This paper constitutes the first and foundational output of the ESHCRU2 project 3 - Analysis of purcher-provider contracts: modelling risk sharing and incentive implications. In this project, we have focused on the implications of payment reform of what is called blended payment for emergency care. This paper sets out the theoretical model developed to understand how behavioural choices could be influenced by this payment reform. We construct a framework in which two organisations - a hospital and a purchaser - influence respectively admissions from, and attendance at, emergency departments. These decisions are each influenced by the payment system and interact to determine an equilibrium. We show how the equilibrium is affected by the characteristics of the hospital and the purchaser and how it will be changed by shifting towards a greater reliance on fixed payment. We further establish what outcomes (in terms of admissions and attendances) can be sustained as an equilibrium under different parameters of the payment system
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