# Climate Policy, GDP and Welfare

The 5th assessment report of the IPCC is drawing a lot of attention for its claim that reducing greenhouse gas emissions would only have small costs in terms of gross social product, that “saving the planet” is cheaper than we might think. I have not read the report in detail and I am in no position to say whether the IPCC got it right or wrong.

However, it occurred to me that the IPCC is asking the wrong question. They ask how much mitigation policies would cost in terms of (world) GDP. But climate policy is a classic case where GDP is a very bad indicator of economic welfare. Greenhouse gas emissions are a byproduct of producing goods and services and they cause global warming, which is arguably a bad thing, i.e. a negative externality. Individual consumers and producers do not take account of the negative effects of their consumption/production decisions on society and therefore consume and produce too much.

Here is how that works in a simple model. (For the visual types, here is how it works graphically: climate policy graph.)

Individuals get utility from consumption C and leisure L. Utility is negatively affected by Z, i.e. global warming directly affects the welfare of individuals: U=U(C, L, Z). Uc>0 is the marginal utility of consumption, Ul>0 is the marginal utility of leisure, and Uz<0 the marginal disutility of global warming. We make the usual assumptions about diminishing marginal utilities of consumption and leisure, and we add the assumption of increasing disutility of global warming (Nerds: the Hessian is assumed to be negative definite). Production of goods requires A labor hours per unit: Y=(1-L)/A. It also causes global warming, which we assume to be a linear function of output: Z=k*Y, where k measures the marginal impact of GDP on the earth’s climate.

When the individual decides how much to consume and how much to work, she takes Z as given. This is what makes Z an externality. The private marginal rate of substitution between consumption and leisure, i.e. the amount of leisure the individual is willing to give up to get one extra unit of consumption, is Uc/Ul.

Individually optimal consumption/leisure choice requires that the marginal private value of consumption (in terms of leisure) be equal to the marginal opportunity cost of production:

(1)            Uc/Ul = A.

Meanwhile the social marginal rate of substitution, i.e. the amount of leisure the individual would be willing to give up for one more unit of consumption if she took into account the effect on global warming, is (Uc+k*Uz)/Ul.

It should be clear why the social MRS is smaller than the private MRS: Taking into account the adverse effect of higher consumption on the climate reduces the marginal value of consumption in terms of leisure. The socially optimal consumption/leisure choice requires that the marginal social value of consumption be equal to the marginal opportunity cost of production:

(2)         (Uc+k*Uz)/Ul = A.

Compare (1) with (2) and you realize that the privately chosen (or laissez-faire) allocation contains more consumption and less leisure than the socially optimal allocation. In other words, the economy produces “too much” under laissez-faire.

It follows that there is room for a welfare-improving policy intervention. Whatever such a policy looks like in detail, one thing is clear: in order to be welfare-improving it must reduce consumption and increase leisure. In other words: climate policy, if it is to be socially desirable, leads to lower GDP. But that’s not a bug, it’s a feature!

Bottom line: When discussing the welfare effects of greenhouse gas reducing policies, looking at GDP is no good. GDP is not welfare.

## One thought on “Climate Policy, GDP and Welfare”

1. katharina maria says:

Interesting analysis. If you’ve never heard about it, there’s an growing branch in human ecology, which argues for degrowth for more inequality and environmental sustainability. Most of it is pretty radical, but it’s fun to dive into it for a couple of hours, if you get bored. http://www.degrowth.org/definition-2