q^N,h){\mu }^N(h)dh\ge \overline{U}\hfill \end{array}$$ (15)

Define (I,m) as the solution to this problem. Since there is a single contract, and since C types always value insurance more than N types, the firm will not be able to capture consumer surplus from both these consumer types. One of the participation constraints will thus fail to bind. Moreover, if the equilibrium contract extracts all available surplus from the C types, it will violate the participation constraint for the N types. Therefore, there are two cases to consider: (1) the participation constraint binds for the N types only, and both types receive insurance; and (2) the participation constraint binds for the C types, and only that type receives insurance.

Begin with the first case, where both types are insured. Since only the N type participation constraint binds, the problem simplifies to:

$$\begin{array}{l}{max}_{I,m}2I+(m-MC)E(q^C(W,m,h))+(m-MC)E(q^N(W,m,h))\hfill \\ s.t.{\int }_0^1{u}^N(W-I-m{q}^N+s^N\pi ,q^N,h)dh\ge \overline{U}\hfill \end{array}$$ (16)

Define π̅ as the equilibrium level of profit that solves this problem, which can then be equivalently rewritten as:

$$\begin{array}{l}{max}_{I,m}{\int }_0^1{u}^N(W-I-m{q}^N+s^N\overline{\pi },q^N,h)dh\hfill \\ s.t.2I+(m-MC)E(q^C(W,m,h))+(m-MC)E(q^N(W,m,h))\ge \overline{\pi }\hfill \end{array}$$ (17)

Substituting the reservation profit constraint into the objective function transforms this into an unconstrained utility-maximization problem, as follows:

$${max}_m{\int }_0^1{u}^N(W-MC(\frac{E(q^C)+E(q^N)}{2})-m(q^N-\frac{E(q^C)+E(q^N)}{2})+s^N\overline{\pi }-\frac{\overline{\pi }}{2},q^N,h)dh$$ (18)

Simple algebra reveals that this problem is equivalent to the formulation in equation 14, provided that both types own equal shares of the firm. Clearly, monopoly may have distributional consequences if the shares of the firm are not distributed in the prescribed manner, but it continues to produce copayment and quantity levels equivalent to a fully competitive case.

However, monopoly can create efficiency losses when there are incentives for uninsurance. Define (I^C*,m^C*) as the optimal insurance contract that would be offered to C types in the absence of N types. The equilibrium contract when both types remain insured is (I*,m*). This may generate fewer profits than the firm could earn by offering (I^C*, m^C*) to the C types alone. For example, suppose that the copayment m* generates one-quarter of the gross consumer surplus for N types as C types. Denote the consumer surplus level for the N types as X. In a pooling equilibrium, the firm earns no more than $X across all consumers (of measure one), because it is limited to extracting $X or less from each consumer.⁶ In a C-type only equilibrium, however, the firm can earn at least 4 * $X * S in profits, where s is the share of C types in the population. If the C types represent greater than one-quarter of the population, it is more profitable to sell a policy that only the C types will purchase.

In this case, the firm will choose to price the N types out of the market. This is the only efficiency consequence of distortionary pooling equilibria. The healthier (or poorer) consumers with less demand for insurance end up uninsured, in which case they face a linear monopoly price and all its corresponding deadweight losses. However, the C types continue to enjoy the same healthcare utilization levels that they would under full competition. Deadweight loss from monopoly is equal to the welfare lost by those who are “priced out” of the insurance market. The empirical consequences of health care monopoly for uninsurance have been considered by Town et al (2006).⁷

B.7 Summary of Positive Predictions

The theory yields a number of positive predictions regarding the effect of changes in market power, and how these effects vary with the rate of insurance. These predictions allow us to test the “two-part” pricing theory of health insurance.

First, all permutations of the two-part pricing theory predict that insured consumers utilize care at competitive levels, even when they face monopoly in health care provision. On the other hand, uninsured consumers utilize care at standard monopoly levels.⁸ Moreover, changes in market power have no effect on utilization for insured consumers, but the usual benefits on utilization for uninsured consumers. These facts generate the following testable implication:

• (H-1)Holding the rate of insurance and other market characteristics fixed, when market power is eliminated, markets with a higher fraction of insured consumers display smaller changes in quantity than less-insured markets.

In addition, it is useful to state our implications in terms of demand elasticities. Under standard monopoly in uninsured markets, the elasticity of demand at the monopoly price exceeds unity. In insured markets, we have shown that monopoly leads to higher prices, but no change in quantity. This implies a zero elasticity of demand at the monopoly price, under two-part pricing. This leads to our second testable implication:

• (H-2)Once again, assume the rate of insurance and other market characteristics remain fixed. In uninsured markets, the demand elasticity observed when market power falls will be less than -1.0. In fully insured markets, however, this demand elasticity will be zero or higher. In mixed markets, the demand elasticity will be a weighted average of these two elasticities, with the weights given by the share of uninsured and insured quantity consumed. As a result, the weighted average may be greater than -1.0.

Since insurers and providers can price-discriminate across insured and uninsured consumers, the elasticity in mixed markets is a simple weighted average of the elasticity in the insured and uninsured market segments.

Note that the theoretical predictions are identical regardless of the source of variation in rates of insurance, which can occur due to insurance market imperfections, upstream market power, public health insurance eligibility rules, or other institutional factors.

