Prices vs. quantities in presence of a second, unpriced, externality

We study a situation in which two goods jointly generate an externality but only one of them is regulated. Unilateral regulation of greenhouse gas emissions and related carbon leakage is a well known example. We compare tax and quantity instruments under uncertainty à la Weitzman (1974). Because of the uncertainty surrounding the unregulated good, the external cost is stochastic with both instruments. Whether the unregulated good quantity is more or less variable under a tax or under a quota depends on the degree of substitutability and the correlation between uncertainties on private valuations. In case of a positive correlation and imperfect substitution, a tax better stabilize the unregulated good quantity and can therefore dominate a quota when the slope of the external cost associated to the unregulated good is large. In a specification, relevant for leakage, it is shown that if uncertainty about the unregulated good (imports) is large, a tax might be preferable to a quota, regardless of the convexity of the external cost.