<blockquote>
<p>What does instantaneous mean here?</p>
</blockquote>
<p>It means at particular <span class="math-container">$t$</span>. If <span class="math-container">$t$</span> is continuous then <span class="math-container">$t$</span> represents a single instant.</p>
<blockquote>
<p>In addition is the social welfare function then the sum of all U?</p>
</blockquote>
<p>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.</p>
<blockquote>
<p>And why dont we maximize the welfare function?</p>
</blockquote>
<p>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.</p>

CC BY-SA 4.0
2023-01-01T21:58:10.723Z
2023-01-01T21:58:10.723Z
1muflon1
<p>This function is the welfare function of an individual, representative agent—or household—as I believe that it is referred to in Ramsey-Koopmans-Cass (RKC) framework and as the DICE model interprets it. The sum of this representative household's welfare multiplied by every household in society is the sum of society's welfare.</p>
<p>Consumption, c, and global temperatures, T change instantaneously as a function of t, time. The social welfare function is the sum of the utility of consumption which is a the value of consumption decayed by D(T), climate damage and discounted for the elasticity of marginal utility. I.E. Consumption is growing, at the rate g, (you can think of this as GDP growth) which occurs smoothly overtime. However, social welfare is reduced by climate damage and the value of utility at the margin due to the law of diminishing marginal utility given the implicit increasing rate of economic growth (c).</p>
<p>I am not sure where you are getting that the welfare function isn't being &quot;maximized.&quot; The function is, in itself, a descriptive function ultimately designed to find the social cost of carbon based on exogenous values. I don't think that it is either maximized or not by policy choices <em>outside of the fact that its value can be changed by changing the social discount rate—one of the—if not the—main reasons that Nordhaus has been so controversial</em> or <em>outside of increasing climate mitigation (which may also effect the growth of c) and concomitantly reducing T</em>. These values are sort of the rub, however this function needs be understood as an incomplete version of the equation used to calculate the social cost of carbon.</p>

CC BY-SA 4.0
2024-07-29T23:28:38.927Z
2024-07-29T23:30:05.567Z
2024-07-29T23:30:05.567Z
Eric Glock
<p>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?</p>
<p>Picture is from Geoffrey Heal in &quot;The Economics of the Climate&quot;</p>
<p><a href="https://i.sstatic.net/LK7Gn.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/LK7Gn.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2023-01-02T01:02:22.797Z
Why do you think this is the utility function of a household?
Michael Greinecker
<utility><ramsey>
Integral in front of utility function
BlankerHans
# Integral in front of utility function

(Asked by: username_0 on 2023-01-01)

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"

[![enter image description here](https://i.sstatic.net/LK7Gn.png)](https://i.sstatic.net/LK7Gn.png)

**Tags:** utility, ramsey

> **Comments:**
> **username_1**: Why do you think this is the utility function of a household?  

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## 2 answers

### Answer by username_2 on 2023-01-01. Score: 1

> 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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### Answer by username_3 on 2024-07-29. Score: 0

This function is the welfare function of an individual, representative agent—or household—as I believe that it is referred to in Ramsey-Koopmans-Cass (RKC) framework and as the DICE model interprets it. The sum of this representative household's welfare multiplied by every household in society is the sum of society's welfare.

Consumption, c, and global temperatures, T change instantaneously as a function of t, time. The social welfare function is the sum of the utility of consumption which is a the value of consumption decayed by D(T), climate damage and discounted for the elasticity of marginal utility. I.E. Consumption is growing, at the rate g, (you can think of this as GDP growth) which occurs smoothly overtime. However, social welfare is reduced by climate damage and the value of utility at the margin due to the law of diminishing marginal utility given the implicit increasing rate of economic growth (c).

I am not sure where you are getting that the welfare function isn't being "maximized." The function is, in itself, a descriptive function ultimately designed to find the social cost of carbon based on exogenous values. I don't think that it is either maximized or not by policy choices *outside of the fact that its value can be changed by changing the social discount rate—one of the—if not the—main reasons that Nordhaus has been so controversial* or *outside of increasing climate mitigation (which may also effect the growth of c) and concomitantly reducing T*. These values are sort of the rub, however this function needs be understood as an incomplete version of the equation used to calculate the social cost of carbon.


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