B.8 Comparison to Alternative Models

The two-part pricing theory of insurance needs to be empirically tested against two principal alternatives. One is Gaynor et al's theory of monopoly under health insurance. Our model shares many common features and predictions with this model. The key distinction is our prediction that changes in monopoly power have little or no effect on quantity. On the other hand, the Gaynor et al. model implies that monopoly price hikes are passed through to insured consumers, whose quantity falls in response. Normative differences also arise. The two-part pricing model predicts that market power is less harmful in better insured markets. This is not the case in Gaynor et al, which predicts that the deadweight loss due to market power (weakly) flows through even in the presence of health insurance.

Another alternative theory is the “insurance as subsidy” model (cf, Lakdawalla and Sood 2009). Under this view, an insured marketplace behaves just like a standard monopoly model in which consumers face a subsidized price. If we define σ as the share of the manufacturer price paid by consumers, for example, the monopolist facing demand D(pσ) and marginal cost c solves the problem:

$$\underset{p}{max}pD(p\sigma )-cD(p\sigma )$$

This model shares the prediction that monopolists facing insured markets earn higher profits. Unlike Gaynor et al, it also shares the prediction that eliminating monopoly will have smaller quantity effects in insured markets. However, analysis of the first-order condition for this problem immediately implies the standard monopoly result that the elasticity of demand, $\frac{dD}{dp}\frac{p}{D}$ has an absolute value greater than unity.

Apparently, Hypothesis 1 is inconsistent with Gaynor et al, but consistent with the two-part pricing theory of insurance. Hypothesis 2 is inconsistent with the insurance as subsidy model, but consistent with two-part pricing. The two-part pricing theory is the only one consistent with both hypotheses simultaneously.

C. An Empirical Test of Insurance as a Two-Part Pricing Contract

We test the two hypotheses stated in Section B.7 in the empirical context of the pharmaceutical market, where patent expirations provide convenient examples of stark changes in market power. In this context, we think of a “market” as a particular molecule.

As mentioned above, the reasons behind variation in rates of insurance are not so central to the analysis, but it is nonetheless useful to note that insurance rates in pharmaceutical markets vary for two primary reasons. The first reason is the proportion of users who are over 65 years of age, since (at the time of the data) Medicare coverage did not include a prescription drug component. For example, the correlation in our data between percent of expense paid by the insurer and proportion of users above 65 years of age is 0.41. The second reason is hospital-administration versus self-administration of drugs. The correlation between percent of expense paid by the insurer and whether the drug is administered in a hospital is 0.40. Hospital drugs are typically covered by medical insurance rather than prescription drug insurance. Medical insurance is both more common and more generous than prescription drug insurance.⁹

C.1 Data

We use the IMS Generic Spectra database for this analysis. These data represent 101 unique molecules, whose patents expired between 1992 and 2002. For each molecule, we use up to 5 years of monthly data, which span the interval from 3 years prior to 2 years after patent expiration. The monthly data include both revenues and quantities measured at the ex-manufacturer level, which represents the revenues directly received and quantities directly supplied by the manufacturer in that month, absent any mark-ups or amounts added by wholesalers or other intermediaries. Drug quantity data, in grams, are collected at both the wholesale and retail level (the latter includes hospital pharmacies). Revenue data are collected at the retail level. IMS then adjusts the revenue data, using its data from drug wholesalers, to estimate the implied ex-manufacturer revenue. We drop 6 drugs with missing sales data. For the 95 remaining drugs in our sample, average monthly quantity was 3.77 million grams and average monthly revenues were $19.3 million. The complete list of molecules appears in Appendix C.

Both branded and generic versions of each molecule are present in the data. Therefore, after patent expiration, “quantity” for each molecule is defined as total branded plus generic quantity, and “revenue” is defined as total branded plus generic revenue. This approach is consistent with the theory, which applies to the price and quantity of a particular, homogeneous good. Since branded and generic versions of the same molecule are perfect substitutes, it is appropriate to treat both as belonging to the same good.

We use two sources of information to determine the insurance status of drugs. First, IMS flags drugs that are primarily consumed and available in hospitals. We had 16 such drugs in our data. Second, we merged the IMS databases with the 1996 to 2002 Medical Expenditure Panel Survey (MEPS). MEPS contains detailed information on prescription drug use and insurance coverage for a nationally representative population. For each drug we calculate the share of total drug cost paid by the insurer, one year before patent expiration, as a measure of insurance coverage for the drug. However, since MEPS data are available only from 1996 onwards, this measure is only available for the 43 drugs whose patent expired in 1997 or later. The share of expenses borne by insurers varied significantly across these 43 drugs – the first quartile was 41%, the median was 57%, and the third quartile was 78%.

C.2 Empirical Framework

All the hypotheses listed above can be tested in the context of models that estimate demand for pharmaceuticals, stratified by the degree of insurance. The source of identifying variation for the demand curve is the change in market power induced by the expiration of the molecule's patent.

