<p>Yes, <span class="math-container">$IM$</span> increases in the equilibrium, but, no, <span class="math-container">$IM$</span> cannot increase more than <span class="math-container">$X$</span> does.</p>

<p>Logical explanation: "<span class="math-container">$\Delta X &lt; \Delta IM$</span> in the equilibrium" means that <span class="math-container">$A$</span>'s GNP <strong>decreases</strong>. When GNP decreases, we have <span class="math-container">$\Delta IM &lt; 0$</span> while <span class="math-container">$0 &lt; \Delta X$</span> so we can't have <span class="math-container">$\Delta X&lt;\Delta IM$</span>. Contradiction! We can never have <span class="math-container">$X-IM$</span> decreasing in the equilibrium.</p>

<p>Mathematical illustration: Consider the model <span class="math-container">$Y=C+I+G+X-IM$</span>, <span class="math-container">$C=a+bY$</span>, <span class="math-container">$IM=c+dY$</span>. Then the equilibrium is <span class="math-container">$Y = (a-c+I+G+X)/(1-b+d)$</span>. When <span class="math-container">$X$</span> increases by <span class="math-container">$\Delta X$</span>, <span class="math-container">$\Delta Y = \Delta X / (1-b+d)$</span> and <span class="math-container">$\Delta IM = d\Delta X / (1-b+d)$</span>. Thus,
<span class="math-container">$$\Delta X - \Delta IM = \left(1 - \frac{d}{1-b+d} \right) \Delta X = \left( \frac{1-b}{1-b+d} \right) \Delta X &gt; 0.$$</span></p>

CC BY-SA 4.0
2018-09-30T15:26:29.150Z
2018-09-30T15:26:29.150Z
chan1142
<p>Suppose we have a country <span class="math-container">$A$</span> with a fixed exchange rate regime.</p>

<p>Suppose that, suddenly, the foreign demand for <span class="math-container">$A$</span>'s made products rose up.</p>

<p>What will happen to <span class="math-container">$X-IM$</span>?</p>

<p>As far as I can tell <span class="math-container">$X$</span> grows and thus <span class="math-container">$GNP$</span> grows. Finally since <span class="math-container">$GNP$</span> grows and the exchange rate is fixed <span class="math-container">$IM$</span> grows. So, finally we can't say anything about <span class="math-container">$X-IM$</span>?</p>

<macroeconomics>
influence of growing foreign demand for local products on the net exports in a fixed exchange rate regime
Don Fanucci
# influence of growing foreign demand for local products on the net exports in a fixed exchange rate regime

(Asked by: username_0 on 2018-09-30)

Suppose we have a country $A$ with a fixed exchange rate regime.

Suppose that, suddenly, the foreign demand for $A$'s made products rose up.

What will happen to $X-IM$?

As far as I can tell $X$ grows and thus $GNP$ grows. Finally since $GNP$ grows and the exchange rate is fixed $IM$ grows. So, finally we can't say anything about $X-IM$?

**Tags:** macroeconomics


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## 1 answers

### Answer by username_1 on 2018-09-30. Score: 2 | Accepted answer

Yes, $IM$ increases in the equilibrium, but, no, $IM$ cannot increase more than $X$ does.

Logical explanation: "$\Delta X < \Delta IM$ in the equilibrium" means that $A$'s GNP **decreases**. When GNP decreases, we have $\Delta IM < 0$ while $0 < \Delta X$ so we can't have $\Delta X<\Delta IM$. Contradiction! We can never have $X-IM$ decreasing in the equilibrium.

Mathematical illustration: Consider the model $Y=C+I+G+X-IM$, $C=a+bY$, $IM=c+dY$. Then the equilibrium is $Y = (a-c+I+G+X)/(1-b+d)$. When $X$ increases by $\Delta X$, $\Delta Y = \Delta X / (1-b+d)$ and $\Delta IM = d\Delta X / (1-b+d)$. Thus,
$$\Delta X - \Delta IM = \left(1 - \frac{d}{1-b+d} \right) \Delta X = \left( \frac{1-b}{1-b+d} \right) \Delta X > 0.$$


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