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Keywords:

  • medical innovations;
  • price regulation;
  • dynamic and static efficiency

ABSTRACT

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. THE MODEL
  5. EQUILIBRIUM
  6. DISCUSSION
  7. CONCLUSIONS
  8. APPENDIX
  9. ACKNOWLEDGEMENTS
  10. REFERENCES

We study the market for new medical technologies from a life cycle perspective, incorporating the fact that healthcare utilization is biased towards old age. Contrary to conventional wisdom, we find that price controls on medical innovations can expand investment in medical R&D and results in Pareto superior social outcomes, a consequence of the price controls' ability to increase saving. Importantly, this finding occurs only when the price cap regime is extensive: selective regulation on few technologies – such as pharmaceuticals alone – have the conventional negative effect on innovation. Copyright © 2013 John Wiley & Sons, Ltd.

INTRODUCTION

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. THE MODEL
  5. EQUILIBRIUM
  6. DISCUSSION
  7. CONCLUSIONS
  8. APPENDIX
  9. ACKNOWLEDGEMENTS
  10. REFERENCES

According to conventional wisdom, the design of optimal price regulation for innovative industries should strike a balance between making patented technologies more affordable for consumers and maintaining producers' incentive to innovate. The present study shows that in long-term perspective, price regulation on medical technologies may actually enhance medical innovation and lead to Pareto improvements.

The study of optimal regulation of monopoly that addresses both product quality and price was introduced by Spence (1975), Sheshinski (1976) and Dixit (1979). These studies, however, relied on a static framework in which both quality and price are set simultaneously. Later studies showed that in cases where pricing takes place after R&D (or capacity) investment was made, price regulation involves a tradeoff between the static and dynamic efficiency (see for example, Gilbert and Newbery 1994, Biglaiser and Riordan 2000, and Lyon and Mayo, 2005).

In these models, ‘static efficiency’ refers to welfare gains from setting the regulated price closer to marginal production cost, after R&D effort was taken. The ‘dynamic efficiency’, by contrast, accounts also for the welfare effects of the regulated price on the incentive to innovate. This literature has demonstrated the inconsistency of regulator's optimal plan, which tends to overemphasize static efficiency at the expense of dynamic efficiency.

The medical sector is one of the most heavily regulated in all developed economies and is continually the focus of public deliberation and political debate. For example, price controls on new pharmaceuticals have been considered in some countries (as in the USA during President Clinton's first administration), whereas actual implementation has occurred in others (as in Canada and EU countries). Both empirical and theoretical studies have examined the possible implications of regulating the prices of innovative medicines.1 However, all of these studies consider price regulation (and patent policy) only for specific sorts of medical innovations, for example, pharmaceuticals, and they account only for innovators' inter-temporal consideration of setting optimal R&D investment in light of future price and market size.

The present study introduces inter-temporal considerations on the consumers' part, by accounting for the life cycle nature of medical needs and spending: the old consume more medical care than the young. In the year 2004, 85% of lifetime healthcare expenditure for the average American was spent after the age of 55 years, and healthcare expenditure of the typical American retiree (age 65 years and older) was 3.3 times larger than for the working age person.2 We postulate that this life cycle profile of medical needs produces potential complementarities between R&D investment and saving decisions: the greater the saving and thereby, future demand, the more profitable it will be to invest in medical R&D. Further, higher future technological quality encourages savings as long as the price of innovative technologies does not increase too much.3

Nevertheless, as saving decisions are made before future prices are set, these potential complementarities cannot be realized because of the typical holdup scenario: absent regulation or credible commitment to a low quality-adjusted price, young consumers expect innovators to fully exercise their market power in the future and thus, they save less. Lower savings, in turn, result in lower demand for medical technologies by the old and therefore, lower R&D investment. Effective price controls, set in advance or credibly expected, can replace the lack of self-commitment by innovators. Hence, we identify a positive market size effect of price regulation on medical innovation, which works through the saving channel and show that it can surpass the conventional negative effect of the regulated markup.4

Similar holdup problems in the absence of commitment to future price or quality were analyzed by Farrell and Gallini (1988) and Shepard (1987), respectively. These studies have shown that, when the utilization of a certain technology or service involves lock-in effects, the monopolistic supplier may benefit from committing to a low price or high quality. In these studies, the monopoly licenses the technology in advance to potential competitors, and thus, licensing serves as a commitment device. Nevertheless, we show that when there are multiple medical technologies being developed by non-cooperative innovators, any private incentive for strategic price commitment vanishes, and thus price controls are needed.

The remainder of the paper is organized as follows: Section 2 presents the basic model. Section 3 studies market equilibrium in the absence and presence of price controls. Section 4 discusses the results in light of possible extensions of the model, and Section 5 concludes the study.

