<p>Perfectly fair question. Let the price vector be expressed in terms of a numeraire- i.e. a physical good. Stipulate that all economic activity is voluntary, there is no preference revelation problem (i.e. no strategic behaviour), no hedging etc (i.e. the standard perfect competition assumptions) then the answer is no if there is preference and endowment diversity provided some goods are consumed in each period. If agents are identical, then the answer is yes.
This is because a Wt is Pareto efficient if you can make a mutually advantageous trade which enables you to consume more- assuming that is your preference- provided you find someone who wants more assets and prefers to be thrifty for the moment. If Preference diversity obtains this happens so Dt will differ from the previous Dt-1.
Interestingly, if preference diversity is too great or too little and markets use up scarce resources then no conclusion can be drawn. The same thing happens when you introduce a little uncertainty- i.e. hedging appears- or a bit of information asymmetry- so preference revelation becomes problematic.</p>

<p>I take it you want an answer the question 'what type of allocatively efficient Growth is distributionally neutral'- this was a big topic in the Sixties- turnpike theorems and so on. It's good to see young people pondering these things in our present climate!
My tuppence is that it may be that some distributions are better for human beings than others- if so there is a Muth Rational economic theory which, under common knowledge, would be the Schelling focal solution to Society's coordination problem. This means Preferences change so that Society can still get to where it really wants to be- even if the Maths is intractable!
There was a Japanese 'peasant sage'- Ninomiya- who redefined what we call saving as 'concession'- i.e. a voluntary foregoing of consumption so the worst off can eat- and what we call Return on Investment- as 'obligation to acknowledge Virtue' which can be discharged collectively. There has been some General Eqbm work based on this sort of thinking. Here there is no 'Paradox of Thrift' nor naughty 'Income effects' to spoil our nice models because people are Muth rational- not zero intelligence rule following droids!
This does not mean that basic existential problems- Uncertainty, Concurrency, Co-ordination etc disappear- it's just that mathematical models can give better, more human, insights into profound dilemmas.
You asked a good question- that's the point of going to College. The good questions you ask there- not the answers you are required to give- will enrich your life to the end of your days. </p>

CC BY-SA 3.0
2015-09-25T17:54:56.887Z
Thanks for the detailed response! I have one more quesiton, if you don't mind:

Could we consider capital as a commodity $c_t$ (that is, a capital which matures at time $t$), whose utility is the increase of maximum utility at $t$, discounted for time preference?
Pablo Derbez
CC BY-SA 3.0
2015-09-26T18:25:50.643Z
Hi Pablo, not sure what is meant by Capital with matures at time t. Suppose Capital item x is a machine which lasts t years producing a certain amount of Consumer good y per annum. Then, you could say its Utility is the Present Value of the consumption stream. The problem is that K is the summation of all Capital goods- some are breaking some are being replaced and there is also 'Capital deepening'- so you get an aggregation problem. Also, you can have 'reswitching' and cases where a consumer good can become a capital good and vice versa. With Uncertainty, things get really scary!
Vivek Iyer
CC BY-SA 3.0
2015-09-27T17:27:52.063Z
Why no up vote?
Vivek Iyer
CC BY-SA 3.0
2015-09-27T17:29:11.650Z
Sorry, voted now
Pablo Derbez
CC BY-SA 3.0
2015-09-27T18:53:32.237Z
Thanks. A lot of bright Indian people wasted their time chasing after Sraffa. My teacher was Morishima who had a 'rational distribution' theory- basically shadow prices do the work. Silly- I know.
Vivek Iyer
CC BY-SA 3.0
2015-09-27T18:59:22.207Z
Thanks. A lot of bright Indian people wasted their time chasing after Sraffa. My teacher was Morishima who had a 'rational distribution' theory- basically shadow prices do the work. Silly- I know. Ken Binmore, my other Prof at age 16 tried hard with a Game theoretic approach. I suggest Muth Rationality and Aumman signalling. It's important to show that Wealth is Shit. Spread it around and the grass is greener. Not otherwise. Marxist or Ricardian models are the enemy here. They assume the Capitalist can always gain security at the expense of the worker. See Alan Kirman
Vivek Iyer
CC BY-SA 3.0
2015-09-25T08:03:35.123Z
2015-09-25T08:03:35.123Z
Vivek Iyer
<p>In general classical economics, the answer to your question is "ABSOLUTELY!" </p>

