Distributed public economics and decentralised public finance via network optimisation

By Ioannis Papastaikoudis, CERF and CCFin Associate, Cambridge Judge Business School, University of Cambridge

This work addresses the optimisation problem in decentralised public finance, focusing on allocating public goods and services across multiple regions. It models the interaction of inter-regional and intra-regional public infrastructure from a network perspective, framing it as a multi-objective optimisation problem solved using distributed optimisation techniques. The study aims to provide policymakers with a practical framework for efficient resource allocation to maximise regional welfare.

Decentralised optimisation in economics

Optimisation plays a central role in economics, with its foundational applications established in seminal works such as (Arrow, [1]). In classical economic theory, the Utility Maximisation Problem (UMP) often assumes that an agent’s utility is represented by a single objective function with the respective decision variables under consideration to lie on a specific domain (Mas-Colell et al., [2]).

However, in reality, an agent’s utility is shaped by multiple factors, each potentially governed by different functions with distinct domains whose structure is suitable to describe the characteristics of the various factors, where the total objective function is the sum of the individual factor functions. For instance, a city’s utility may depend on both its residents’ access to affordable housing and the quality of its public transportation system, each described by separate functions. Similarly, a firm’s utility may be influenced by both production output and employee satisfaction, with each factor modelled by distinct functions.

Additionally, a household’s utility could depend on both energy consumption and environmental sustainability measures, each described by different functions. This introduces a form of decentralisation within the objective function based on the different factors that provide the total utility. These different facto functions frequently share common decision variables in their domains, referred to as coupling variables, which create network effects across the different factor functions.

Public economics and fiscal decentralisation

In the field of public economics, the focus is on the role of government policy in ensuring economic efficiency and equity. The goal is to improve social welfare through the application of microeconomic tools. Public finance, a subfield of public economics, examines government expenditure and tax policy, alongside their broader impacts on the economy. In this study, the focus is on government expenditure, where fixed budgets are allocated to municipalities by the central government. Policymakers, such as mayors or governors, are responsible for addressing the public needs of their respective regions in terms of goods and services. This problem can be framed within the context of decentralised public finance, where multiple policymakers work to optimally distribute budgets to achieve economic goals, such as providing public goods and services. The
theory also extends to the case of cooperative policymaking, where neighbouring regions collaborate to address common objectives.

This framework could further be applied to higher levels of coordination, such as inter-state or international cooperation, as exemplified by entities like the European Union. Fiscal decentralisation refers to the process by which central governments empower subnational authorities to provide services and goods to their populations (Bahl et al., [3]). The 3 primary fiscal functions – stabilisation, redistribution, and resource allocation—are generally divided between the central government and subnational levels (Oates, [4]).

While stabilisation and redistribution remain under the purview of central governments, resource allocation is where fiscal decentralisation can play a significant role. Proponents argue that local policymakers possess a better understanding of their constituents’ preferences and can, therefore, allocate resources more efficiently to meet local needs. However, fiscal decentralisation also has potential drawbacks, such as inefficiencies in service provision and unequal distribution of resources (Fedelino et al., [5]).

In our model, we consider policymakers as social planners who aim to maximise the welfare of their constituents, making decisions regarding public goods and services that benefit the population. These goods may be either intraregional (specific to one region) or inter-regional (benefiting multiple regions). Examples of intra-regional public goods include flood prevention systems or healthcare units, while inter-regional goods may consist of large transportation infrastructure, such as highways or rail systems.

By utilising the decentralised optimisation setting presented earlier, we recognise that various factors – such as healthcare, transportation, and education – affect regional welfare. Since some of these factors may be shared across regions, network effects are created, linking the welfare of these regions.

Distributed Utility Maximisation Problem (UMP)

To capture the full objective function of a policymaker, we treat inter-regional public infrastructure as coupling variables, shared decision variables that appear in the utility functions of multiple regions. In contrast, intra-regional public infrastructure is treated as local decision variables, decision variables specific to each region.

The welfare maximisation problem is thus framed as a utility maximisation problem, where the objective is to determine the optimal allocation of public goods across different regions. The interactions between the different regions via inter-regional public goods create a multi-agent, multi-objective optimisation problem that can be efficiently solved using distributed optimisation techniques and thus we are able to calculate the Marshallian demand for the Utility Maximisation Problem (UMP) for both coupling and local variables, determining how to optimally allocate both types of public goods across regions to maximise welfare.

Our approach provides useful insights for policymakers and inter-regional coordination committees responsible for managing territorial development funds. This represents a significant step forward in solving multi-party optimisation problems in public finance, which were once considered intractable (Samuelson, [6]).

Alignment with standard economic theory

Our model aligns with standard economic theory, where input vectors (decision variables) under a given mechanism (utility function) lead to specific utility levels. The mechanism is separable, allowing the total utility to be expressed as the sum of individual utility functions with coupling among their input variables.

This framework builds upon traditional utility theory and extends it to a decentralised, multi-objective setting. This methodology may also be applicable to other static optimisation problems, such as profit maximisation in the private sector.