<p>Hidden in the postulated positive relationship is an assumption about tastes. In footnote 2 the authors state this assumption: citizens of both countries evenly spread their expenditure over all goods.
In particular, this implies that the total expenditure (in real terms) on all goods produced in England is given by:</p>
<p><span class="math-container">$$\bar{j}  L^*  +\bar{j}  \omega  L$$</span></p>
<p>Since this is the share (<span class="math-container">$\bar{j}$</span>) spent on England produced goods (<span class="math-container">$0&lt;j&lt;\bar{j}$</span>) of Portuguese income and English income.</p>
<p>Next, English income is naturally equal to the expenditure on England produced goods. But the English income also equals <span class="math-container">$\omega L$</span>, which is the labor income of English citizens. This gives us</p>
<p><span class="math-container">$$\omega L=\bar{j}(L^*+\omega L)$$</span></p>
<p>I challenge you to rewrite this into the expression in the figure.</p>

CC BY-SA 4.0
2021-11-12T22:55:18.097Z
Thanks for your answer. I update my question to clarify my question.
Alalalalaki
CC BY-SA 4.0
2021-11-12T23:05:32.910Z
To be honest, I have already figured out the logics of the positive relationship while updating my question. But I think it might be better if you can make the answer more explicit here rather than I write another answer to answer myself.
Alalalalaki
CC BY-SA 4.0
2021-11-12T14:24:21.447Z
2021-11-12T14:24:21.447Z
user18214
<p>I am learning the Ricardian trade model by reading <a href="https://www.aeaweb.org/articles?id=10.1257/jep.26.2.65" rel="nofollow noreferrer">Eaton &amp; Kortum 2012 JEP</a>. The equilibrium is easy to understand when there are finite goods, as shown in their Figure 1. <a href="https://i.sstatic.net/CDTQ1.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/CDTQ1.png" alt="enter image description here" /></a></p>
<p>However, they then introduce the Dornbusch, Fischer, Samuelson (1977) model with &quot;a set of goods correspond to all the points on an interval between 0 and 1&quot; and &quot;defined a function <span class="math-container">$A(j)$</span> as the ratio of Portugal's labor requirements to England's labor requirements for good <span class="math-container">$j$</span> .. For any English wage <span class="math-container">$\omega$</span> between <span class="math-container">$A(0)$</span> and <span class="math-container">$A(1)$</span> there is some good, let's call it <span class="math-container">$\bar{j}$</span>, satisfying <span class="math-container">$\mathrm{A}(\bar{j})=\omega$</span>.&quot;.</p>
<p>They then state &quot;To figure out what <span class="math-container">$\omega$</span> will break the chain, we need to look at the demand side. A higher <span class="math-container">$\bar{j}$</span> means that England is producing a larger share of goods, increasing demand for its labor and hence its wage <span class="math-container">$\omega$</span>. Figure 2 depicts this positive relationship between <span class="math-container">$\omega$</span> and <span class="math-container">$\bar{j}$</span>. Where it intersects the downward sloping <span class="math-container">$A(j)$</span> curve determines the equilibrium.&quot;</p>
<p><a href="https://i.sstatic.net/fZWQQ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/fZWQQ.png" alt="enter image description here" /></a></p>
<p>I fail to understand the &quot;demand side&quot; of the equilibrium wage determination. Where does this positive relationship between  <span class="math-container">$\omega$</span> and <span class="math-container">$\bar{j}$</span> actually come from? And more generally I want to know how exactly the preferences of consumers and exogenous labor supply in two countries affect the equilibrium wage in this case?</p>
<p><strong>Update</strong>: Yes footnote 2 shows under a strong symmetric CD preference same in all countries, this upward line can be written as the income of one country equals to the production fraction of the world income  <span class="math-container">$\omega L=\bar{j}\left(\omega L+L^{*}\right)$</span>. I think this is not very intuitive in explaining a positive relationship between wage and <span class="math-container">$\bar{j}$</span>. In particular, if we think <span class="math-container">$A$</span> is the (relative) labor demand curve, we need have a (relative) labor supply curve to find the equilibrium wage. This is the case in the Figure 1, where the relative labor supply curve is a vertical line given the fact that labor supply are exogenous. However, in Figure 2, it seems even though we assume full employment, <span class="math-container">$\bar{j}$</span> can still control the relative labor supply ratio. And how is the relative labor supply connected with the income without endogenous labor supply? This is the thing that I fail to get around with. And as the symmetric CD assumption is very strong, I want to see how in general cases the income-consumption equality forms a relative labor supply condition to obtain equilibrium wage and how different utility assumptions affect this equilibrium wage.</p>