C.2.1 Hypothesis 1: Quantity

The most direct way to test Hypothesis 1 is with the reduced-form version of a model that regresses patent expiration on quantity. Specifically, we estimate:

$$LnQ=a_1+b_1\mathit{\text{PatExp}}+c_1\mathit{\text{PatExp}}\ast \mathit{\text{Ins}}+\mathit{\text{poly}}(\mathit{\text{month}})+\mathit{\text{poly}}(\mathit{\text{month}})\ast \mathit{\text{Ins}}+d+\varepsilon$$ (19)

$$\mathit{\text{LnQ}}=a_2+b_2\mathit{\text{PatExp}}+c_2\mathit{\text{PatExp}}\ast \mathit{\text{Hosp}}+\mathit{\text{poly}}(\mathit{\text{month}})+\mathit{\text{poly}}(\mathit{\text{month}})\ast \mathit{\text{Hosp}}+d+\varepsilon$$ (20)

LnQ is the log of total grams of the drug sold in a given month. PatExp is an indicator variable for the months after patent expiration. Ins measures the share of drug expenditures borne by insurers the year before patent expiration. Hosp is an indicator variable for whether the drug is a hospital product. poly(month)is a cubic polynomial in months since patent expiration, and d is a drug fixed-effect.

The first equation models the increase in the quantity of the drug sold after patent expiration and how this varies with the degree of insurance for the drug. The cubic in month absorbs a common life-cycle trend in drug sales. The drug fixed-effects absorb time-invariant differences across drugs. Hypothesis 1 predicts c₁ <0 and b₁ + c₁ = 0. The second equation models whether the change in total quantity following patent expiration is different for hospital drugs. Relying on the fact that hospital drugs are better insured, Hypothesis 1 predicts c₂ < 0 and (in the polar case where hospital products are perfectly insured) b₂ + c₂ = 0.

C.2.2 Hypothesis 2: Pricing on the Demand Curve

To test the second hypothesis, we estimate the full instrumental variables model, as in:

$$\begin{array}{l}\mathit{\text{LnQ}}=A_1+B_1\mathit{\text{LnP}}+C_1\mathit{\text{LnP}}\ast \mathit{\text{Ins}}+\mathit{\text{poly}}(\mathit{\text{month}})+\mathit{\text{poly}}(\mathit{\text{month}})\ast \mathit{\text{Ins}}+d+\varepsilon \\ \mathit{\text{LnP}}=A_2+D_1\mathit{\text{PatExp}}+D_2\mathit{\text{PatExp}}\ast \mathit{\text{Ins}}+\mathit{\text{poly}}(\mathit{\text{month}})+\mathit{\text{poly}}(\mathit{\text{month}})\ast \mathit{\text{Ins}}+d+\varepsilon \end{array}$$ (21)

Hypothesis 2 predicts that B₁ < −1, since this represents the estimated elasticity of uninsured drugs, and it predicts that C₁ > 0. Significantly, it also allows for the possibility that B₁ + C₁ > −1.

C.2.3 Identification

The overall elasticity of demand is identified by the patent expiration, which we argue represents a shift in market power that is independent of contemporaneous and immediate shifts in the demand curve.¹⁰ While demand may be changing continuously over time, the patent expiration variable in our model captures the discontinuous effect at the month of expiration.

There is a further identification assumption needed in order to recover the interaction between patent expiration and the degree of coverage. We assume that the patent expiration has similar effects on the supply curve for insured and uninsured molecules. We present some evidence supporting this assumption in Section C.4.1. Note that our approach can accommodate differences in the shape of demand for uninsured and insured molecules, as explained below in Section C.4.2.

C.3 Empirical Results

C.3.1 Market Power, Quantity, and Branded Revenues

The results from our empirical tests of hypothesis 1 are presented in Table 1.

Table 1. Results of Empirical Tests.

	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6
	log total grams			log brand dollars
Patent Expired	0.067	0.093	0.249	-0.175	-0.148	-0.018
	[0.020]***	[0.021]***	[0.105]**	[0.029]***	[0.029]***	[0.113]
Hospital Product* Patent Expired		-0.158			-0.165
		[0.048]***			[0.087]*
Share Insured* Patent Expired			-0.344			-0.492
			[0.135]**			[0.175]***
Constant	12.323	12.322	12.572	15.968	15.968	16.272
	[0.020]***	[0.020]***	[0.033]***	[0.024]***	[0.024]***	[0.040]***
Observations	5002	5002	2488	5002	5002	2488
Number of drugs	95	95	43	95	95	43

Notes: Robust standard errors in brackets. Standard errors are adjusted for clustering at the drug level. Other covariates in the model include drug fixed effects, cubic polynomial in months since patent expiration and cubic polynomial in months since patent expiration interacted with indicator for hospital drugs or percent of expenses borne by insurer.

^*significant at 10%;

^**significant at 5%;

^***significant at 1%

Models 1 to 3 present the effects of patent expiration on total quantity. Model 1 presents benchmark results for the average drug. At patent expiration, the total quantity sold increases by 6.7% for the mean drug. Model 2 demonstrates that, for hospital-administered products, quantity rises by 16 percentage points less. For hospital products, patent expiration is predicted to lower quantity by 6.5%, which is not statistically different from zero. Model 3 repeats this analysis using share of expenses paid by insurers as an alternative measure of how well a molecule is insured. The coefficient estimates imply that, for molecules covered at the first quartile of insurance generosity (41% of expenses paid by insurers), patent expiration raises quantity by 11%. In contrast, for molecules at the third quartile of insurance generosity (78% of expenses paid by insurers), patent expiration leaves quantity statistically unchanged (the point estimate is -2.0%). The results from all of the above models are consistent with Hypothesis 1.

