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The authors build a simple analytical general equilibrium model and linearize it, to find a closed-from expression for the effect of a small change in carbon tax on leakage - the increase in emissions elsewhere. The model has two goods produced in two sectors or regions. Many identical consumers buy both goods using income from a fixed stock of capital that is mobile between sectors. An increase in one sector's carbon tax raises the price of its output, so consumption shifts to the other good, causing positive carbon leakage. However, the taxed sector substitutes away from carbon into capital. It thus absorbs capital, which shrinks the other sector, causing negative leakage. This latter effect could swamp the former, reducing carbon emissions in both sectors.
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