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The theory of virtual quantities, the dual to virtual prices, provides a framework to analyze competitive multiproduct firm behavior under multiple quantity controls on inputs and outputs, including command-and-control quotas and transferable property rights. The framework addresses the firm׳s reactions to regulatory controls, impacts of adding or dropping quantity controls, inferring unrationed from rationed production, and conversion from command-and-control quotas to cap-and-trade systems with transferable property rights and secondary market behavior. The paper develops reasons for failure of quasi-concavity of technology, extends the elasticity of intensity׳s properties, and integrates the virtual price and virtual quantity frameworks. Virtual quantities are applied to assess potential firm responses to quantity controls and a potential transferable property right in a Malaysian fishery. [ABSTRACT FROM AUTHOR]

Eliminating rationing in the United Kingdom following the Second World War was a concern for policy-makers because of potentially large fluctuations in post-war prices and the impact on unrationed goods. This study shows that in using virtual prices, elasticities can be estimated from a ‘free’ demand system consistent with observed consumer choices. Substitution estimates without accounting for rationing are misleading. In contrast, using virtual prices and estimating a ‘free’ market system yield results similar to those of the pre-war period. Results show that food rationing affected expenditure across unrationed goods. Rationing on other services had little effect on expenditure across unrationed goods. [ABSTRACT FROM PUBLISHER]

The purpose of this paper is to investigate the impacts of rationing on firm behavior. A virtual price approach is adopted to derive the rationed elasticities of variable input demands and output supply under a translog profit function. To illustrate the difference between the rationed and unrationed elasticities, we conduct an analysis using a firm-level annual survey data of China over the period 1985-88. Our estimation results indicate that the values of most elasticities would have been affected significantly if the government had imposed rationing on material inputs. The behavior of Chinese firms would have been seriously distorted in a complicated way. The firms would have over-responded to market signals in making some of their input or output decisions and, at the same time, might have under-reacted, or would have not changed their reaction, in making the other input or output decisions, under a rationing regime. [ABSTRACT FROM AUTHOR]