Underinvestment, Renegotiation and Bridge Financing in Emergency Medical Service Public–Private Partnerships: A Stackelberg Analysis of For-Profit and Non-Profit Providers

Abstract Emergency medical services (EMS) in India are delivered almost entirely through public–private partnerships (PPPs) in which a state government supplies capital and a private operator, corporate or non-profit, supplies non-contractible operating effort. We model this arrangement as a Stackelberg game with moral hazard on a Cobb–Douglas model-based service technology, and obtain closed-form solutions for equilibrium investment, effort, output and payoffs. Four results follow. First, an interior equilibrium exists if and only if the effective return to public capital, \(\:\eta\:=2{\alpha\:}_{2}/\left(2-{\alpha\:}_{1}\right)\), is below unity, which requires \(\:{\alpha\:}_{1}+2{\alpha\:}_{2}<2\); this condition, rather than constant returns to scale, governs the existence of the partnership, and its violation produces the numerically degenerate solutions reported in earlier work on this model (Anantharaman, 2022). Second, the government structurally underinvests: whenever the effort elasticity exceeds a low threshold (\(\:{\stackrel{⃐}{\alpha\:}}_{1}\approx\:0.09\) under our calibration), equilibrium investment is below first best, at our central parameters, 28.9 per cent of it, because the principal internalises only the tax share of the operator’s marginal return. Third, a tax-exempt non-profit operator dominates a taxed corporate operator for every non-negative mission weight, and a non-profit whose mission weight equals \(\:{\lambda\:}^{\text{*}}=1-1/m\) (where \(\:m\) is the social multiplier on service output) implements the first best exactly; but because the government does not bear the operator’s effort cost, its ranking of providers is monotone in the mission weight while welfare is single-peaked, so the principal over-selects high-mission providers. Fourth, under a demand surge, renegotiation is feasible only up to a surge intensity \(\:\stackrel{⃐}{\theta\:}\), efficient bargaining assigns essentially the whole surge cost to the government, and investor bridge financing, the fallback when the public budget binds, sustains service only up to \(\:\widehat{\theta\:}\ll\:\stackrel{⃐}{\theta\:}\); at our calibration the investor route covers just 15.7 per cent of the surge range that renegotiation covers. The welfare-maximising investor revenue share is \(\:{\delta\:}^{\text{*}}=2{\alpha\:}_{2}/\left({\alpha\:}_{1}+2{\alpha\:}_{2}\right)\), invariant to the investor’s required rate of return. We also show that a per-case insurance subsidy, widely advocated to reduce out-of-pocket exposure, crowds out public capital formation in the second best unless capital budgets are ring-fenced. The analysis implies that pre-committed, state-contingent surge clauses dominate ex post renegotiation, and that tax exemption and non-profit empanelment are second-best instruments of first order in EMS PPPs. JEL codes: H44, I18, L33, D82, C72