Models 4 to 6 repeat the above analysis but use branded drug revenues as the dependent variable. While the revenue models do not directly test the theory, the effect of patent expiration on revenue is of independent interest as a means of filling out a broader picture of how patent expiration affects pharmaceutical sales. Model 4 suggests that patent expiration leads to a 17.5% decline in branded revenues for the average drug. Model 5 demonstrates that, for hospital-administered products branded revenues fall by 17% more. Model 6 implies that, for molecules at the first quartile of insurance generosity patent expiration reduces branded revenues by 22%. In contrast, for molecules at the third quartile of insurance generosity patent expiration reduces revenues by 40%. These results suggest that branded revenues fall by more for better insured drugs.

C.3.2 Pricing on the Demand Curve

The theory predicts standard monopoly pricing behavior for drugs without insurance, but pricing off the demand curve for drugs that are heavily insured. For uninsured drugs, we expect demand elasticities less than -1.0. For insured drugs, we expect demand elasticities substantially smaller in absolute value and possibly greater than -1.0.

We estimate the price elasticity of demand for drugs by generosity of insurance, using patent expiration as an instrument for ln(price). Other variables in the model are identical to those reported in equations 19 and 20. Results are displayed in Table 2.

Table 2. Price Elasticity of Demand by Insurance Generosity.

	Model 1	Model 2	Model 3
	Log Total Grams	Log Total Grams	Log Total Grams
Coefficient [Std. Error]
Log Price	-0.977	-1.449	-2.641
	[0.348]***	[0.427]***	[1.136]**
Hospital Product* Log Price		2.156
		[0.605]***
Share Insurance* Log Price			3.611
			[1.430]**
Constant	15.658	16.571	16.885
	[0.674]***	[0.826]***	[1.441]***
First Stage Results
F-Statistics (P-value)
Log Price	19.03	9.72	13.38
	(0.0000)	(0.0001)	(0.0000)
Hospital Product* Log Price		18.10
		(0.0000)
Share Insurance* Log Price			15.84
			(0.0000)
Effect of Patent Expiration on
Log Price
Coefficient [Std. Error.]:
All Drugs	-0.069
	[0.016]***
Hospital Drugs		-0.092
		[0.017]***
Fully Insured Drugs			-0.138
			[0.056]**
Observations	5002	5002	2488
Number of Drugs	95	95	43

Notes: Standard errors are adjusted for clustering at the drug level. Patent expiration is used as an instrument for price.

^*significant at 10%;

^**significant at 5%;

^***significant at 1%

Model 1 shows that the price elasticity of demand for the average drug is approximately -1.0. Here and elsewhere, the first-stage F-statistic is well above the standard “rule of thumb” value of 10.0. The only minor exception is in Model 2, where the F-statistic for the prediction of price changes falls to 9.72.

There are substantial differences in the demand elasticities across insurance status. According to Model 2, products administered outside the hospital have demand elasticities of -1.4. In contrast, hospital-administered products have a point estimate elasticity of +0.7, which is significantly different from -1 but not significantly different from 0. This result is inconsistent with the “insurance as subsidy” model, which predicts elasticities less than -1.0and is consistent with the two-part model that predicts price elasticity close to 0 for well insured products.

Consistent with Model 2, the results from Model 3 show that drugs with a larger share of expenses borne by insurers have significantly less elastic demand. Drugs at the first quartile of insurance coverage (40% expenses paid by insurers) have a price elasticity of 1.2. In contrast, drugs at the third quartile of insurance coverage (80% expenses paid by insurers) have a dramatically different price elasticity of +0.25. The latter is significantly different from -1 but not significantly different from 0, which is consistent with two-part pricing but inconsistent with the “insurance as subsidy” model.

On the other hand, the price elasticities of drugs with relatively less insurance accord well with the standard theory of monopoly, which predicts that the demand elasticity should be approximately equal to the inverse of the monopoly markup, or that $-\frac{p{D}^{\prime }(p)}{D(p)}=\frac{1}{1-\frac{MC}{p}}$. Based on this result, drugs administered outside the hospital would exhibit $\frac{MC}{P}\approx 0.28$, while drugs at the first quartile of insurance coverage would exhibit $\frac{MC}{P}\approx 0.17$. Both these numbers are within the range of estimates for monopoly markups on pharmaceuticals (Caves, Whinston et al. 1991).

C.4 Alternative Explanations

C.4.1 Heterogeneous Entry Costs

A potential threat to the validity of our results is a difference in entry costs between insured and uninsured drugs, due to underlying differences in production technology, regulatory hurdles, or differences in the strategic responses of incumbents. For example, if insured products have higher entry costs, patent expiration would lead to less generic entry, and a smaller increase in quantity. To test this hypothesis, we estimate the effect of patent expiration on generic market share, by type of drug. Results from this analysis are presented in Table 3 below.

Table 3. Testing for Differences in Generic Share after Patent Expiration.

