If the revenue from the carbon tax is completely offset by reductions in other taxes, then T does not change. The components of T do, but the total T does not. The burden of the tax will shift more toward consumption, so there could be an increase in I that offsets a decrease in C. Measured GDP will not necessarily increase to reflect the welfare gain from more efficient taxes and reduced pollution. A reduction in personal income taxes could lead to an increase in labor supply, which would show up as increased GDP, but reduced respiratory illness from burning less coal is less likely to be reflected in the GDP measure.