Emissions Taxes and Abatement Regulation Under Uncertainty

We consider environmental regulation in a context where firms invest in abatement technology under conditions of uncertainty about subsequent abatement cost, but can subsequently adjust output in the light of true marginal abatement cost. Where an emissions tax is the only available instrument, policy faces a trade-off between the incentive to invest in abatement technology and efficiency in subsequent output decisions. More efficient outcomes can be achieved by supplementing the emissions tax with direct regulation of abatement technology, or by combining the tax with an abatement technology investment subsidy. We compare the properties of these alternative instrument combinations

Externality-correcting taxes and regulation

Much of the literature on externalities has considered taxes and direct regulation as alternative policy instruments. Both instruments may in practice be imperfect, reflecting informational deficiencies and other limitations. We analyse the use of taxes and regulation in combination, to control externalities arising from individual consumption behaviour. We consider cases where taxes are either imperfectly differentiated to reflect individual differences in externalities, or where some consumption escapes taxation. In both cases we characterise the optimal instrument mix, and show how changing the level of direct regulation alters the optimal externality tax

Self-adjoint difference operators and classical solutions to the Stieltjes--Wigert moment problem

The Stieltjes-Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We consider the orthogonality measures for which the difference operator is symmetric in the corresponding weighted $L^2$-spaces. These measures are exactly the solutions to the q-Pearson equation.In the case of discrete and absolutely continuous measures the difference operator is essentially self-adjoint, and the corresponding spectral decomposition is given explicitly. In particular, we find an orthogonal set of q-Bessel functions complementing the Stieltjes-Wigert polynomials to an orthogonal basis for $L^2(\mu)$ when $\mu$ is a discrete orthogonality measure solving the q-Pearson equation. To obtain the spectral decomposition of the difference operator in case of an absolutely continuous orthogonality measure we use the results from the discrete case combined with direct integral techniques.Comment: 22 pages; section 2 rewritten, to appear in Journal of Approximation Theor