	Model 1	Model 2	Model 3
	Generic share in quantity
Patent Expired	0.196	0.202	0.222
	[0.013]***	[0.015]***	[0.049]***
Hospital Product* Patent Expired		−0.032
		[0.035]
Share Insured* Patent Expired			0.061
			[0.075]
Constant	0.087	0.087	0.087
	[0.006]***	[0.006]***	[0.009]***
Observations	5002	5002	2488
Number of drugs	95	95	43

Notes: Robust standard errors in brackets

^*significant at 10%;

^**significant at 5%;

^***significant at 1%

Model 1 shows that patent expiration leads to a 19.6 percentage point increase in generic market share. Models 2 and 3 show that this impact on generic entry is statistically similar for drugs administered inside and outside the hospital, and for drugs with more or less generous insurance coverage.

In addition, we explored a particular mechanism that branded pharmaceutical firms might use to deter entry: introducing newly patented reformulations of the drug approaching patent expiration (Marjit, Kabiraj et al. 2009). Such reformulations are minor alterations of the original patented drug – e.g., extended-release versions -- that allow the manufacturer to compete with generics. We investigated whether this type of behavior is more likely for drugs that are more heavily insured. We found no statistically significant difference in the number of reformulations for drugs administered inside and outside the hospital, and for drugs with more or less generous insurance coverage.

Another mechanism for deterring generic entry is to build brand loyalty for one's drug by heavily advertising it to physicians prior to patent expiration (Caves, Whinston et al. 1991; Scott Morton 2000). We investigated whether drugs administered inside the hospital and with more generous insurance coverage had greater number of detailing visits to physicians per dollar of revenue one year prior to patent expiration. We found no evidence that drugs with greater insurance coverage were deterring entry more aggressively through advertising.

Finally, it is worth noting that differential entry deterrence can potentially explain the observed differences in quantity (Hypothesis 1), but on its own cannot account for demand elasticities that exceed -1.0 (Hypothesis 2). Specifically, even if heterogeneous entry costs cause supply curves to shift out by less in insured markets, such a scenario would never yield estimated demand elasticities greater than -1.0 in a standard model of monopoly. As far as we can tell, any alternative theory that prices on the demand curve and generates demand elasticities above 1.0 would require that firms selling insured molecules shift market demand inward at the time of patent expiration. It is not readily apparent how this would arise, although we cannot rule out the existence of such an explanation.

C.4.2 Heterogeneous Demand Elasticities

One might wonder if heterogeneous demand elasticities could also threaten the approach here. Theory predicts that consumers exhibit less elastic demand for insured drugs, due to the presence of insurance. Alternatively, consumers may have systematically lower demand elasticities for insured drugs due purely to differences in preferences, rather than insurance status per se.¹¹

From a theoretical point of view, however, heterogeneous demand elasticities do not compromise estimates of elasticities on the margin and cannot easily account for the results we observe. For instance, suppose that consumers exhibit systematically less elastic demand for insured drugs, due to differences in underlying preferences for such drugs. Even so, the alternatives to the two-part pricing theory would still imply aggregate market elasticities less than 1 for both insured and uninsured drugs. This is inconsistent with the elasticity values we observe for highly insured molecules.

This result is reinforced by our finding of little to no quantity change for insured molecules: since there is little movement along the demand curve, one cannot posit that patent expiration induces a shift to the inelastic portion of the curve, after the expiration occurs.

D. Conclusions and Implications for Policy

The presence of health insurance alters the welfare analysis of monopoly. Price-cost margins and even copayment-cost margins become unreliable yardsticks of welfare loss, which is more reliably measured in terms of reductions in quantity or marginal increases in rates of uninsurance. Analysis of pharmaceutical markets provides positive evidence consistent with the theory, since drug therapies with less insurer presence exhibit greater deadweight loss from monopoly and greater gains from the elimination of market power. On the other hand, drugs with greater insurer presence seem to gain less, if they gain anything at all, from reductions in market power. They also seem to be priced off the consumer demand curve in ways that are inconsistent with alternative theories of monopoly under insurance.

From a normative point of view, our theory predicts that healthcare monopoly leads to efficiency losses from higher rates of uninsurance, but does not affect efficiency for insured consumers. This implies that greater penetration of health insurance lowers the deadweight loss associated with market power in health care provision. In the polar case of full insurance, market power among providers is entirely a distributional rather than efficiency issue. More generally, policies that expand health insurance take-up can limit the deadweight loss from market power, without direct regulation of health care providers. In sum, a well-functioning and complete insurance market transforms the problem of health care market power from one of deadweight loss into one of distribution.

The design of public health insurance often considers the trade-offs among optimal risk-bearing, moral hazard, and adverse selection. However, our analysis suggests that it ought to consider how a two-part health insurance contract can best maximize social surplus. An optimally designed public health insurance scheme would set co-payments at or below marginal cost, depending on the extent of moral hazard. The division of resources among consumers can then be determined by the schedule of premia, which allows the government to extract (and then redistribute) as much or as little consumer surplus as it chooses. In markets where innovative products are sold, two-part health insurance can also be configured to generate any desired change in the profits that serve as the incentive for innovation, without compromising static efficiency in the utilization of health care goods (Lakdawalla and Sood 2009). For example, setting premiums so that providers keep more profit will stimulate greater innovation, and vice-versa. Critically, these incentives for innovation can be manipulated without affecting the efficiency of utilization, which is governed by copayment levels.

The normative implications of the theory lead to several important lessons for policymakers.