<p><em>Now the TL;DR answer ...</em> </p>

<blockquote>
  <p>Classical models assume that all actors are rational, discount the future equivalently and equally concerned about
  their future well-being over time AND able to comprehend the future
  with perfect certainty ... a <a href="https://en.wikipedia.org/wiki/Pareto_efficiency" rel="nofollow">Pareto efficient</a>  allocation of
  resources exists when it is impossible to make any one individual
  better off without making at least one individual worse off.  </p>
  
  <p>Clearly the real issue is not Pareto efficiency, but rather in whether
  or not the actors really are rational, have static preferences over
  time, are able to coherently use all information available and know
  the future [and impacts of growth in their lives] with perfect
  certainty.</p>
  
  <p>Your conclusion is going to depend on how you construct your model ...
  you model might be flawed (HINT: all models are flawed) ...  or you
  have introduced [artificial] constraints to help you [implicitly] test
  some hypothesis or prove a point. If you change the premises and
  architecture of your model, you can prove anything ... that's why no
  one should ever trust <a href="http://www.nytimes.com/column/paul-krugman" rel="nofollow">some opinionated joker</a> claiming to be an
  economic expert, simply because he received some <a href="https://en.wikipedia.org/wiki/Nobel_Memorial_Prize_in_Economic_Sciences" rel="nofollow"><em>teacher's pet
  award</em> for brilliant models that were popular with powerful
  people</a>.</p>
</blockquote>

CC BY-SA 3.0
2015-09-24T19:56:02.320Z
(+1-1-1=-1): This is epistemologically sound, politically heated, and Q&A-wise useless: when an undergraduate student asks, "particulars of model A", it rarely helps to counter "you should abandon your studies and go occupy yourself with the _real_ world, since all Social Sciences and their models are flawed or a fraud".
Alecos Papadopoulos
CC BY-SA 3.0
2015-09-24T22:50:57.563Z
There is a fair bit in this answer which is irrelevant. Also, it is very light on the sort of explanation I feel the questioner was looking for.
Jamzy
CC BY-SA 3.0
2015-09-24T23:07:52.520Z
My question was, given assumptions A B C does X follow? It was about trying to understand the structure of a model, not about its empirical or scientific validity. I did not say, either, that A B C must be true.
Pablo Derbez
CC BY-SA 3.0
2015-09-25T16:22:00.800Z
My answer stands ... the answer is Pareto efficiency ABSOLUTELY takes growth into account.

I particularly appreciate your critiques and your downvotes because of how that behavior illustrates the incorrectness of your assumptions and the flaws in your thinking, i.e. you fundamentally have no comprehension of growth, the foundations of growth, the genesis of growth.

You are in *good* company...most academics, Mr. Krugman, Mr Bernanke, Ms. Yellen ...also incorrectly assume that [the disaster that they have created](https://research.stlouisfed.org/fred2/series/M1/) can somehow result in growth.
markbruns
CC BY-SA 3.0
2015-09-25T18:40:28.230Z
I still don't see what you are critiquing. The whole point of asking a question about a model is of dissecting its argument.

Anyways, if I understand this correctly, a Pareto Efficiency model can take growth into account if time preference is introduced along with capital. You're right about that. But that doesn't mean that the Pareto Efficiency distribution is stable over time, as I stated in my question. That distinction is pretty interesting by itself, I think.
Pablo Derbez
CC BY-SA 3.0
2015-09-25T20:30:48.753Z
The model construction itself matters; especially since [modelling growth](https://en.wikipedia.org/wiki/Economic_growth#Theories_and_models) is far from trivial and certainly not something that economists agree upon. An elegant model is one that as simple as possible; but not simpler.  There are more nuances to growth modelling than first meet the eye.

If a modeller is serious about looking at growth [and Pareto efficiency], it is necessary to compare and contrast different approaches.  

