Harmonic Cost Sharing

ABSTRACT

This paper examines the total cost of public good provision when contributors face heterogeneous quadratic cost functions. We demonstrate that while the total cost of equal provision depends only on the arithmetic mean of marginal cost slopes, the total cost of cost‐effective provision depends on their harmonic mean. This relationship reveals that greater heterogeneity monotonically increases the cost savings from cost‐effective instead of equal provision. We propose a zero‐sum transfer system that implements cost‐effective levels while achieving equal cost sharing. Our framework offers a practical method to operationalize principles like Common but Differentiated Responsibilities (CBDR) in international environmental agreements, resolving the tension between cost‐effectiveness and equity concerns.