The Social Marginal Cost Curve and a Corner Solution of the Second-Best Level of Public Good Provision: A Review and an Extension

• Published in: Schweizerische Zeitschrift für Volkswirtschaft und Statistik Vol. 152; no. 3; pp. 209 - 241
• Main Authors: Chang, Ming Chung, Peng, Hsiao-Ping, Ho, Yan-Ching
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01.07.2016; Springer International Publishing; Springer Nature B.V; SpringerOpen
• Subjects: demand-shift effect; Economics; Economics and Finance; Production costs; Public good; second-best public good provision; social marginal cost; Statistics; Supply & demand; Tax rates; Taxation; Utility functions; weak Laffer effect; Willingness to pay; social marginal cost; weak Laffer effect; H41; demand-shift effect; H21; second-best public good provision
• ISSN: 2235-6282; 2235-6282
• DOI: 10.1007/BF03399427

Assume that the private goods and the public good are weakly separable, the private goods are gross complements, and the private utility function is a homogeneous of degree one function with constant elasticity of substitution. We demonstrate that, under commodity taxation, the social marginal cost curve of public good provision is initially upward sloping and eventually becomes downward sloping. Moreover, the social marginal cost eventually falls below the private marginal cost. These unusual properties arise from a demand-shift effect: An increase in the tax rate raises the marginal willingness to pay for the public good since it pushes up the unit cost of private utility, hence making the public good more attractive than private goods. In other words, the supply of the public good creates its own demand when the funding to cover production costs is raised through distortionary commodity taxes. It follows that there may exist three solutions to the first-order condition for the second-best problem: two of them are interior solutions and one is a corner solution.