The **classical** [overly simplistic] answer is that Pareto efficiency takes growth into account, but...
markbruns
CC BY-SA 3.0
2015-09-27T20:32:16.710Z
Fair enough. Any literature you would suggest on the matter?
Pablo Derbez
CC BY-SA 3.0
2015-09-28T06:53:06.983Z
When it comes to literature, it is important to read things that challenge assumptions especially of mainstream thinking ... Taleb's work on how economists have been fooled by randomness, for example ... the growing body of work Bitcoin and blockchain is worthwhile-- if only because some of it gets at the essential linkage between growth and the foundation of trust in any medium of exchange.
markbruns
CC BY-SA 3.0
2015-09-24T19:29:01.913Z
2015-09-24T22:47:39.453Z
2015-09-24T22:47:39.453Z
markbruns
<p>It seems to me that as long as every person likes wealth any allocation $W_t$ will be Pareto-optimal.</p>

<p>Even if this was not the case, so supposing that $w_1, w_2,...$ are not real numbers representing wealth but vectors representing bundles of goods the distribution from one time to another can change drastically if you do not specify how growth occurs. At $t=1$ someone might have everything, then at $t=2$ someone else might have everything. Both of these states are Pareto-optimal, but the distributions are quite different.</p>

<p>So no, it does not follow from your conditions that $D_t$ necessarily equals $D_{t+1}$.</p>

CC BY-SA 3.0
2015-09-24T22:55:35.880Z
Yup! I see that now. In hindsight, I don't know why I thought 

**D**t = **D** (t+1) 

should hold true.
Pablo Derbez
CC BY-SA 3.0
2015-09-24T22:58:33.193Z
I'm still musing about Pareto Optimality over time, but my particular question was answered. Thanks!
Pablo Derbez
CC BY-SA 3.0
2015-09-24T22:46:46.557Z
2015-09-24T22:53:55.827Z
2015-09-24T22:53:55.827Z
Giskard
<p>I'll try to state my question clearly:</p>

<p>&nbsp;</p>

<p>For a given a "wealth" allocation <strong>W</strong><sub>t</sub> = (w<sub>1</sub>, w<sub>2</sub>, w<sub>3</sub>, ... ) for individuals <strong>I</strong> = (i<sub>1</sub>, i<sub>2</sub>, i<sub>3</sub>, ... ).</p>

<p>And a distribution of <strong>D</strong>= (w<sub>1</sub>/|<strong>W</strong>|, w<sub>2</sub>/|<strong>W</strong>|, w<sub>3</sub>/|<strong>W</strong>|, ... ), that is, as a percentage of the total.</p>

<p>Where <strong>W</strong><sub>t</sub> is Pareto Efficient at a given time frame &nbsp;t&nbsp;, and <strong>W</strong><sub>(t+1)</sub> is Pareto Efficient at &nbsp;t+1&nbsp;.</p>

<p>When there is growth such that &nbsp; &nbsp;&nbsp;|<strong>W</strong><sub>(t+1)</sub>| > |<strong>W</strong><sub>t</sub>| </p>

<p>Is <strong>D</strong><sub>t</sub>=<strong>D</strong><sub>(t+1)</sub>?</p>

<p>If so, why? If not, how do you allocate say, capital, whose value is intrinsically linked to growth?</p>

<p>I understand many of my assumptions may be plain wrong or badly stated, I am still an undergrad. Sorry about that. And thanks in advance.</p>

<hr>

<p>Further clarifications:</p>

<p>For each element &nbsp;w&nbsp; of <strong>W</strong><sub>t</sub> = (w<sub>1</sub>, w<sub>2</sub>, w<sub>3</sub>, ... ),</p>

<p>w= <strong>P</strong> * <strong>B</strong></p>

<p>Where <strong>P</strong> is the price vector of a commodity bundle <strong>B</strong>.</p>

<p>I hope that my representation of growth as an increase in the magnitude of the <strong>W</strong> vector is correct. This is what has been bugging me the most. It's safe to assume that growth causes an increase in |<strong>W</strong>|, right?</p>

CC BY-SA 3.0
2015-09-24T17:13:52.203Z
I don't  have time at all to look at your equations right now. Here's the kicker: Pareto-Efficiency is in utility terms. If 
"growth" (of whatever kind) is represented correctly in preferences, then Pareto-efficiency takes that into account. Otherwise it doesn't.
FooBar
CC BY-SA 3.0
2015-09-24T20:01:34.983Z
You identify wealth with purchasing power, which is not wrong, but by writing

$$w_i = \mathbf p\cdot \mathbf b_i$$

you identify it with _nominal_ purchasing power. Note that in this way, total "wealth" may "increase" because prices have increased, while the quantity bundle of goods has remained unchanged. No growth here. Perhaps you should re-think this part of your question.
Alecos Papadopoulos
CC BY-SA 3.0
2015-09-24T22:54:08.240Z
Oh, you're both right. Thanks about the input. I'm thinking this through.
Pablo Derbez
CC BY-SA 3.0
2015-09-25T18:57:39.383Z
@AlecosPapadopoulos So it turns out I was making a crass mistake by identifying the influence of time-discounted utility on the present distribution with a unique distribution at any point in time. 

