Swiss Journal of Economics and Statistics

, Volume 152, Issue 3, pp 209–241 | Cite as

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

  • Ming Chung Chang
  • Hsiao-Ping Peng
  • Yan-Ching Ho
Open Access


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.


second-best public good provision social marginal cost demand-shift effect weak Laffer effect 


H21 H41 


  1. Aronsson, Thomas (2008), “Social Accounting and the Public Sector”, International Economic Review, 49(1), pp. 349–75.CrossRefGoogle Scholar
  2. Atkinson, Anthony B., and Nicholas H. Stern (1974), “Pigou, Taxation and Public Goods”, Review of Economic Studies, 41, pp. 119–28.CrossRefGoogle Scholar
  3. Atkinson, Anthony B., and Joseph E. Stiglitz (1980), Lectures on Public Economics, McGraw-Hill, New York.Google Scholar
  4. Ballard, Charles L. and Don Fullerton (1992), “Distortionary Taxes and the Provision of Public Goods”, Journal of Economic Perspective, 6(3) pp. 117–31.CrossRefGoogle Scholar
  5. Batina, Raymond G. (1990), “On the Interpretation of the Modified Samuelson Rule for Public Goods in Static Models with Heterogeneity,” Journal of Public Economics, 42, pp. 125–33.CrossRefGoogle Scholar
  6. Batina, Raymond G., and Toshihiro Ihori (2005), Public Goods: Theories and Evidence, New York: Springer.Google Scholar
  7. Browning, Edgar K., Timothy Gronberg and Liqun Liu (2000), “Alternative Measures of the Marginal Cost of Funds,” Economic Inquiry, 38(4), pp. 591–9.CrossRefGoogle Scholar
  8. Chang, Ming C. (2000), “Rules and Levels in the Provision of Public Goods: the Role of Complementarities between the Public Good and Taxed Commodities,” International Tax and Public Finance, 7, pp. 83–91.CrossRefGoogle Scholar
  9. Chang, Ming C., and Hsiao-Ping Peng (2009), “Laffer Effect, Gross Substitution, Marginal Cost of Public Funds and the Level Property of Public Good Provision,” International Tax and Public Finance, 19(5), pp. 650–9.CrossRefGoogle Scholar
  10. Christiansen, Vidar (2007), “Two Approaches to Determine Public Good Provision under Distortionary Taxation,” National Tax Journal, 2007, 60 (1), 25–43.CrossRefGoogle Scholar
  11. Dahlby, Bev (2008), The Marginal Cost of Public Funds: Theory and Applications, MIT Press, Cambridge, Mass. and London.CrossRefGoogle Scholar
  12. de Bartolome, Charles A. M. (1996), “Is Pigou Wrong? Can Distortionary Taxation Cause Public Spending to Exceed the Efficient Level?” unpublished mimeo.Google Scholar
  13. de Bartolome, Charles A. M. (1997), “Slow Adjustment and the Level of Government Spending,” Journal of Urban Economics, 42(2), pp. 285–311.CrossRefGoogle Scholar
  14. Diamond, Peter A. (1975), “A Many-Person Ramsey Rule”, Journal of Public Economics, 4, pp. 335–42.CrossRefGoogle Scholar
  15. Diamond, Peter A., and James A. Mirrlees (1971), “Optimal Taxation and Public Production I: Production Efficiency,” American Economic Review, 61, pp. 261–78.Google Scholar
  16. Gaube, Thomas (2000), “When do Distortionary Taxes Reduce the Optimal Supply of Public Goods?” Journal of Public Economics, 76(2), pp. 151–80.CrossRefGoogle Scholar
  17. Gronberg, Timothy, and Liqun Liu (2001), “The Second-Best Level of a Public Good: An Approach Based on the Marginal Excess Burden,” Journal of Public Economic Theory, 3(4), pp. 431–53.CrossRefGoogle Scholar
  18. King, Mervyn A. (1986), “A Pigovian Rule for the Optimum Provision of Public Goods”, Journal of Public Economics, 30, pp. 273–91.CrossRefGoogle Scholar
  19. Ng, Yew-Kwang (2000), “The Optimal size of Public Spending and the Distortionary Cost of Taxation”, National Tax Journal, 53(2), pp. 253–72.CrossRefGoogle Scholar
  20. Pigou, Arthur C. (1947), Public Finance, Macmillan, London.Google Scholar
  21. Slemrod, Joel, and Shlomo Yitzhaki (2001), “Integrating Expenditure and Tax Decisions: The Marginal Cost of Funds and the Marginal Benefit of Projects,” National Tax Journal, 54(2), pp. 189–201.CrossRefGoogle Scholar
  22. Stern, Nicholas (1986), “A Note on Commodity Taxation: The Choice of Variable and the Slutsky, Hessian and Antonelli Matrices (SHAM)”, Review of Economic Studies, 53, pp. 293–9.CrossRefGoogle Scholar
  23. Triest, Robert K. (1990), “The Relationship between the Marginal Cost of Public Funds and Marginal Excess Burden,” The American Economic Review, 80(3), pp. 557–66.Google Scholar
  24. Wilson, John D. (1991), “Optimal Public Good Provision in the Ramsey Tax Model - A Generalization,” Economics Letters, 35, pp. 57–61.CrossRefGoogle Scholar
  25. Wilson, John D. (1991), “Optimal Public Good Provision with Limited Lump-Sum Taxation,” American Economic Review, 81(1), pp. 153–66.Google Scholar

Copyright information

© Swiss Society of Economics and Statistics 2016

Authors and Affiliations

  • Ming Chung Chang
    • 1
  • Hsiao-Ping Peng
    • 2
  • Yan-Ching Ho
    • 3
  1. 1.Graduate Institute of Industrial EconomicsNational Central UniversityChung-Li CityTaiwan
  2. 2.Yu Da UniversityTaiwan
  3. 3.Graduate Institute of Industrial EconomicsNational Central UniversityTaiwan

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