First, new approaches are needed for identifying the presence of inefficient market power in health care

Specifically, high price-cost margins in healthcare are not sufficient indicators of deadweight loss from market power. The theory predicts that when all consumers are insured, high price-cost margins do not create deadweight loss. Even copayment-cost margins are insufficient indicators, as these reflect the degree of moral hazard, rather than deadweight loss from health care provider market power. Anti-trust enforcers, courts, and policymakers should instead look for high price-cost margins coupled with high or rising rates of uninsurance. These are more reliable signs of deadweight loss. To our knowledge, the take-up of insurance is rarely if ever taken into consideration by courts or anti-trust enforcement agencies. This practice should be revisited.

Second, from a deadweight loss perspective, healthcare anti-trust enforcement is less valuable in markets with full insurance or high levels of insurance

More generally, antitrust enforcement in insured markets is purely redistributive, and should thus be compared against other policy options for redistribution like taxation and subsidies. To be specific, in an insured marketplace, “letting monopoly stand” might be no different than breaking it up, except in terms of distributional impacts. Therefore, the scope and aggressiveness of antitrust policy should turn on society's preferred approach to distribution, rather than on its approach to efficiency.

Third, when evaluating aggressive anti-trust in healthcare, policymakers should be comparing it alternative distributional policies, rather than as a unique tool for promoting efficiency

For example, the social costs and benefits of antitrust enforcement should be compared against the costs and benefits of taxing the profits of powerful health care providers, making transfers to poorer health care consumers, and related policies. This contrasts with the typical approach, which primarily compares the virtues of monopoly to the virtues of competition – e.g., the valuable scale economies of large firms might be compared to the price-discipline of competition between small firms.

Fourth, there is a unique efficiency rationale for policies that expand the take-up of health insurance, when health care providers possess market power

In this case, greater insurance take-up lowers deadweight loss due to market power. As a corollary to this point, health insurance expansion can be viewed as a policy substitute to anti-trust enforcement. Indeed, in a marketplace where health policy guarantees universal coverage, there is much less, or perhaps even no, efficiency gain from anti-trust enforcement against healthcare providers. Significantly, policy discussions surrounding health insurance expansions often focus on equity issues, or perhaps even health spending issues, but they often fail to consider the value of health insurance expansions for more efficient healthcare provision by powerful providers.

Research Highlights.

1. Health insurance limits deadweight losses from market power in health care.

2. Market power among health care firms does not affect insured consumers

3. Market power among health care firms may boost rates of uninsurance

4. Data from the pharmaceutical market supports these predictions

5. Pharmaceutical patent expirations have little value in heavily insured segments

Appendix

A. Moral Hazard

Associating the multiplier μ with the break-even constraint, the first-order conditions from the problem in Section B.2 can be expressed as:

$$\begin{array}{c}[I]:E{u}_W=\mu (1-(m-MC)E(q_W))\\ [m]:{\int }_0^1\frac{q}{E(q)}{u}_W(W-I-mq,q,h)dh=\mu (1-(m-MC)(-\frac{E(q_m)}{E(q)})\end{array}$$

These first-order conditions illustrate the standard trade-off between risk-bearing and incentives in the presence of moral hazard. The left-hand side of the first order condition for m always exceeds the left-hand side of the condition for I, because u_w and q* are decreasing in h.¹² This fact, coupled with the two first-order conditions, implies that

$$(m-MC)(\frac{E(q_m)}{E(q)}+E(q_W))>0$$

Observe that E(q_m) + E(q)E(q_W) is the expected effect on q of a Hicksian-compensated increase in the co-payment m. Since the compensated demand for medical care is downward-sloping,¹³ it follows that $(\frac{E(q_m)}{E(q)}+E(q_W))<0$, and m < MC. In turn, this implies that the marginal utility of wealth will be higher than in the first-best, according to the first-order condition for insurance.

B. Theoretical Analysis of Adverse Selection

Under adverse selection, consumers are heterogeneous ex ante. There are chronically ill patients (type C) and not chronically ill patients (type N). Firms cannot observe consumer types. Define μ^C(h) and μ^N(h) as the measures of chronically ill and not chronically ill people, respectively. The distribution of health for the chronically ill is assumed to dominate the other in the first-order stochastic sense. An insurance contract is an ex ante insurance premium (I), coupled with an ex post copayment (m).

B.1 The Competitive Solution to Adverse Selection

A pooling equilibrium is not possible for the usual reasons (Rothschild and Stiglitz 1976): given any putative pooling equilibrium, there is always a profitable contract that attracts only the low-risk insureds. Therefore, if an equilibrium exists, it must be a separating equilibrium. As such, the competitive insurance industry chooses two contracts that maximize the welfare of each type of agent, subject to incentive compatibility constraints (ensuring the contracts are chosen by the correct agents) and break-even constraints. The contract (m^C,I^C) for the chronically ill solves:

$$\begin{array}{l}{max}_{m^C,I^C}{\int }_0^{1}u(W-I^C-m^C{q}^C,q^C,h){\mu }^C(h)dh\hfill \\ s.t.\hfill \\ [\gamma ]:{\int }_0^{1}u(W-I^N-m^N{q}^N,q^N,h){\mu }^N(h)dh\hfill \\ \ge {\int }_0^{1}u(W-I^C-m^C{q}^C,q^C,h){\mu }^N(h)dh\hfill \\ [\beta ]:I^C+{\int }_0^1{q}^C{\mu }^C(h)dh(m^C-p)\ge 0\hfill \\ q^N\equiv q(W-I^N,m^N,h),q^C\equiv q(W-I^C,m^C,h)\hfill \end{array}$$ (22)