Anyways, what I'm intuitively grasping at is that, it seems problematic that a distribution at $t$ is determined by future discounted utility, but the distribution itself affects utility at $t$. To avoid the C word (capital), we could think about this in terms of seeds. Say we have corn, wheat, corn seeds and wheat seeds (...)
Pablo Derbez
CC BY-SA 3.0
2015-09-25T19:14:38.270Z
(...) and the utility value of a corn seed is the value of the utility we can get for the grown produce then (by consuming or trading the corn), time-discounted. But this new allocation affects the quantity of corn at t+1 and consequently, its relative price, and utility (say we are producing corn for trade, as we are interested in a trade economy). 

I say this seems problematic because it seems difficult to achieve a Pareto-efficient outcome by having each individual maximize his Utility function. For example, if too many people plant corn.
Pablo Derbez
<economic-growth><pareto-efficiency>
Does Pareto-efficency take into account growth?
Pablo Derbez
# Does Pareto-efficency take into account growth?

(Asked by: username_0 on 2015-09-24)

I'll try to state my question clearly:

For a given a "wealth" allocation **W**t = (w1, w2, w3, ... ) for individuals **I** = (i1, i2, i3, ... ).

And a distribution of **D**= (w1/|**W**|, w2/|**W**|, w3/|**W**|, ... ), that is, as a percentage of the total.

Where **W**t is Pareto Efficient at a given time frame  t , and **W**(t+1) is Pareto Efficient at  t+1 .

When there is growth such that     |**W**(t+1)| > |**W**t|

Is **D**t=**D**(t+1)?

If so, why? If not, how do you allocate say, capital, whose value is intrinsically linked to growth?

I understand many of my assumptions may be plain wrong or badly stated, I am still an undergrad. Sorry about that. And thanks in advance.

---

Further clarifications:

For each element  w  of **W**t = (w1, w2, w3, ... ),

w= **P** \* **B**

Where **P** is the price vector of a commodity bundle **B**.

I hope that my representation of growth as an increase in the magnitude of the **W** vector is correct. This is what has been bugging me the most. It's safe to assume that growth causes an increase in |**W**|, right?

**Tags:** economic-growth, pareto-efficiency
> **Comments:**
> **username_1**: I don't  have time at all to look at your equations right now. Here's the kicker: Pareto-Efficiency is in utility terms. If  "growth" (of whatever kind) is represented correctly in preferences, then Pareto-efficiency takes that into account. Otherwise it doesn't.  
> **username_2**: You identify wealth with purchasing power, which is not wrong, but by writing  $$w_i = \mathbf p\cdot \mathbf b_i$$  you identify it with _nominal_ purchasing power. Note that in this way, total "wealth" may "increase" because prices have increased, while the quantity bundle of goods has remained unchanged. No growth here. Perhaps you should re-think this part of your question.  
> **username_0**: Oh, you're both right. Thanks about the input. I'm thinking this through.  
> **username_0**: @AlecosPapadopoulos So it turns out I was making a crass mistake by identifying the influence of time-discounted utility on the present distribution with a unique distribution at any point in time.   Anyways, what I'm intuitively grasping at is that, it seems problematic that a distribution at $t$ is determined by future discounted utility, but the distribution itself affects utility at $t$. To avoid the C word (capital), we could think about this in terms of seeds. Say we have corn, wheat, corn seeds and wheat seeds (...)  
> **username_0**: (...) and the utility value of a corn seed is the value of the utility we can get for the grown produce then (by consuming or trading the corn), time-discounted. But this new allocation affects the quantity of corn at t+1 and consequently, its relative price, and utility (say we are producing corn for trade, as we are interested in a trade economy).   I say this seems problematic because it seems difficult to achieve a Pareto-efficient outcome by having each individual maximize his Utility function. For example, if too many people plant corn.  

