<p>Youre erring in the definition of Kaldor-Hicks efficiency. K-H improvement is a change where those who lose from the change, lose less than the gain obtained by those who benefit from it. Pareto improvement is a change from which no-one loses and some gain. Thus all Pareto improvements are also K-H improvements but many K-H improvements are not Pareto improvements. A classical example of this is international trade. If a country opens its market to the world, some domestic producers will inevitably loose, but the gain of the domestic consumers from opening the market will be much larger than the loss of the domestic producers. I.e. opening the market for foreign producers is a K-H improvement but it is not a Pareto improvement. Hence autarky is Pareto efficient but it is not K-H efficient.</p>

<p><strong><em>EDIT</em></strong> </p>

<p>The possibility of side payments you are talking about is a <strong><em>consequence</em></strong> of defining K-H improvements properly, not a part of the definition. This actually matters here. These side payments are not a part of the choice set when youre choosing between opening the market for foreign suppliers or keeping it closed.</p>

<p>I.e. if the market is currently autark and your choice set consists of exactly two options: X = {keep market closed, open market for foreigners}, there is no possibility for side payments and no Pareto improvement but there is a K-H improvement.</p>

<p>In this case both choices in X are Pareto efficient but only open market for foreigners is K-H efficient.</p>

<p>Talking about possible side payments is only a rationalization of the concept of K-H efficiency. The idea of side payments is based on the same logic as the Coase theorem on externalities. It simply is a nice property to have.</p>

CC BY-SA 4.0
2019-12-09T05:28:07.123Z
What you said and what I said about Kaldor-Hicks improvements are equivalent - if the winners gain more than the losers lose, then you can redistribute money from the winners to the losers so that no one is worse off than they were before.  In the case of trade, free trade combined with a redistribution from domestic consumers to domestic producers is a Pareto improvement.
Keshav Srinivasan
CC BY-SA 4.0
2019-12-09T06:00:42.863Z
@KeshavSrinivasan the possibility of side payments you are talking about is a ***consequence*** of defining K-H improvements properly, not a part of the definition. This actually matters here. These side payments are not a part of the choice set when youre deciding whether to open the market for foreign suppliers or keep it closed.
Grada Gukovic
CC BY-SA 4.0
2019-12-09T06:09:24.577Z
OK, but whether it’s part of the definition or a consequence of the definition, is it or is it not true that if you start Pareto efficient outcome that is not Kaldor-Hicks efficient, then you can implement a Kaldor-Hicks improvement followed by the associated side payment, and the combination will be a Pareto improvement of the outcome you started initially?  And if it is true, isn’t that a contradiction?
Keshav Srinivasan
CC BY-SA 4.0
2019-12-09T06:11:02.410Z
What do you mean by “not part of the choice set”?  Are you saying that outcomes which are Kaldor-Hicks efficient but not Pareto-efficient can only exist if you’re not allowed to pursue redistribution policies?
Keshav Srinivasan
CC BY-SA 4.0
2019-12-09T06:13:47.110Z
@KeshavSrinivasan if the market is currently autark and your choice set consists of exactly two options: X = {keep market closed, open market for foreigners}, there is no possibility for side payments and no Pareto improvement but there is a K-H improvement
Grada Gukovic
CC BY-SA 4.0
2019-12-09T06:15:16.497Z
So are you saying that given a sufficiently large choice set, all Pareto efficient outcomes are Kaldor-Hicks efficient?
Keshav Srinivasan
CC BY-SA 4.0
2019-12-09T06:20:45.373Z
@KeshavSrinivasan no, all I am saying is that talking about possible side payments is only a rationalization of the concept of K-H efficiency and not a part of its nature.
Grada Gukovic
CC BY-SA 4.0
2019-12-09T06:22:54.420Z
@KeshavSrinivasan side payments are called side payments exactly because they are outside of the choice set
Grada Gukovic
CC BY-SA 4.0
2019-12-09T06:29:23.800Z
@KeshavSrinivasan There are many cases where K-H improvements and Pareto improvements coincide by necessity. The simplest example is the textbook-type Edgeworth box. One of the goals of the notion of K-H efficiency is to make more situations uniquely decidable(more, sparser  choice sets). The idea of side payments is based on the same logic as the Coase theorem.
Grada Gukovic
CC BY-SA 4.0
2019-12-09T06:44:01.527Z
@GradaGukovic What you write sounds compelling. However I hesitate to upvote it because this is a matter of definition and I cannot decide whether this is the correct one. Could you please back your claims up with a source?
Giskard
CC BY-SA 4.0
2019-12-09T07:16:52.763Z
But is it or is it not true that if the choice set includes arbitrary redistributions of wealth, then Pareto efficient outcomes and Kaldor-Hicks efficient outcomes coincide?
Keshav Srinivasan
CC BY-SA 4.0
2019-12-09T07:23:02.080Z
@KeshavSrinivasan I dont think they necessarily coincide if redistributions are available inside the choice set. If X={keep market closed, open market, open market with compensations} both open market and open market with compensations are K-H improvements but only open market with compensations is a Pareto improvement.
Grada Gukovic
CC BY-SA 4.0
2019-12-09T07:25:31.883Z
@GradaGukovic I’m not talking about Pareto improvements coinciding with Kaldor-Hicks improvements, I’m talking about Pareto efficient outcomes coinciding with Kaldor-Hicks efficient outcomes.  You can have the latter without the former.
Keshav Srinivasan
CC BY-SA 4.0
2019-12-09T07:29:27.273Z
OK, but how is that an example of Pareto efficient outcomes not coinciding with Kaldor-Hicks efficient outcomes.
Keshav Srinivasan
CC BY-SA 4.0
2019-12-09T05:16:05.807Z
2019-12-09T08:06:20.290Z
2019-12-09T08:06:20.290Z
Grada Gukovic
<p>An policy is a Pareto improvement if it makes some people better off and no one worse off.  And a policy is a Kaldor-Hicks improvement if it can be turned into a Pareto improvement by redistributing money.  Every Pareto improvement is a Kaldor-Hicks improvement, but not every Kaldor-Hicks improvement is a Pareto improvement.  </p>