This problem has the following first-order conditions:

$$\begin{array}{l}[I]:E_C(u_W)-\gamma E_N(u_W)=\beta (1-E_C(q_W)(m^N-p))\hfill \\ [m]:E_C(u_W\frac{q^C}{E_C(q^C)})-\gamma E_N(u_W\frac{q^C}{E_C(q^C)})=\beta (1-\frac{E_C(-q_m)}{E_C(q_c)}(m^C-p))\hfill \end{array}$$ (23)

The indirect utility conferred by a specific contract is defined by v^C(I,m) and v^N(I,m) for the chronically ill and not chronically ill patients, respectively; these are defined as follows.

$$v(I,m)\equiv {max}_q{\int }_0^{1}u(W-I-mq(W-I,m,h),q(W-I,m,h),h)\mu (h)dh$$ (24)

We impose two assumptions that make this environment similar to the Rothschild-Stiglitz one. First, the chronically ill are willing to pay more for a given change in the copayment rate, in the sense that:

$$-\frac{dI}{dm}{|}_{v^C}>-\frac{dI}{dm}{|}_{v^N}$$ (25)

This is the typical “single-crossing” property from Rothschild and Stiglitz's (1976) analysis of adverse selection.¹⁴ Second, a given change in the co-payment rate for the chronically ill has a bigger impact on a firm's profits, so that:

$$\begin{array}{l}-\frac{dI}{dm}{|}_{\pi =0}=\frac{E(q)+(MC-m)E(q_m)}{E(q_W)(MC-m)}\hfill \\ -\frac{dI}{dm}{|}_{{\pi }^C=0}>-\frac{dI}{dm}{|}_{{\pi }^N=0}\hfill \end{array}$$ (26)

Figure 1 illustrates the separating equilibrium in (I,m)-space. The curves Z^N and Z^C represent the zero-profit curves for the not chronically ill and chronically ill, respectively. v^C is the indifference curve for the chronically ill tangent to the zero-profit line — this represents the optimal contract that is possible under moral hazard. Observe that if the moral hazard contract for the not chronically ill falls on the curve segment A, there is no adverse selection problem, because the moral hazard contracts for both types are incentive-compatible with each other.

Figure 1.

Equilibrium with adverse selection and moral hazard.

Now consider the case where adverse selection has an impact: if the moral hazard contract for type N falls on the curve segment B. In this case, the chronically ill will receive their second-best moral hazard contract, while the other type will receive the contract at the intersection of v^C and Z^N.

B.2 Adverse Selection with Two-Part Health Insurance

A monopolist who charges an upfront premium and an ex post copayment maximizes profits subject to reservation utility conditions (i.e., participation constraints) and incentive constraints.

$$\begin{array}{l}{max}_{m^C,I^C,m^N,I^N}{I}^C+(m^C-MC){\int }_0^1{q}^C{\mu }^C(h)dh+I^N+(m^N-MC){\int }_0^1{q}^N{\mu }^N(h)dh\hfill \\ s.t.\hfill \\ {\int }_0^{1}u(W-I^N-m^N{q}^N,q^N,h){\mu }^N(h)dh\hfill \\ \ge {\int }_0^{1}u(W-I^C-m^C{q}^C,q^C,h){\mu }^N(h)dh\hfill \\ {\int }_0^{1}u(W-I^C-m^C{q}^C,q^C,h){\mu }^C(h)dh\hfill \\ \ge {\int }_0^{1}u(W-I^N-m^N{q}^N,q^N,h){\mu }^C(h)dh\hfill \\ {\int }_0^{1}u(W-I^C-m^C{q}^C,q^C,h){\mu }^C(h)dh\ge {\overline{u}}^C\hfill \\ {\int }_0^{1}u(W-I^N-m^N{q}^N,q^N,h){\mu }^N(h)dh\ge {\overline{u}}^N\hfill \\ q^N\equiv q(W-I^N,m^N,h),q^C\equiv q(W-I^C,m^C,h)\hfill \end{array}$$ (27)

Since this problem is additively separable in (I^C,m^C) and (I^N,m^N), the joint profit-maximization problem is identical to two separate problems, in which the monopolist maximizes profits over each contract. Specifically, the maximization problem in 27 is equivalent to the pair of maximization problems below:

$$\begin{array}{l}{max}_{m^C,I^C}{I}^C+(m^C-MC){\int }_0^1{q}^C{\mu }^C(h)dh\hfill \\ s.t.\hfill \\ {\int }_0^{1}u(W-I^{N\ast }-m^{N\ast }{q}^{N\ast },q^{N\ast },h){\mu }^N(h)dh\hfill \\ \ge {\int }_0^{1}u(W-I^C-m^C{q}^C,q^C,h){\mu }^N(h)dh\hfill \\ {\int }_0^{1}u(W-I^C-m^C{q}^C,q^C,h){\mu }^C(h)dh\ge {\overline{u}}^C\hfill \\ q^N\equiv q(W-I^{N\ast },m^{N\ast },h),q^C\equiv q(W-I^C,m^C,h)\hfill \end{array}$$ (28)