---

## 3 answers

### Answer by username_6 on 2015-09-24. Score: 3 | Accepted answer

It seems to me that as long as every person likes wealth any allocation $W\_t$ will be Pareto-optimal.

Even if this was not the case, so supposing that $w\_1, w\_2,...$ are not real numbers representing wealth but vectors representing bundles of goods the distribution from one time to another can change drastically if you do not specify how growth occurs. At $t=1$ someone might have everything, then at $t=2$ someone else might have everything. Both of these states are Pareto-optimal, but the distributions are quite different.

So no, it does not follow from your conditions that $D\_t$ necessarily equals $D\_{t+1}$.

> **Comments:**
> **username_0**: Yup! I see that now. In hindsight, I don't know why I thought   **D**t = **D** (t+1)   should hold true.  
> **username_0**: I'm still musing about Pareto Optimality over time, but my particular question was answered. Thanks!  

---

### Answer by username_3 on 2015-09-25. Score: 0

Perfectly fair question. Let the price vector be expressed in terms of a numeraire- i.e. a physical good. Stipulate that all economic activity is voluntary, there is no preference revelation problem (i.e. no strategic behaviour), no hedging etc (i.e. the standard perfect competition assumptions) then the answer is no if there is preference and endowment diversity provided some goods are consumed in each period. If agents are identical, then the answer is yes.
This is because a Wt is Pareto efficient if you can make a mutually advantageous trade which enables you to consume more- assuming that is your preference- provided you find someone who wants more assets and prefers to be thrifty for the moment. If Preference diversity obtains this happens so Dt will differ from the previous Dt-1.
Interestingly, if preference diversity is too great or too little and markets use up scarce resources then no conclusion can be drawn. The same thing happens when you introduce a little uncertainty- i.e. hedging appears- or a bit of information asymmetry- so preference revelation becomes problematic.

I take it you want an answer the question 'what type of allocatively efficient Growth is distributionally neutral'- this was a big topic in the Sixties- turnpike theorems and so on. It's good to see young people pondering these things in our present climate!
My tuppence is that it may be that some distributions are better for human beings than others- if so there is a Muth Rational economic theory which, under common knowledge, would be the Schelling focal solution to Society's coordination problem. This means Preferences change so that Society can still get to where it really wants to be- even if the Maths is intractable!
There was a Japanese 'peasant sage'- Ninomiya- who redefined what we call saving as 'concession'- i.e. a voluntary foregoing of consumption so the worst off can eat- and what we call Return on Investment- as 'obligation to acknowledge Virtue' which can be discharged collectively. There has been some General Eqbm work based on this sort of thinking. Here there is no 'Paradox of Thrift' nor naughty 'Income effects' to spoil our nice models because people are Muth rational- not zero intelligence rule following droids!
This does not mean that basic existential problems- Uncertainty, Concurrency, Co-ordination etc disappear- it's just that mathematical models can give better, more human, insights into profound dilemmas.
You asked a good question- that's the point of going to College. The good questions you ask there- not the answers you are required to give- will enrich your life to the end of your days.

> **Comments:**
> **username_0**: Thanks for the detailed response! I have one more quesiton, if you don't mind:  Could we consider capital as a commodity $c_t$ (that is, a capital which matures at time $t$), whose utility is the increase of maximum utility at $t$, discounted for time preference?  
> **username_3**: Hi Pablo, not sure what is meant by Capital with matures at time t. Suppose Capital item x is a machine which lasts t years producing a certain amount of Consumer good y per annum. Then, you could say its Utility is the Present Value of the consumption stream. The problem is that K is the summation of all Capital goods- some are breaking some are being replaced and there is also 'Capital deepening'- so you get an aggregation problem. Also, you can have 'reswitching' and cases where a consumer good can become a capital good and vice versa. With Uncertainty, things get really scary!  
> **username_3**: Why no up vote?  
> **username_0**: Sorry, voted now  
> **username_3**: Thanks. A lot of bright Indian people wasted their time chasing after Sraffa. My teacher was Morishima who had a 'rational distribution' theory- basically shadow prices do the work. Silly- I know.  
> **username_3**: Thanks. A lot of bright Indian people wasted their time chasing after Sraffa. My teacher was Morishima who had a 'rational distribution' theory- basically shadow prices do the work. Silly- I know. Ken Binmore, my other Prof at age 16 tried hard with a Game theoretic approach. I suggest Muth Rationality and Aumman signalling. It's important to show that Wealth is Shit. Spread it around and the grass is greener. Not otherwise. Marxist or Ricardian models are the enemy here. They assume the Capitalist can always gain security at the expense of the worker. See Alan Kirman  

---

### Answer by username_4 on 2015-09-24. Score: -2

In general classical economics, the answer to your question is "ABSOLUTELY!"

