<p>Its not correct to say that production will be lower in the solution to the Ricardian model (in your case full specialization of US is not equilibrium outcome). In general in Ricardian model the production after specialization will always be either the same (if the relative opportunity costs are exactly same) or production will be higher. The reason why you got it lower in your case is that your model omits demands for the two goods and by your assumption on production technology US is economically big country while France is economically small (meaning the production possibility frontier (PPF) of US severely outstrips the PPF of France).</p>

<p>In situations like these you will find that only small country fully specializes while the big country specializes only partially. The reason for this is that even if the small country produces on full capacity it simply wont be able to satisfy the world demand, so once the US produces enough wine to fill up the word demand it will be also allocating the rest of the resources to cheese.</p>

<p>Fully deriving the optimum solution with adding utilities would take too much space so instead of full proof consider the following numerical simulation with your own example.</p>

<p>As you have shown in autarky we will have the following production:</p>

<ul>
<li>US Cheese: 500 US Wine:  1000</li>
<li>France Ch: 250 France W:  333</li>
<li>World  Ch: 750 World  W: 1333 </li>
</ul>

<p>Now consider possible scenario with full specialization France (all in cheese) and partial US (1500 labor in wine and 500 in cheese): </p>

<ul>
<li>US Cheese: 250 US wine: 1500 </li>
<li>France Ch: 500 France W:   0</li>
<li>world Ch:  750 world W: 1500</li>
</ul>

<p>Now you can see the production of cheese is exactly the same as before plus world has more wine. With just one extra unit of labor in cheese in US you would still get more cheese and also more wine compared to autarky.</p>

<p>Now to get an exact optimal solution you need to explicitly include consumer utility and demand, and you would see that in this case there would be excess demand that France could not satisfy which would be allocated to US. For the full treatment see Feenstra, R. C. (2015). Advanced international trade: theory and evidence. Princeton university press.</p>

<p>The undergraduate treatment of Ricardian model does not include demand functions explicitly because as long as none of the two countries have production frontiers that do not strictly outstrips the PPF of the other at all points you will always get full and never partial specialization so the exact nature of demand function does not matter (notice that in undergraduate Ricardian model you wont even find the final distribution of the goods unless the final demands are assumed in the question - this is to simplify the model to make it easier to solve but it does not represent the full model in its modern specification) </p>

<p>PS: of course on off equilibrium path any combination of outputs that satisfies the resource constraint is possible </p>

CC BY-SA 4.0
2019-12-12T16:39:32.193Z
"The problem here is that you start with the position where both countries produce only cheese. " No, they both produce both goods! I just didn't show it!
KarmaPeasant
CC BY-SA 4.0
2019-12-12T16:41:11.763Z
@user161005 how’s that possible if before trade they produce 500 cheese in US and 250 in France and if you say they only have 1000 labor and in US cheese costs 2 units of labor and in France 4. Then if they produce both cheese and wine before trade you made a mistake here
1muflon1
CC BY-SA 4.0
2019-12-12T16:42:13.950Z
"if you say they only have 1000 labor" They have 1000 labor in each industry, i.e. 2000 labor total per country
KarmaPeasant
CC BY-SA 4.0
2019-12-12T16:42:43.367Z
Can I just give you my spreadsheet?
KarmaPeasant
CC BY-SA 4.0
2019-12-12T16:55:53.127Z
sure if you can upload it somewhere i can have look at it later
1muflon1
CC BY-SA 4.0
2019-12-12T17:00:39.437Z
https://drive.google.com/file/d/1dO0LzkrRrUCK9wcq_Ics63ofWCeX93v2/view?usp=sharing
KarmaPeasant
CC BY-SA 4.0
2019-12-12T20:20:20.730Z
@user161005 see my updated answer
1muflon1
CC BY-SA 4.0
2019-12-12T20:25:14.997Z
"*Its not correct to say that production will be lower.*" In his case, after full specialization, production is clearly lower. You are arguing that full specialization is unlikely in this case. Which is fine.
Giskard
CC BY-SA 4.0
2019-12-12T20:38:27.570Z
@Giskard its not unlikely it wont happen because if there would be full specialization markets would not clear. There would be excess demand in cheese market and excess supply in wine. That cant happen as it is inconsistent with the background assumptions of Ricardian model like that there are rational agents, non-satiation (without which optimal output in any case could be 0) etc. My point was that the presented solution is not correct solution to the *Ricardian* model and in actual solution it can be proven mathematically the world output will be same or larger
1muflon1
CC BY-SA 4.0
2019-12-13T04:55:32.180Z
I have no issues with the current wording.
Giskard
CC BY-SA 4.0
2019-12-12T15:27:43.177Z
2019-12-13T13:46:36.473Z
2019-12-13T13:46:36.473Z
1muflon1
<p>I have the model in my electronic spreadsheet (created by me) and its results quite suprised me. In short, complete specialization (I just call it specialization) in good where a country has comparative advantage CAN lead to inefficiency, to decrease of production of one of the goods (cheese in this case). This result suprised me and I would like it checked in case a mistake (in my reasoning or calculations) was made. (I can also share the spreadsheet if you want)</p>