$$\begin{array}{l}{max}_{m^N,I^N}{I}^N+(m^N-MC){\int }_0^1{q}^N{\mu }^N(h)dh\hfill \\ s.t.\hfill \\ {\int }_0^{1}u(W-I^{C\ast }-m^{C\ast }{q}^C,q^C,h){\mu }^C(h)dh\hfill \\ \ge {\int }_0^{1}u(W-I^N-m^N{q}^N,q^N,h){\mu }^C(h)dh\hfill \\ {\int }_0^{1}u(W-I^N-m^N{q}^N,q^N,h){\mu }^N(h)dh\ge {\overline{u}}^N\hfill \\ q^N\equiv q(W-I^N,m^N,h),q^C\equiv q(W-I^{C\ast },m^{C\ast },h)\hfill \end{array}$$ (29)

As in the baseline case, it is straightforward to show that these problems yield Pareto-equivalent allocations to the competitive problems.

Without loss of generality, we show this for the type N contract. To net out distributional effects, we assume that the representative type N consumer holds a claim on all profits that flow from contracts with type N consumers. Note that there may not be a well-defined equilibrium in the case of adverse selection; we limit ourselves to the case where an equilibrium exists. If no equilibrium exists, deadweight loss from monopoly is undefined. Define π̅^N as the equilibrium profit associated with the solution to 29. If so, then 29 is identical to a problem in which the firm maximizes consumer utility subject to a reservation profit constraint, and the incentive constraint. This problem will also yield profits equal to π̅, incentive-compatibility, and utility at least equal to u̅^N:

$$\begin{array}{l}{max}_{m^N,I^N}{\int }_0^{1}u(W-I^N-m^N{q}^N+{\overline{\pi }}^N,q^N,h){\mu }^N(h)dh\hfill \\ s.t.\hfill \\ {\int }_0^{1}u(W-I^{C\ast }-m^{C\ast }{q}^C,q^C,h){\mu }^C(h)dh\hfill \\ \ge {\int }_0^{1}u(W-I^N-m^N{q}^N,q^N,h){\mu }^C(h)dh\hfill \\ I^N+(m^N-MC){\int }_0^1{q}^N{\mu }^N(h)dh\ge {\overline{\pi }}^N\hfill \\ q^N\equiv q(W-I^N,m^N,h),q^C\equiv q(W-I^{C\ast },m^{C\ast },h)\hfill \end{array}$$ (30)

Substituting the reservation profit constraint into the consumer's objective function yields:

$$\begin{array}{l}{max}_{m^N,I^N}{\int }_0^{1}u(W-m^N(q^N-E(q^N))-MC\ast E(q^N),q^N,h){\mu }^N(h)dh\hfill \\ s.t.\hfill \\ {\int }_0^{1}u(W-I^{C\ast }-m^{C\ast }{q}^C,q^C,h){\mu }^C(h)dh\hfill \\ \ge {\int }_0^{1}u(W-I^N-m^N{q}^N,q^N,h){\mu }^C(h)dh\hfill \\ q^N\equiv q(W-I^N,m^N,h),q^C\equiv q(W-I^{C\ast },m^{C\ast },h)\hfill \end{array}$$ (31)

This problem is identical to the version of the competitive problem in 22 where the firm's binding participation constraint is substituted into the objective function.¹⁵ Therefore, the monopoly allocation is identical to the competitive one.

C. Pharmaceutical Data

Table B-1: List of drugs in the analysis

Product Name
ACTIGALL
AMIDATE
AMIKIN
ANAFRANIL
ANSAID
AREDIA
ATROVENT
BETAGAN
BETAPACE
BUMEX
BUSPAR
CAPOTEN
CAPOZIDE
CARAFATE
CARDENE
CARDIZEM
CARDURA
CECLOR
CEFTIN
CLOZARIL
CORGARD
COUMADIN
CYLERT
DAYPRO
DIABETA
DOBUTREX
DOLOBID
ELDEPRYL
ESTRACE
EULEXIN
FLUMADINE
GLUCOPHAGE
GLUCOTROL
HALCION
HYDREA
HYTRIN
IMURAN
INTAL
KLONOPIN
LODINE
LOPID
LOPRESSOR
LOTRIMIN
LOZOL
LUVOX
MEFOXIN
MEVACOR
MEXITIL
MUTAMYCIN
NAPROSYN
NEORAL
NEPTAZANE
NIZORAL TA
NOLVADEX
OGEN
ORUDIS
PARLODEL
PEPCID
PLAQUENIL
PRIMACOR
PROCARDIA
PROPINE
PROSOM
PROZAC
QUESTRAN
RELAFEN
RIFADIN
RYTHMOL
SECTRAL
SELDANE
SINEMET
STADOL
TAGAMET
TAMBOCOR
TAXOL
TEMOVATE
TENEX
TENORETIC
TORADOL
TRACRIUM
TRENTAL
VASOTEC
VEPESID
VERSED
VISKEN
VIVACTIL
VOLTAREN
WELLBUTRIN
WYTENSIN
XANAX
ZANTAC
ZARONTIN
ZIAC
ZINACEF
ZOVIRAX