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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:
Journal of Industry, Commerce and Trade
What has changed in the hospital market?
Literature (continued) – Explanations for mixed competition
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.
where the utility function has normal properties and costs are increasing in quality investment (t1n) and decreasing in cost saving investment (t2n).
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.
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.
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:
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.
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.
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.