<p>Now an outcome is called Pareto efficient if there are no possible Pareto improvements of it, and Kaldor-Hicks efficient if there are no Kaldor-Hicks improvement of it.  Now clearly every Kaldor-Hicks efficient outcome is Pareto-efficient, because if a Pareto improvement were possible it would also be a Kaldor-Hicks improvement.  But my question is, why is the converse not true?</p>

<p>Here is my argument for why the converse is true.  Suppose that X is a Pareto-efficient outcome which is not Kaldor-Hicks efficient.  Then there exists a Kaldor-Hicks improvement which can be turned into a Pareto improvement by a redistribution of money.  But then that Kaldor-Hicks improvement together with that redistribution is a Pareto improvement, so there exists a possible Pareto improvement of X, contradicting the fact that X was Pareto efficient.  Where am I going wrong?</p>

<microeconomics><pareto-efficiency><welfare-economics><social-welfare>
How can an outcome be Pareto efficient but not Kaldor-Hicks efficient?
Keshav Srinivasan
# How can an outcome be Pareto efficient but not Kaldor-Hicks efficient?

(Asked by: username_0 on 2019-12-09)

An policy is a Pareto improvement if it makes some people better off and no one worse off. And a policy is a Kaldor-Hicks improvement if it can be turned into a Pareto improvement by redistributing money. Every Pareto improvement is a Kaldor-Hicks improvement, but not every Kaldor-Hicks improvement is a Pareto improvement.

Now an outcome is called Pareto efficient if there are no possible Pareto improvements of it, and Kaldor-Hicks efficient if there are no Kaldor-Hicks improvement of it. Now clearly every Kaldor-Hicks efficient outcome is Pareto-efficient, because if a Pareto improvement were possible it would also be a Kaldor-Hicks improvement. But my question is, why is the converse not true?

Here is my argument for why the converse is true. Suppose that X is a Pareto-efficient outcome which is not Kaldor-Hicks efficient. Then there exists a Kaldor-Hicks improvement which can be turned into a Pareto improvement by a redistribution of money. But then that Kaldor-Hicks improvement together with that redistribution is a Pareto improvement, so there exists a possible Pareto improvement of X, contradicting the fact that X was Pareto efficient. Where am I going wrong?