<p>Suppose there are two countries, USA and France. Each country has industries: cheese production industry and wine production industry. Each industry in each country has exactly 1000 workers(the top is the American workforce, the bottom is the French workforce)</p>

<p><a href="https://i.sstatic.net/xOJR2.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/xOJR2.png" alt="enter image description here"></a></p>

<p>But technologies are different. 
<a href="https://i.sstatic.net/DG1jj.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DG1jj.png" alt="enter image description here"></a></p>

<p>From this we conclude that opportunity costs are following:
<a href="https://i.sstatic.net/3NMOV.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/3NMOV.png" alt="enter image description here"></a></p>

<p>France has comparative advantage in cheese, while USA hold comparative advantage in wine. So France should concentrate all its laborforce in its chesee industry while USA should concentrate all its labor force in wine industry.</p>

<p>... except it will be bad news for world cheese production.</p>

<p>Production of cheese and wine in both countries before trade and (complete) specialization (the top is the American production, the bottom is the French production):</p>

<p><a href="https://i.sstatic.net/gfht0.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/gfht0.png" alt="enter image description here"></a></p>

<p>Production of cheese and wine in both countries after trade and (complete) specialization (the top is the American production, the bottom is the French production):</p>

<p><a href="https://i.sstatic.net/DjTFT.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DjTFT.png" alt="enter image description here"></a></p>

<p>Now France produces all cheese in the world. But its cheese production technologies are too labor-intensive to produce enough cheese to compensate for fall of cheese production in USA. In order to avoid this USA will have to employ at the least 500 of its workers in cheese production, despite it beign American comparative disadvantage.</p>

<p>Thus we can conclude that in this case full specialization in cheese is a bad idea.</p>

<international-trade><comparative-advantage>
(Ricardian model)Is it correct that complete specialization in comparative advantage CAN lead to DECREASE in total production?
KarmaPeasant
# (Ricardian model)Is it correct that complete specialization in comparative advantage CAN lead to DECREASE in total production?

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

I have the model in my electronic spreadsheet (created by me) and its results quite suprised me. In short, complete specialization (I just call it specialization) in good where a country has comparative advantage CAN lead to inefficiency, to decrease of production of one of the goods (cheese in this case). This result suprised me and I would like it checked in case a mistake (in my reasoning or calculations) was made. (I can also share the spreadsheet if you want)

Suppose there are two countries, USA and France. Each country has industries: cheese production industry and wine production industry. Each industry in each country has exactly 1000 workers(the top is the American workforce, the bottom is the French workforce)

[![enter image description here](https://i.sstatic.net/xOJR2.png)](https://i.sstatic.net/xOJR2.png)

But technologies are different.
[![enter image description here](https://i.sstatic.net/DG1jj.png)](https://i.sstatic.net/DG1jj.png)

From this we conclude that opportunity costs are following:
[![enter image description here](https://i.sstatic.net/3NMOV.png)](https://i.sstatic.net/3NMOV.png)

France has comparative advantage in cheese, while USA hold comparative advantage in wine. So France should concentrate all its laborforce in its chesee industry while USA should concentrate all its labor force in wine industry.

... except it will be bad news for world cheese production.