THE MODEL

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. THE MODEL
  5. EQUILIBRIUM
  6. DISCUSSION
  7. CONCLUSIONS
  8. APPENDIX
  9. ACKNOWLEDGEMENTS
  10. REFERENCES

Consumers

The economy is populated by a unit mass of consumers who live through two periods: ‘adulthood’ and ‘elderly’. During adulthood, consumers are ‘young’, and during elderly, they are ‘old’. When young, they are endowed with a given monetary income, I, and derive utility from consumption, denoted c1. When old, consumers derive utility from consumption, c2, and from medical good, z. The quality of the medical technology in use, denoted q, multiplies the effective utilization of the medical good.5 To simplify exposition and without altering our qualitative results, we assume no time preference and zero interest rate. Putting the previous characteristics together, we formulate consumer's lifetime utility:

  • display math(1)

This functional form allows us to focus on the relevant inter-temporal substitution affects, because of the unit elasticity of substitution between consumption and medical goods within the second period (that is, c2 and z are independent goods). The price of the medical good is denoted p, and the price of the consumption good is normalized to 1. Consumers maximize their lifetime utility (1) by allocating income over the two periods of life and choosing the preferred medical technology among those available in the market, subject to the budget constraint:

  • display math(2)

We denote saving – s, where

  • display math(3)

The optimal allocation of savings over medical and consumption goods during elderly provides the following demand functions:

  • display math(4a)
  • display math(4b)

By using Equations (3)(4b), we write the lifetime indirect utility function in terms of savings and the quality and price of medical technology in use:

  • display math(5)

Maximizing Equation (5) with respect to s, we obtain the optimal savings level s ∗:

  • display math(6)

An interior solution that satisfies Equation (6) requires a minimal ratio of quality to price of health technology: inline image, which we assume to hold. Substituting the optimal saving level back into Equation (5), we obtain the following indirect utility function:

  • display math(7)

Note that consumers' welfare depends positively on income and the ratio of quality to price of the medical technology in use.

Innovation and production

In each period, two generations of the medical technology are available: ‘old’ and ‘new’ to which we refer also as ‘generic‘ and ‘innovative’, respectively. The new generation of the medical technology is developed via investments in R&D process with certain known outcomes.6 The development process lasts one period. Once developed, the innovative technology is sold in the market under patent protection for one period. After one period, the patent expires and market price falls down to the marginal production cost, as generic versions are launched to the market with zero imitation cost, under price competition. We denote the innovative and generic technology of each period as qm and qc, respectively, where inline image; namely the innovative technology of the first period becomes the generic technology of the second period. Innovation (quality-improving) technology is linear:

  • display math(8)

To simplify exposition, we save timing notation for the innovation process, and thus, Equation (8) becomes: qm = ϕ ⋅ Rm. The vertical competition with old technology defines the limit (per unit) price for the new technology, denoted pm:

  • display math(9)

According to Equation (9), innovator's markup is equal to the relative quality of the new technology compared with the old one. Given that the innovator chooses optimal R&D investment to maximize the following profit function and accounting for possible effect of current R&D investment on future demand for the innovative technology

  • display math(10)

EQUILIBRIUM

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. THE MODEL
  5. EQUILIBRIUM
  6. DISCUSSION
  7. CONCLUSIONS
  8. APPENDIX
  9. ACKNOWLEDGEMENTS
  10. REFERENCES

The non-regulated equilibrium is characterized by a triplet (qm, pm, s∗) that solves the following sequential interaction: in the first period, the innovator chooses R&D investment. Then, young consumers observe current innovative technology and current R&D investments, so they may correctly evaluate the quality of innovative and generic medical technologies that will be available in the market when they become old. They use these observable qualities and corresponding prices to decide how much to save. In the second period, trade in medical goods takes place.7

Absent price controls, consumers expect the new technology to be sold at the limit price defined in Equation (9). Thus, optimal saving level is irresponsive to current R&D investment as obtained by substituting the monopolistic price and quality into Equation (6):

  • display math(11)

By substituting the optimal saving (11) into the profit equation (10) and maximizing with respect to q, we obtain the following first-order condition:

  • display math(12)

Under the optimal investment in quality (12), profit is positive if8

  • display math(12a)

The left side of Equation (12a) decreases with qc and mc, and it increases with income and R&D productivity. The share of consumption spending out of saving, α, has negative effect on the left side of Equation (12a) and a positive effect on its right side. Note that the positive profit condition implies that inline image, and let us assume that it holds.

