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Reimbursement and Investment: Prospective Payment and For-Profit Hospital’s Market Share. Seungchul Lee Robert Rosenman Forthcoming, Journal of Industry, Commerce and Trade. Motivation for the research comes from two observations:

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reimbursement and investment prospective payment and for profit hospital s market share

Reimbursement and Investment: Prospective Payment and For-Profit Hospital’s Market Share

Seungchul Lee

Robert Rosenman


Journal of Industry, Commerce and Trade


Motivation for the research comes from two observations:

  • Over the past decade hospitals are increasingly concerned with cost control.
    • More investment in cost-saving technologies.
    • Less investment (proportionately) in quality enhancing technologies.
  • There has been a significant growth in for-profit hospital’s market share.
    • From 1980 to 2007, the share of for-profit hospitals grew 5.3% while private not-for-profit grew 2.7%.
    • Government hospitals share fell by 7.8%.

Raises the question:

  • Are these changes coincidental or has there been a fundamental structural change that explains these why hospitals invest differently and for-profit market share has increased?

What has changed in the hospital market?

  • Since 1980, there has been a big shift from retrospective payment to prospective payment.
    • Medicare
    • Growth of managed care
    • Even among indemnity payers with “preferred providers”

What this paper does:

  • Provides a theoretical argument that the move to prospective payment from retrospective payment
    • partially explains the change in hospital investment behavior to cost savings from quality enhancing technologies;
    • allowed for profit hospitals to be more competitive in the market for hospital services.
  • Explains the results in a competitive environment for patients. Hospitals can improve their “bottom line” by
    • attracting more patients with higher quality (from investment in quality enhancing technology) than its competitor, or;
    • lowering costs by investing in cost-controlling technology.
  • How a hospital is reimbursed changes the payoffs from these two different investment strategies. Hence, how hospitals are reimburseed can be a policy tool to enhance quality as well as control costs.


  • Weisbrod (1991) first discussed how payment form affects investment in just the way we argue.
    • That part of our analysis is not novel.
    • What is novel is how we link this to the growing share of for-profit hospitals in the market.
  • Three relevant issues:
    • How the shift in payment changed investment strategies by hospitals.
    • The link between the payment system and quality.
    • What all this means for mixed competition between not-for-profit and for profit hospitals.

Literature (continued)

  • Gaynor and Town (2012) comprehensive review of the literature on mixed competition.
    • Note that under administratively set prices, the currency of competition is quality.
    • Applies to the British National Health Service, and sectors of the US health care market like Medicare.
    • With entry allowed, what matters is the elasticity of demand with respect to quality and the total demand.
    • Equilibrium quality is higher if most hospitals are not-for-profit.
    • Empirical analysis mixed, but most find increased competition increases quality.
  • Brekke, et al (2011) explain the ambiguity by letting quality and (low) costs vary from complements to substitutes

Literature (continued) – Explanations for mixed competition

  • Friesner and Rosenman (2002) explain mixed competition by differences in consumer preferences for quality or price.
  • Lakdawallaand Philipson(2006) explain it by differences in provider preferences, with a shortage of providers with not-for-profit preferences.
  • Our approach embraces both explanations, although is closer to Friesner and Rosenman
    • We have a duopoly supply facing heterogeneous consumers
      • They differ in preference for quality and the opportunity cost of their time.
      • The opportunity cost of their time plays the same role as low price.
    • Like Ladawalla and Philipson, the not-for-profit hospital has profit-deviating preferences
      • Not-for-profits dominates the market due to its willingness to accept part of its return in utility rather than money.
      • For-profits compete only if the not-for-profits don’t supply enough to meet the market demand.

Literature (continue)– Prospective Payment and Quality

  • Allen and Gertler(1991) found prospective payment mechanisms cannot induce optimal quality.
  • Siciliani (2006) found prospective payment lowers quality.
  • Selder (2006) finds prospective payment lowers quality for severely ill patients.
  • RAND (2006) found little change in direct care quality, although patients were discharged earlier and sicker with prospective payment .
  • Ma (1994), Selder (2005) and Miraldo (2007) find hospitals invest less in quality improving technologies under prospective payment than under retrospective payment.
  • Empirical evidence from Teplensky, et al. (1995), Hillman and Schwartz (1995) and other studies supports this.

A Model of hospital market competition

  • N patients, each demanding 1 unit of hospital care
  • Patients gain utility from quality, lose utility from waiting for care (a congestion externality). Patient preferences are heterogeneous.
  • Demand for each hospital is


where f is the for-profit hospital and n is the not-for-profit hospital, indexes each hospital’s demand and is the demand for the for-profit hospital, as a share of total demand, given by N.


