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I have a problem understanding the integral in front of the modified Ramsey problem of the DICE model. So U the utility of one household is determined by u(c) the instantaneous utility and the rest of the equation. What does instantaneous mean here? In addition is the social welfare function then the sum of all U? And why dont we maximize the welfare function?

Picture is from Geoffrey Heal in "The Economics of the Climate"

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  • $\begingroup$ Why do you think this is the utility function of a household? $\endgroup$ Jan 2, 2023 at 1:02

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What does instantaneous mean here?

It means at particular $t$. If $t$ is continuous then $t$ represents a single instant.

In addition is the social welfare function then the sum of all U?

It looks like it. Although, it’s not 100% clear just from what’s written in your question having welfare function being sum of individual utilities is not unheard of.

And why dont we maximize the welfare function?

As explained above this could be a welfare function. More generally not all models maximize some welfare function. It depends on context of the problem.

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