📈 economics

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

This paper employs a Stackelberg game model to analyze Emergency Medical Service public–private partnerships in India, demonstrating that structural underinvestment arises from the government's inability to capture full marginal returns, that tax-exempt non-profits with specific mission weights can achieve first-best efficiency while outperforming taxed corporations, and that pre-committed surge clauses are superior to renegotiation or bridge financing for managing demand shocks.

Original authors: Senthilkumar Anantharaman

Published 2026-10-14

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Senthilkumar Anantharaman

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the high-stakes world of emergency medical services, the difference between life and death often hinges on a single, invisible variable: the effort of the people on the ground. While governments provide the ambulances and the communications infrastructure, the actual saving of lives depends on the discipline, speed, and dedication of the crews. These workers cannot be forced to work harder through a contract; their extra effort is a choice, a hidden cost they bear to ensure a patient survives. This creates a delicate economic puzzle known as a principal-agent problem. The government, acting as the principal, wants the maximum possible service for its citizens, but it cannot directly observe or pay for the specific intensity of the crew's work. Instead, it must design a system where the private operator, whether a corporation or a non-profit, finds it in their own interest to exert that necessary effort. The question is not just how to build the system, but how to fund it, how to tax it, and what happens when a disaster strikes and the demand for ambulances suddenly explodes beyond what anyone planned for.

A new study by Senthilkumar Anantharaman tackles these questions by modeling the emergency medical service system in India as a strategic game. The researcher treats the relationship between the government and the private operator as a sequence of moves, where the government moves first by deciding how much to invest in vehicles and infrastructure, and the operator moves second by deciding how hard to work. The study uses a mathematical framework to simulate this interaction, but the findings translate into clear, practical realities about why these partnerships often fall short of their potential and how they can be fixed. The analysis reveals that the government, acting rationally, consistently invests far less than is socially optimal. This is not because the government is trying to trick the operator or cut corners; rather, it is a structural flaw in the accounting. The government only sees the tax revenue it collects from the operator's fees, while society values the saved lives at a much higher multiple. Because the government does not capture the full social value of the service in its own budget, it naturally underestimates the return on its investment, leading to a fleet that is too small and a system that is under-resourced from the start.

The study also investigates the type of organization running the service. It compares for-profit corporations, which pay taxes, against non-profit organizations, which are tax-exempt and often driven by a mission to serve. The results show that the government strictly prefers the non-profit model, even if that non-profit has no specific mission beyond simply running the service. The reason is simple: taxing the revenue of a for-profit company reduces the money available to pay for effort, which in turn reduces the number of lives saved. The tax takes away more value from the system than it raises in revenue. However, the study uncovers a surprising danger in this preference. While a non-profit with a strong mission to save lives can perfectly align the operator's incentives with the government's goals, the government itself has a blind spot. Because the government does not pay the cost of the operator's extra effort, it tends to over-select operators with very high mission weights. It pushes these dedicated providers to work so hard that they burn out, creating a situation where the government gets a high payoff in terms of service volume, but the overall well-being of the system suffers due to exhausted crews and unpaid overtime.

When a crisis hits, such as a pandemic or a cyclone, the demand for ambulances surges, and the original contract often breaks down. The study examines two ways to handle this: renegotiating the deal with the government, or bringing in a third-party investor to provide emergency funding. The analysis finds that renegotiation is the far superior option, but only if the government is willing to absorb the entire cost of the crisis. Because the government values the service so highly, it captures most of the benefit of keeping the system running, so it is the only party that can afford to pay for the shock. If the contract tries to force the operator to pay for the surge, the deal collapses. The alternative, bringing in a private investor to bridge the funding gap, is a much weaker solution. The study shows that this investor route can only sustain the service for a tiny fraction of the possible crisis scenarios. The investor's claim on the revenue eats into the operator's margin, leaving them unable to absorb the extra costs of the emergency. In the simulations, the investor route covers less than sixteen percent of the crisis range that a simple renegotiation with the government could handle.

Finally, the research looks at the impact of public insurance that pays for the service on behalf of citizens, reducing the out-of-pocket cost for patients. While this is a popular policy for protecting the poor, the study warns that it can backfire if the funding is not separated from the capital budget. If the money for insurance subsidies comes from the same pot of money used to buy new ambulances, the government will cut back on buying vehicles to pay for the insurance. This creates a hidden trade-off where protecting patients from cost leads to a smaller fleet and fewer services overall. The solution, according to the model, is to ring-fence the capital budget, ensuring that the money for buying ambulances is protected from the demands of the insurance subsidy. The study concludes that the most effective way to run these emergency services is to pre-commit to state-contingent clauses that automatically trigger government funding during a crisis, to exempt operators from revenue taxes, and to carefully monitor the workload of mission-driven non-profits to prevent them from being pushed past the point of sustainability. The path to a better emergency system lies not in more complex contracts, but in aligning the financial incentives so that the government invests enough, the operator is not overworked, and the system is ready for the unexpected.

Technical Summary: Underinvestment, Renegotiation and Bridge Financing in Emergency Medical Service Public–Private Partnerships

Problem Statement
This paper addresses the contracting problem inherent in Emergency Medical Services (EMS) Public–Private Partnerships (PPPs) in India, specifically the "108" and "112" ambulance programs. The core economic challenge is a principal–agent relationship where the state government (principal) finances capital (fleet and communications) and sets tariffs, while a private operator (agent) supplies non-contractible operating effort (crew discipline, response time management, vehicle availability). The social value of EMS exceeds the transaction price due to the multiplier effect of averted mortality and morbidity, yet the operator's effort is costly and unobservable, creating a moral hazard problem. The paper investigates four specific questions: (1) What conditions allow a viable partnership to exist? (2) Is government investment efficient? (3) Does the ownership form (for-profit vs. non-profit) matter? and (4) How do demand surges (e.g., pandemics, cyclones) affect contract stability and financing options?

