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Carbon Taxation, Prices and Household Welfare in New Zealand - WP 04/23

2 A Carbon Tax and Prices

The first stage of the analysis is to apply a carbon tax and examine its effects on consumer prices. This section derives the expressions used to calculate such price changes. A carbon tax is specified as a number of dollars per tonne of carbon generated by the production of each good. It is therefore necessary to translate from a tax specified in term of physical amounts of carbon into an equivalent tax imposed per dollar of expenditure by final consumers of each good. This is achieved through the carbon intensity of each good.

As with other studies of carbon taxes, the tax examined is actually considered to be imposed on carbon dioxide intensity, rather than carbon intensity. However, carbon content and carbon dioxide emissions are directly proportional by molecular weight, and the equivalent tax on carbon content can be obtained by multiplying the carbon dioxide tax by 44/12. Hence a tax is specified in terms of tonnes of carbon dioxide and consumer prices rise in proportion to their carbon dioxide intensity.

This intensity, defined by measures the tonnes of carbon dioxide emissions per dollar of final consumption of the output from industry . Therefore, a carbon dioxide tax of which is placed on carbon dioxide emissions is equivalent to an ad valorem tax-exclusive rate on the th commodity group of , where:[2]


As the intensity is expressed in terms of each dollar’s worth of the output that contributes to final demands, the total amount of carbon dioxide arising from all industries, , is given by:


where is the value of final demand for industry for . The terms and denote corresponding column vectors and the prime indicates transposition.

The carbon dioxide intensities depend in a direct way on the types and amounts of fossil fuels used by each industry, and the emissions per unit of those fossil fuels. However, the problem is complicated by the need to consider the total output of each industry, rather than merely the amount of that output which is consumed, that is the final demand. This problem is examined in subsection 2.1. Having obtained the equivalent tax rates, the next stage is to obtain an expression for the overall tax rate imposed on each unit of the good consumed. This is discussed in subsection 2.2.


  • [2]It is important to recognise that the carbon (dioxide) tax is quite different from something like a value added tax, for which the effective rate imposed on final consumers does not depend on the precise stage at which the tax’s legal incidence falls, since the tax is simply passed forwards and eventually falls on consumers.
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