CC BY-SA 4.0
2021-11-12T14:08:58.287Z
Have you checked out footnote 2?
user18214
<international-trade><competitive-equilibrium>
The Equilibrium Wage in Ricardian Trade Model
Alalalalaki
# The Equilibrium Wage in Ricardian Trade Model

(Asked by: username_0 on 2021-11-10)

I am learning the Ricardian trade model by reading [Eaton & Kortum 2012 JEP](https://www.aeaweb.org/articles?id=10.1257/jep.26.2.65). The equilibrium is easy to understand when there are finite goods, as shown in their Figure 1. [![enter image description here](https://i.sstatic.net/CDTQ1.png)](https://i.sstatic.net/CDTQ1.png)

However, they then introduce the Dornbusch, Fischer, Samuelson (1977) model with "a set of goods correspond to all the points on an interval between 0 and 1" and "defined a function $A(j)$ as the ratio of Portugal's labor requirements to England's labor requirements for good $j$ .. For any English wage $\omega$ between $A(0)$ and $A(1)$ there is some good, let's call it $\bar{j}$, satisfying $\mathrm{A}(\bar{j})=\omega$.".

They then state "To figure out what $\omega$ will break the chain, we need to look at the demand side. A higher $\bar{j}$ means that England is producing a larger share of goods, increasing demand for its labor and hence its wage $\omega$. Figure 2 depicts this positive relationship between $\omega$ and $\bar{j}$. Where it intersects the downward sloping $A(j)$ curve determines the equilibrium."

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

I fail to understand the "demand side" of the equilibrium wage determination. Where does this positive relationship between $\omega$ and $\bar{j}$ actually come from? And more generally I want to know how exactly the preferences of consumers and exogenous labor supply in two countries affect the equilibrium wage in this case?

**Update**: Yes footnote 2 shows under a strong symmetric CD preference same in all countries, this upward line can be written as the income of one country equals to the production fraction of the world income $\omega L=\bar{j}\left(\omega L+L^{\*}\right)$. I think this is not very intuitive in explaining a positive relationship between wage and $\bar{j}$. In particular, if we think $A$ is the (relative) labor demand curve, we need have a (relative) labor supply curve to find the equilibrium wage. This is the case in the Figure 1, where the relative labor supply curve is a vertical line given the fact that labor supply are exogenous. However, in Figure 2, it seems even though we assume full employment, $\bar{j}$ can still control the relative labor supply ratio. And how is the relative labor supply connected with the income without endogenous labor supply? This is the thing that I fail to get around with. And as the symmetric CD assumption is very strong, I want to see how in general cases the income-consumption equality forms a relative labor supply condition to obtain equilibrium wage and how different utility assumptions affect this equilibrium wage.

**Tags:** international-trade, competitive-equilibrium
> **Comments:**
> **username_1**: Have you checked out footnote 2?  

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## 1 answers

### Answer by username_1 on 2021-11-12. Score: 1

Hidden in the postulated positive relationship is an assumption about tastes. In footnote 2 the authors state this assumption: citizens of both countries evenly spread their expenditure over all goods.
In particular, this implies that the total expenditure (in real terms) on all goods produced in England is given by:

$$\bar{j} L^\* +\bar{j} \omega L$$

Since this is the share ($\bar{j}$) spent on England produced goods ($0) of Portuguese income and English income.

Next, English income is naturally equal to the expenditure on England produced goods. But the English income also equals $\omega L$, which is the labor income of English citizens. This gives us

$$\omega L=\bar{j}(L^\*+\omega L)$$

I challenge you to rewrite this into the expression in the figure.

> **Comments:**
> **username_0**: Thanks for your answer. I update my question to clarify my question.  
> **username_0**: To be honest, I have already figured out the logics of the positive relationship while updating my question. But I think it might be better if you can make the answer more explicit here rather than I write another answer to answer myself.  

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