Price regulation

We now turn to analyze the equilibrium under a price control over medical innovations, denoting the statutory price ceiling pmax, and the corresponding quality chosen by the innovator qmax = qm(pmax). Note, however, that to have any effect on saving decisions, the price regulation should be expected in advance, and should result in higher quality to price ratio, that is inline image. When this condition holds, the price ceiling is ‘effective’. The innovator that operates under the effective price ceiling solves the following maximization problem:

  • display math(13)

The first-order condition for profit maximization is given by

  • display math(14)

In contrast with condition (12), under effective price regulation, optimal R&D investment is independent of the quality of old technology. Dividing the right side of Equation (14) by pmax, we obtain the regulated quality to price ratio:

  • display math(15)

Differentiating the right side of Equation (15) with respect to pmax, we find that the price ceiling that maximizes Equation (15) and thus consumer's utility is pmax = 2 ⋅ mc. Note that, according to Equation (12a) the price ceiling that maximizes consumers' welfare is always below the non-regulated market price. It can be shown that profit is positive under such regulation if inline image. By comparing the regulated equilibrium with the non-regulated one, we obtain the following two propositions.

Proposition 1. An expected price ceiling pmax = pm can enhance the quality of medical technology and result in Pareto improvement.

Proof. Setting inline image, we rewrite condition (15) for effective price regulation: inline image. Then, substituting the explicit expression for qm into the right side of the inequality, we obtain inline image. Nevertheless, positive profit absent regulation requires inline image. Hence, if inline image, price regulation is effective for pmax = pm, and by revealed preference, innovator's choice for a higher quality under this price regulation implies that it is profitable. Q.E.D.

Proposition 2. There are effective price ceilings set higher or below the non-regulated market price that enhance the quality of medical technology and improve consumers' welfare.

Proof. The reaction function (14) is increasing with pmax and concave. Proposition 1 implies that the curve (14) is above the reservation utility ray inline image for pmax = pm. Then, there exists a range of effective price ceilings inline image for which qmax > qm. Q.E.D.

Figure 1 illustrates the proof for proposition 2. In the diagram, the horizontal and vertical axes measure price and quality of the innovative technology, respectively. The solid ray denoted u0 is the reservation utility curve, defined by inline image. The non-regulated equilibrium is defined by the point NR = (pm,qm), which belongs to u0 and according to Equation (12a), satisfies qm > 2 ⋅ qc. The concave curve qmax(pmax) represents the reaction function (14). Under the conditions defined in the proof of proposition 1, the reaction curve is above the NR. Finally, the ray denoted umax is the indifference curve that represents the maximal utility to be achieved by the effective price ceiling pmax = 2 ⋅ mc.

For any price ceiling inline image, regulation is effective and results in higher quality. Note that in case reservation utility is high enough, price regulation will not be effective as the indifference ray u0 will be entirely above the response curve qmax(pmax).

image

Figure 1. Equilibrium under effective price ceiling

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DISCUSSION

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. THE MODEL
  5. EQUILIBRIUM
  6. DISCUSSION
  7. CONCLUSIONS
  8. APPENDIX
  9. ACKNOWLEDGEMENTS
  10. REFERENCES

Multiple medical technologies and innovators: In accordance with our results thus far, one would expect to empirically observe self-commitment to future prices in the medical sector, in the form of pre-licensing for example, or through reputational strategic pricing (allowing repeated interaction between consumers and innovators). Although testing for reputational pricing considerations is difficult, voluntary pre-licensing in the pharmaceutical industry for example is hard to be found. Nevertheless, commitment should not be expected to prevail once we allow for multiple medical products, innovated by different innovators. Suppose for example that old consumers utilize, n, different medical goods, still under the Cob–Douglas functional form: inline image. Here, savings' response to a marginal decrease in the quality-to-price ratio of a single medical good decreases with the number of medical goods, n, and so the incentive to commit diminishes as n increases. In addition, as the number of innovators increases each innovator tends more to free-ride other innovator's commitments for price.

Global income heterogeneity: The presented analysis is confined to the case of homogenous consumers in a global economy that implements a uniform price regulation, and thus, we abstract from significant income (and possibly demographic) heterogeneity within and across countries. Hence, our analysis should be read as a normative benchmark that emphasizes possible gains from global price controls, rather than a concrete policy recommendation. In case of income (or preference) heterogeneity, the effect of price regulation on saving would differ across countries. For example, any possible saving increase in Sub-Saharan African economies may have insignificant effect on innovation simply because of their low-income level. In a more realistic model, the actual effect of price controls on innovation should average the changes in price and their effect on aggregate saving across different economies.

Innovation uncertainty and market structure: Introducing uncertainty regarding R&D outcomes would not change our main results as long as the expected return on R&D investment increases with saving and the probability for successful innovation increases with R&D effort (which is the natural assumption in the R&D literature). Also, our results are neutral to the assumed market structure for the generic innovation: Facing the unit demand elasticity the innovator finds it optimal equaling the quality-adjusted price of the new technology with that of the old one. Then, through Bertrand competition, the price of the old one will fall down to the MC level regardless the market structure of for the old technology.

