Gardner, Roy, Andrew Herr, Elinor Ostrom, and James A. Walker. “The power and limitations of proportional cutbacks in common-pool resources.” Journal of Development Economics 62, no. 2 (2000): 515-533.
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This paper examines the success and limitations of proportional cutbacks as an allocation rule for improving the performance of common-pool resources (CPRs). Two field cases, one success and one failure, motivate the analysis. For symmetric CPRs, we establish the existence of efficiency-enhancing proportional cutbacks. We then introduce complications that arise in the presence of asymmetries, which induce a continuum of proportional cutbacks that raise efficiency above Nash equilibrium. Calibrating a linear–quadratic CPR model to global carbon dioxide emissions, the efficiency and distributional consequences of proportional cutbacks like those embodied in the Kyoto Protocol are derived.