Dale Jorgenson et al. did do a sensitivity analysis of their climate policy CGE model in 2000. They found that imposing zero substitutability between inputs had a big impact on the estimated costs of emissions reduction policies compared to their base case model. The impact depended on what they assumed the government did with the revenue from a carbon tax.
When they assumed that the revenue from a carbon tax was "recycled" by paying equal lump sums to all individuals, the price of carbon permits was four times higher over the 2000-2060 policy period and the decline in GDP was twice as much under no substitutability as under the base case.
When they assumed that the carbon tax revenue is recycled by reducing marginal income tax rates their model yields a "double dividend"* - GDP increases in the base case when a climate policy is imposed. And it increases four times more when no substitutability is allowed than when it is!
* The double dividend refers to climate policies that not only improve the environment but also increase GDP by cutting existing distorting (inefficient) taxes (like the income tax) using the revenue from a carbon tax. This has been a very controversial issue as things are not this simple.** My impression is that the consensus is that there is no double dividend in practice but that a revenue neutral carbon tax or auctioned emission permits accompanied by cuts in income taxes is superior to the government giving away permits for free (and therefore being unable to cut other taxes) or using the carbon tax to pay out dividends like the Alaska Permanent Fund as suggested by James Hansen.
** This is one of the papers I set my students at RPI on the topic
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