**Tags:** microeconomics, pareto-efficiency, welfare-economics, social-welfare


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## 1 answers

### Answer by username_1 on 2019-12-09. Score: 1

Youre erring in the definition of Kaldor-Hicks efficiency. K-H improvement is a change where those who lose from the change, lose less than the gain obtained by those who benefit from it. Pareto improvement is a change from which no-one loses and some gain. Thus all Pareto improvements are also K-H improvements but many K-H improvements are not Pareto improvements. A classical example of this is international trade. If a country opens its market to the world, some domestic producers will inevitably loose, but the gain of the domestic consumers from opening the market will be much larger than the loss of the domestic producers. I.e. opening the market for foreign producers is a K-H improvement but it is not a Pareto improvement. Hence autarky is Pareto efficient but it is not K-H efficient.

***EDIT***

The possibility of side payments you are talking about is a ***consequence*** of defining K-H improvements properly, not a part of the definition. This actually matters here. These side payments are not a part of the choice set when youre choosing between opening the market for foreign suppliers or keeping it closed.

I.e. if the market is currently autark and your choice set consists of exactly two options: X = {keep market closed, open market for foreigners}, there is no possibility for side payments and no Pareto improvement but there is a K-H improvement.

In this case both choices in X are Pareto efficient but only open market for foreigners is K-H efficient.

Talking about possible side payments is only a rationalization of the concept of K-H efficiency. The idea of side payments is based on the same logic as the Coase theorem on externalities. It simply is a nice property to have.

> **Comments:**
> **username_0**: What you said and what I said about Kaldor-Hicks improvements are equivalent - if the winners gain more than the losers lose, then you can redistribute money from the winners to the losers so that no one is worse off than they were before.  In the case of trade, free trade combined with a redistribution from domestic consumers to domestic producers is a Pareto improvement.  
> **username_1**: @KeshavSrinivasan the possibility of side payments you are talking about is a ***consequence*** of defining K-H improvements properly, not a part of the definition. This actually matters here. These side payments are not a part of the choice set when youre deciding whether to open the market for foreign suppliers or keep it closed.  
> **username_0**: OK, but whether it’s part of the definition or a consequence of the definition, is it or is it not true that if you start Pareto efficient outcome that is not Kaldor-Hicks efficient, then you can implement a Kaldor-Hicks improvement followed by the associated side payment, and the combination will be a Pareto improvement of the outcome you started initially?  And if it is true, isn’t that a contradiction?  
> **username_0**: What do you mean by “not part of the choice set”?  Are you saying that outcomes which are Kaldor-Hicks efficient but not Pareto-efficient can only exist if you’re not allowed to pursue redistribution policies?  
> **username_1**: @KeshavSrinivasan if the market is currently autark and your choice set consists of exactly two options: X = {keep market closed, open market for foreigners}, there is no possibility for side payments and no Pareto improvement but there is a K-H improvement  
> **username_0**: So are you saying that given a sufficiently large choice set, all Pareto efficient outcomes are Kaldor-Hicks efficient?  
> **username_1**: @KeshavSrinivasan no, all I am saying is that talking about possible side payments is only a rationalization of the concept of K-H efficiency and not a part of its nature.  
> **username_1**: @KeshavSrinivasan side payments are called side payments exactly because they are outside of the choice set  
> **username_1**: @KeshavSrinivasan There are many cases where K-H improvements and Pareto improvements coincide by necessity. The simplest example is the textbook-type Edgeworth box. One of the goals of the notion of K-H efficiency is to make more situations uniquely decidable(more, sparser  choice sets). The idea of side payments is based on the same logic as the Coase theorem.  
> **username_2**: @GradaGukovic What you write sounds compelling. However I hesitate to upvote it because this is a matter of definition and I cannot decide whether this is the correct one. Could you please back your claims up with a source?  
> **username_0**: But is it or is it not true that if the choice set includes arbitrary redistributions of wealth, then Pareto efficient outcomes and Kaldor-Hicks efficient outcomes coincide?  
> **username_1**: @KeshavSrinivasan I dont think they necessarily coincide if redistributions are available inside the choice set. If X={keep market closed, open market, open market with compensations} both open market and open market with compensations are K-H improvements but only open market with compensations is a Pareto improvement.  
> **username_0**: @GradaGukovic I’m not talking about Pareto improvements coinciding with Kaldor-Hicks improvements, I’m talking about Pareto efficient outcomes coinciding with Kaldor-Hicks efficient outcomes.  You can have the latter without the former.  
> **username_0**: OK, but how is that an example of Pareto efficient outcomes not coinciding with Kaldor-Hicks efficient outcomes.  

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