Production of cheese and wine in both countries before trade and (complete) specialization (the top is the American production, the bottom is the French production):

[![enter image description here](https://i.sstatic.net/gfht0.png)](https://i.sstatic.net/gfht0.png)

Production of cheese and wine in both countries after trade and (complete) specialization (the top is the American production, the bottom is the French production):

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

Now France produces all cheese in the world. But its cheese production technologies are too labor-intensive to produce enough cheese to compensate for fall of cheese production in USA. In order to avoid this USA will have to employ at the least 500 of its workers in cheese production, despite it beign American comparative disadvantage.

Thus we can conclude that in this case full specialization in cheese is a bad idea.

**Tags:** international-trade, comparative-advantage

---

## 1 answers

### Answer by username_1 on 2019-12-12. Score: 2 | Accepted answer

Its not correct to say that production will be lower in the solution to the Ricardian model (in your case full specialization of US is not equilibrium outcome). In general in Ricardian model the production after specialization will always be either the same (if the relative opportunity costs are exactly same) or production will be higher. The reason why you got it lower in your case is that your model omits demands for the two goods and by your assumption on production technology US is economically big country while France is economically small (meaning the production possibility frontier (PPF) of US severely outstrips the PPF of France).

In situations like these you will find that only small country fully specializes while the big country specializes only partially. The reason for this is that even if the small country produces on full capacity it simply wont be able to satisfy the world demand, so once the US produces enough wine to fill up the word demand it will be also allocating the rest of the resources to cheese.

Fully deriving the optimum solution with adding utilities would take too much space so instead of full proof consider the following numerical simulation with your own example.

As you have shown in autarky we will have the following production:

* US Cheese: 500 US Wine: 1000
* France Ch: 250 France W: 333
* World Ch: 750 World W: 1333

Now consider possible scenario with full specialization France (all in cheese) and partial US (1500 labor in wine and 500 in cheese):

* US Cheese: 250 US wine: 1500
* France Ch: 500 France W: 0
* world Ch: 750 world W: 1500

Now you can see the production of cheese is exactly the same as before plus world has more wine. With just one extra unit of labor in cheese in US you would still get more cheese and also more wine compared to autarky.

Now to get an exact optimal solution you need to explicitly include consumer utility and demand, and you would see that in this case there would be excess demand that France could not satisfy which would be allocated to US. For the full treatment see Feenstra, R. C. (2015). Advanced international trade: theory and evidence. Princeton university press.

The undergraduate treatment of Ricardian model does not include demand functions explicitly because as long as none of the two countries have production frontiers that do not strictly outstrips the PPF of the other at all points you will always get full and never partial specialization so the exact nature of demand function does not matter (notice that in undergraduate Ricardian model you wont even find the final distribution of the goods unless the final demands are assumed in the question - this is to simplify the model to make it easier to solve but it does not represent the full model in its modern specification)

PS: of course on off equilibrium path any combination of outputs that satisfies the resource constraint is possible

> **Comments:**
> **username_0**: "The problem here is that you start with the position where both countries produce only cheese. " No, they both produce both goods! I just didn't show it!  
> **username_1**: @user161005 how’s that possible if before trade they produce 500 cheese in US and 250 in France and if you say they only have 1000 labor and in US cheese costs 2 units of labor and in France 4. Then if they produce both cheese and wine before trade you made a mistake here  
> **username_0**: "if you say they only have 1000 labor" They have 1000 labor in each industry, i.e. 2000 labor total per country  
> **username_0**: Can I just give you my spreadsheet?  
> **username_1**: sure if you can upload it somewhere i can have look at it later  
> **username_0**: https://drive.google.com/file/d/1dO0LzkrRrUCK9wcq_Ics63ofWCeX93v2/view?usp=sharing  
> **username_1**: @user161005 see my updated answer  
> **username_2**: "*Its not correct to say that production will be lower.*" In his case, after full specialization, production is clearly lower. You are arguing that full specialization is unlikely in this case. Which is fine.  
> **username_1**: @Giskard its not unlikely it wont happen because if there would be full specialization markets would not clear. There would be excess demand in cheese market and excess supply in wine. That cant happen as it is inconsistent with the background assumptions of Ricardian model like that there are rational agents, non-satiation (without which optimal output in any case could be 0) etc. My point was that the presented solution is not correct solution to the *Ricardian* model and in actual solution it can be proven mathematically the world output will be same or larger  
> **username_2**: I have no issues with the current wording.  

---