Price controls vs. patent protection: Note that weakening patent protection over medical technologies may have equivalent results: Allowing for imitation of inferior quality variants may ensure a quality to price ratio that is higher than the initial reservation ratio. Such a policy can bound the maximal quality of the imitated technology to the level γ ∈ (0,1). For example, when inline image, the equilibrium that prevails under price regulation will be achieved. However, if imitation is costly, such a policy becomes less effective because no one would like to entail this cost knowing its imitative technology is dominated by innovative one.

CONCLUSIONS

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. THE MODEL
  5. EQUILIBRIUM
  6. DISCUSSION
  7. CONCLUSIONS
  8. APPENDIX
  9. ACKNOWLEDGEMENTS
  10. REFERENCES

We have analyzed the market for new medical technologies from a long-term life cycle perspective. The novelty of the present study lies in considering the response of savings to price regulation and the effect on medical R&D efforts.

Several empirical studies have documented a negative effect of expected or actual price regulation on R&D effort in this industry. See for example, Giaccotto et al. (2005) and Golec and Vernon (2006). These empirical findings, however, do not necessarily contradict our theoretical results; our model does predict that selective price regulation over a small fraction of medical technologies only would yield the standard negative results because savings response in this case would be small. According to OECD Health Data (2010),9 in the year 2008, the expenditures on pharmaceuticals and other non-durable medicals in the USA did not exceed 12% of national health expenditure.

For enhancing savings and R&D effort, it is enough that consumers and innovators expect future price regulation, while the actual implementation of price caps is necessary for improving consumer welfare. Finally, it should be noted that as medical technologies are being sold in the global market, policy implications derived from this study should be viewed in a global perspective. That is, policy coordination among countries will be necessary for the implementation of our theoretical result.

APPENDIX

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. THE MODEL
  5. EQUILIBRIUM
  6. DISCUSSION
  7. CONCLUSIONS
  8. APPENDIX
  9. ACKNOWLEDGEMENTS
  10. REFERENCES

Positive profit in the non-regulated market

The profit as a function of innovated quality is given by

  • display math(A.1)

Substituting the explicit demand function into A.1, we obtain

  • display math(A.2)

Rearranging A.2, we define the positive profit condition

  • display math(A.3)

Simplifying A.3 and substituting the explicit expression for qm,we obtain

  • display math

ACKNOWLEDGEMENTS

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. THE MODEL
  5. EQUILIBRIUM
  6. DISCUSSION
  7. CONCLUSIONS
  8. APPENDIX
  9. ACKNOWLEDGEMENTS
  10. REFERENCES

I am grateful to Jacob Glazer and Daniel Tsiddon for patient guidance and inspiration. Comments by Pedro Barros and anonymous referee of this journal have significantly improved this paper. I benefited also from valuable comments by Adi Pauzner, Manuel Trajtenberg, Chaim Fershtman, Massimo Motta, Roy Shalem, Sivan Frenkel and Adeet Handel as well as from the input of seminar participants at Tel-Aviv University, SUNY at Buffalo, at Albany and at Binghamton, and participants in the PET 2011 conference at IU-Bloomington and the 8th world congress of the International Health Economics Association in Toronto 2011. Special thanks go to Randy Beard for helping in the final editing of the article.

  1. 1

    For recent examples, see Atella et al. 2008, Bekke et al. 2008 and Civan and Maloney 2009.

  2. 2

    Source: US department of Health and Human Services, National Health Expenditures Data, Health Expenditures by age, 2004.

  3. 3

    Whereas the literature on macroeconomic growth has already emphasized the positive effect of progress in medical technology and health conditions on saving and investment decisions, it did not study the implications of price regulations. See for example, Blackburn and Cipriani (2002), Chakraborty (2004) and Sanso and A'isa (2006).

  4. 4

    Acemoglu and Linn (2004) document positive market size effect of demographic aging on pharmaceutical R&D.

  5. 5

    For simplicity, we refer here to a single medical need and medical technology. In Section 4, we consider the case of multiple medical technologies designed to treat different medical needs.

  6. 6

    Our results would not be affected by introducing uncertain R&D outcomes, or changing the market structure for the generic technology. See Section 4 for discussion.

  7. 7

    In fact, the crucial assumption here is that pricing follows savings decisions.

  8. 8

    See complete elaboration in the Appendix.

  9. 9

REFERENCES

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. THE MODEL
  5. EQUILIBRIUM
  6. DISCUSSION
  7. CONCLUSIONS
  8. APPENDIX
  9. ACKNOWLEDGEMENTS
  10. REFERENCES