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The Social Marginal Cost Curve and a Corner Solution of the Second-Best Level of Public Good Provision: A Review and an Extension
Swiss Journal of Economics and Statistics volume 152, pages 209–241 (2016)
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.
Aronsson, Thomas (2008), “Social Accounting and the Public Sector”, International Economic Review, 49(1), pp. 349–75.
Atkinson, Anthony B., and Nicholas H. Stern (1974), “Pigou, Taxation and Public Goods”, Review of Economic Studies, 41, pp. 119–28.
Atkinson, Anthony B., and Joseph E. Stiglitz (1980), Lectures on Public Economics, McGraw-Hill, New York.
Ballard, Charles L. and Don Fullerton (1992), “Distortionary Taxes and the Provision of Public Goods”, Journal of Economic Perspective, 6(3) pp. 117–31.
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.
Batina, Raymond G., and Toshihiro Ihori (2005), Public Goods: Theories and Evidence, New York: Springer.
Browning, Edgar K., Timothy Gronberg and Liqun Liu (2000), “Alternative Measures of the Marginal Cost of Funds,” Economic Inquiry, 38(4), pp. 591–9.
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.
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.
Christiansen, Vidar (2007), “Two Approaches to Determine Public Good Provision under Distortionary Taxation,” National Tax Journal, 2007, 60 (1), 25–43.
Dahlby, Bev (2008), The Marginal Cost of Public Funds: Theory and Applications, MIT Press, Cambridge, Mass. and London.
de Bartolome, Charles A. M. (1996), “Is Pigou Wrong? Can Distortionary Taxation Cause Public Spending to Exceed the Efficient Level?” unpublished mimeo.
de Bartolome, Charles A. M. (1997), “Slow Adjustment and the Level of Government Spending,” Journal of Urban Economics, 42(2), pp. 285–311.
Diamond, Peter A. (1975), “A Many-Person Ramsey Rule”, Journal of Public Economics, 4, pp. 335–42.
Diamond, Peter A., and James A. Mirrlees (1971), “Optimal Taxation and Public Production I: Production Efficiency,” American Economic Review, 61, pp. 261–78.
Gaube, Thomas (2000), “When do Distortionary Taxes Reduce the Optimal Supply of Public Goods?” Journal of Public Economics, 76(2), pp. 151–80.
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.
King, Mervyn A. (1986), “A Pigovian Rule for the Optimum Provision of Public Goods”, Journal of Public Economics, 30, pp. 273–91.
Ng, Yew-Kwang (2000), “The Optimal size of Public Spending and the Distortionary Cost of Taxation”, National Tax Journal, 53(2), pp. 253–72.
Pigou, Arthur C. (1947), Public Finance, Macmillan, London.
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.
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.
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.
Wilson, John D. (1991), “Optimal Public Good Provision in the Ramsey Tax Model - A Generalization,” Economics Letters, 35, pp. 57–61.
Wilson, John D. (1991), “Optimal Public Good Provision with Limited Lump-Sum Taxation,” American Economic Review, 81(1), pp. 153–66.
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Chang, M.C., Peng, HP. & Ho, YC. The Social Marginal Cost Curve and a Corner Solution of the Second-Best Level of Public Good Provision: A Review and an Extension. Swiss J Economics Statistics 152, 209–241 (2016). https://doi.org/10.1007/BF03399427
- second-best public good provision
- social marginal cost
- demand-shift effect
- weak Laffer effect