*Now the TL;DR answer ...*

> Classical models assume that all actors are rational, discount the future equivalently and equally concerned about
> their future well-being over time AND able to comprehend the future
> with perfect certainty ... a [Pareto efficient](https://en.wikipedia.org/wiki/Pareto_efficiency) allocation of
> resources exists when it is impossible to make any one individual
> better off without making at least one individual worse off.
>
> Clearly the real issue is not Pareto efficiency, but rather in whether
> or not the actors really are rational, have static preferences over
> time, are able to coherently use all information available and know
> the future [and impacts of growth in their lives] with perfect
> certainty.
>
> Your conclusion is going to depend on how you construct your model ...
> you model might be flawed (HINT: all models are flawed) ... or you
> have introduced [artificial] constraints to help you [implicitly] test
> some hypothesis or prove a point. If you change the premises and
> architecture of your model, you can prove anything ... that's why no
> one should ever trust [some opinionated joker](http://www.nytimes.com/column/paul-krugman) claiming to be an
> economic expert, simply because he received some [*teacher's pet
> award* for brilliant models that were popular with powerful
> people](https://en.wikipedia.org/wiki/Nobel_Memorial_Prize_in_Economic_Sciences).

> **Comments:**
> **username_2**: (+1-1-1=-1): This is epistemologically sound, politically heated, and Q&A-wise useless: when an undergraduate student asks, "particulars of model A", it rarely helps to counter "you should abandon your studies and go occupy yourself with the _real_ world, since all Social Sciences and their models are flawed or a fraud".  
> **username_5**: There is a fair bit in this answer which is irrelevant. Also, it is very light on the sort of explanation I feel the questioner was looking for.  
> **username_0**: My question was, given assumptions A B C does X follow? It was about trying to understand the structure of a model, not about its empirical or scientific validity. I did not say, either, that A B C must be true.  
> **username_4**: My answer stands ... the answer is Pareto efficiency ABSOLUTELY takes growth into account.  I particularly appreciate your critiques and your downvotes because of how that behavior illustrates the incorrectness of your assumptions and the flaws in your thinking, i.e. you fundamentally have no comprehension of growth, the foundations of growth, the genesis of growth.  You are in *good* company...most academics, Mr. Krugman, Mr Bernanke, Ms. Yellen ...also incorrectly assume that [the disaster that they have created](https://research.stlouisfed.org/fred2/series/M1/) can somehow result in growth.  
> **username_0**: I still don't see what you are critiquing. The whole point of asking a question about a model is of dissecting its argument.  Anyways, if I understand this correctly, a Pareto Efficiency model can take growth into account if time preference is introduced along with capital. You're right about that. But that doesn't mean that the Pareto Efficiency distribution is stable over time, as I stated in my question. That distinction is pretty interesting by itself, I think.  
> **username_4**: The model construction itself matters; especially since [modelling growth](https://en.wikipedia.org/wiki/Economic_growth#Theories_and_models) is far from trivial and certainly not something that economists agree upon. An elegant model is one that as simple as possible; but not simpler.  There are more nuances to growth modelling than first meet the eye.  If a modeller is serious about looking at growth [and Pareto efficiency], it is necessary to compare and contrast different approaches.    The **classical** [overly simplistic] answer is that Pareto efficiency takes growth into account, but...  
> **username_0**: Fair enough. Any literature you would suggest on the matter?  
> **username_4**: When it comes to literature, it is important to read things that challenge assumptions especially of mainstream thinking ... Taleb's work on how economists have been fooled by randomness, for example ... the growing body of work Bitcoin and blockchain is worthwhile-- if only because some of it gets at the essential linkage between growth and the foundation of trust in any medium of exchange.  

---