For-profit share is positively related to its relative quality and its waiting time, T, is negatively related to its quality.

  • The function collapses to that maps to the proportion of patients choosing the for-profit hospital.
  • We assume that licensing requires a minimum level of quality that exceeds zero.
  • We have T endogenous, but if it instead is thought of as travel time to a heterogeneously distributed population, it could be exogenous.

Hospital Investment

  • Quality improving technology

For-profit objective

  • Not-for-profit objective

where the utility function has normal properties and costs are increasing in quality investment (t1n) and decreasing in cost saving investment (t2n).


Retrospective Reimbursement at Average Cost

By definition, profit for the for-profit hospital is 0, since price equals average cost. It invests nothing in quality enhancing because it gains nothing by doing so.


Not-for-profit problem becomes

Leading to proposition 1:

Proposition 1:When the government pays the full cost of treatment and hospitals are reimbursed their average total cost, the not-for-profit hospital invests only in quality enhancing technology and obtains the globally maximal level of quality. Meanwhile the for-profit hospital has no incentive to make investments in either type of technology.


Proof: We assume with no incentive to make an investment, a hospital will not. Because they are reimbursed for AC, neither hospital has any incentive to control costs, hence t2n=t2f=0. By the same logic, t1f=0and so qf(t1f=0)=qmin.

The NFP faces the equivalent of the unconstrained maximization problem

Because retrospective reimbursement ensures that all costs are covered. Hence the FONC is

By strict monotonicity of the utility function and the demand function, this holds only when  qn/ t1n=0 which occurs when t1n=t1opt.

Corollary 1:Under retrospective reimbursement Qn>Qf.

Proof: Because of the nature of demand, a higher quality hospital gets a larger market share. By proposition 1, t1n=t1opt>0=t1fso the NFP has higher quality.


Prospective Reimbursement

assume both hospitals are reimbursed prospectively, and the prices of both hospitals are identical ().

FONC for for-profit hospital:


FONC for not-for-profit hospital:




Leading to

Proposition 2Under full government payment of patients’ costs, when hospitals are reimbursed prospectively the same amounts;

P21: The for-profit hospital invests in both technologies but does not reach the globally maximum quality.

P22: The not-for-profit hospital invests in both technologies if the revenue constraint is binding, but does not reach the globally maximizing quality.

P23: The not-for-profit hospital invests only in quality technology if the revenue constraint is not binding, and reaches the globally maximum quality.

P24: If the revenue constraint is binding the not-for-profit hospital invests more in both technologies than does the for-profit hospital.



P21: From FOC of the FP hospital which requires t2f >0. We also see that

which requires that 0<t1f<t1opt.

P22: From the FOC for the NFP hospital

The term in brackets on the RHS is positive if >0 which means that 0<t1n<t1opt to ensure the LHS is also positive. If t1n=t1opt the LHS=0. Additionally,

requires t2n >0.


P23: If =0 the revenue constraint is non-binding and so

which is achieved only if t1n=t1opt. The investment in cost saving technology is undefined but there is no incentive to do so.


P24: >0. For quality improving technology notice that for the NFP hospital

We know the LHS is positive, hence so is the RHS. But for the FP hospital


The graph on the next slide shows that this inequality requires t1n>t1f.


Corollary 2:The dominance of the not-for-profit hospital under both retrospective and prospective reimbursement is not due to its ability to raise revenue through donations. They have no effect on market share under retrospective payment. Donations increase the not-for-profit hospital dominance when payment is prospective.

Corollary 3

1: The quality of care given by the not-for-profit hospital under a retrospective reimbursement system exceeds the quality it provides under the prospective payment unless the revenue constraint is non-binding, and its market dominance is stronger.

2:The quality of care given by the for-profit hospital under a retrospective reimbursement system is less than the quality it provides under the prospective payment and it better competes for market share.



  • Medicare was intended to lower costs. It had the intended result: Both hospitals invest more in cost-saving technology.
  • But some unintended results:
    • For-profit hospitals became more competitive (an innocuous outcome)
    • Not-for-profit hospitals invest less, most likely, in quality enhancing technology (a potentially negative outcome).
    • For-profit hospitals invest more in quality investment (off-setting the lower not-for-profit investment).
    • What happens to average quality is ambiguous and an empirical question.
    • Interestingly Gaynor and Town (2012) find a convergence of quality after prospective payment was implemented between for-profit and not-for-profit hospitals.