Methodology
The study employs a tractable Stackelberg game model with moral hazard.

Technology: Service output follows a Cobb–Douglas production function, $q(e, I; \theta) = A \Gamma(\theta) e^{\alpha_1} I^{\alpha_2}$ , where $e$ is effort, $I$ is public capital, and $\Gamma(\theta) = e^{-\theta}$ represents output degradation during a demand surge of intensity $\theta$ .
Timing: The government acts as the Stackelberg leader, setting the tariff ( $r$ ) and tax rate ( $t$ ), then choosing capital investment ( $I$ ). The operator observes $I$ and chooses effort ( $e$ ) to maximize utility.
Payoffs: The government values output at a social multiplier $m > 1$ times the tariff ($k = mr$). The operator's revenue is taxed at rate $t$ . Effort costs are convex ( $\psi(e) = \frac{1}{2}\rho e^2$ ).
Extensions: The model is extended to compare corporate (taxed) and non-profit (tax-exempt with mission weight $\lambda$ ) operators. It further analyzes two regimes for demand surges: Regime $R_1$ (renegotiation where the government absorbs shock costs) and Regime $R_2$ (bridge financing where a third-party investor supplies capital in exchange for a revenue share $\delta$ ).
Calibration: The model is calibrated using Indian EMS data (e.g., EMRI reports, Ministry of Health surveys) to derive closed-form solutions and numerical results.

Key Contributions and Results

Existence Condition and Numerical Pathology:
The paper derives a precise existence condition for an interior Stackelberg equilibrium: $\eta = \frac{2\alpha_2}{2 - \alpha_1} < 1$ , which is equivalent to $\alpha_1 + 2\alpha_2 < 2$ . This condition, rather than constant returns to scale ( $\alpha_1 + \alpha_2 = 1$ ), governs the partnership's viability. The author demonstrates that previous numerical results in the literature (Anantharaman, 2022) reporting extremely low payoffs were "boundary artefacts" resulting from violating this condition, where equilibrium investment collapses doubly exponentially as $\eta \to 1$ .
Structural Underinvestment:
The government structurally underinvests relative to the first-best social optimum whenever the effort elasticity $\alpha_1$ exceeds a low threshold ( $\approx 0.09$ ). This is not due to opportunism but to the fiscal architecture: the government internalizes only the tax share of the operator's marginal return ($tr$) rather than the full social value ($k=mr$). At central calibration, equilibrium investment is only 28.9% of the first-best level, resulting in welfare that is 50.4% of the first best.
Provider Type and Mission Alignment:
- Tax Exemption: A tax-exempt non-profit operator strictly dominates a taxed corporate operator for any positive tax rate, as the tax destroys more social value than it raises in revenue.
- First-Best Implementation: A non-profit with a specific mission weight $\lambda^* = 1 - 1/m$ implements the first-best outcome exactly. This represents a rare case where a second-best instrument (ownership form) is fully corrective.
- Over-Selection: However, because the government's payoff function omits the operator's effort cost, the government's objective is monotonically increasing in the mission weight $\lambda$ , whereas social welfare is single-peaked at $\lambda^*$ . Consequently, a government maximizing its own payoff will "over-select" high-mission providers, inducing socially excessive effort and leading to operational pathologies like crew burnout.
Surges, Renegotiation, and Bridge Financing:
- Renegotiation Frontier: Renegotiation is feasible only up to a surge intensity $\bar{\theta}$ . Efficient Nash bargaining assigns the entire surge cost to the government (up to the point of feasibility) because the government captures the bulk of the joint surplus.
- Bridge Financing Inferiority: Bridge financing (investor capital) is a strictly inferior fallback. It sustains service only up to a surge intensity $\hat{\theta}$ , where $\hat{\theta} \ll \bar{\theta}$ (0.074 vs. 0.474 in calibration). The investor's claim erodes the operator's margin, making it unable to absorb shocks. Bridge financing covers only ~15.7% of the surge range that renegotiation covers.
- Optimal Revenue Share: The welfare-maximizing investor revenue share is $\delta^* = \frac{2\alpha_2}{\alpha_1 + 2\alpha_2}$ , which is invariant to the investor's required rate of return.
Insurance and Capital Crowding Out:
A public insurance subsidy that reduces out-of-pocket exposure (paying a share $\sigma$ of the tariff) crowds out public capital formation in the second-best equilibrium. By reducing the government's residual valuation of output, the subsidy lowers equilibrium investment (to 63.3% at full coverage). This distortion can be eliminated only if capital budgets are "ring-fenced" from reimbursement budgets.

Significance and Claims
The paper claims to provide sharper, analytical insights than the qualitative claims dominating the EMS PPP literature. Its primary significance lies in:

Correcting Numerical Errors: Identifying and explaining the numerical degeneracy in prior models of this type.
Reframing Underinvestment: Establishing underinvestment as a structural feature of the fiscal architecture (taxation vs. social value) rather than a behavioral failure or opportunism.
Policy Design: Arguing that pre-committed, state-contingent surge clauses are superior to ex post renegotiation. It posits that tax exemption and non-profit empanelment are "second-best instruments of first order" for efficiency, provided mission weights are carefully managed to avoid over-exertion.
Budget Architecture: Highlighting that the interaction between demand-side subsidies and capital budgets creates significant distortions unless separated.

The author concludes that the single highest-value empirical investment for this field is the estimation of the production elasticities ( $\alpha_1, \alpha_2$ ) and the social multiplier ( $m$ ) from state-level EMS panel data, as these parameters drive all key policy thresholds.

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