<p>Let's say there are only two countries in the entire world, Argentina and Chile, and there is free trade between them. The aggregated investments in both countries are <span class="math-container">$I^A$</span> and <span class="math-container">$I^C$</span> that are both exogenous variables. The saving is giving by
<span class="math-container">$S^A = A+ar$</span> where A,a&gt; for Argentina and for Chile it is given by S^C that is an exogenous variable. I have to find the equilibrium interest rate.
My TA said it is the one that equates the total savings and the total investments in both countries.
<span class="math-container">$$S^A+S^C = I^A + I^C$$</span>
<span class="math-container">$$A+ar+S^C = I^A + I^C$$</span>
Solving for r we get
<span class="math-container">$$r = \frac{I^A+I^C-A-S^C}{a}$$</span>
But my TA said this was wrong. What am I missing here?</p>

CC BY-SA 4.0
2024-01-12T13:42:20.377Z
In your final equation for r, it looks like you've divided by A rather than a. Could this be the error?
Jamie Smith
CC BY-SA 4.0
2024-01-12T14:27:56.873Z
Of course! That must have been it, because I can't see any other error.
Ari Samueli
CC BY-SA 4.0
2024-01-12T17:27:41.137Z
what assumptions you can make about I, I^C and S^C? are they exogenous?
WilliamT
<macroeconomics><mathematical-economics><gdp><interest-rate>
Finding the equilibrium interest rate
Ari Samueli
# Finding the equilibrium interest rate

(Asked by: username_0 on 2024-01-12)

Let's say there are only two countries in the entire world, Argentina and Chile, and there is free trade between them. The aggregated investments in both countries are $I^A$ and $I^C$ that are both exogenous variables. The saving is giving by
$S^A = A+ar$ where A,a> for Argentina and for Chile it is given by S^C that is an exogenous variable. I have to find the equilibrium interest rate.
My TA said it is the one that equates the total savings and the total investments in both countries.
$$S^A+S^C = I^A + I^C$$
$$A+ar+S^C = I^A + I^C$$
Solving for r we get
$$r = \frac{I^A+I^C-A-S^C}{a}$$
But my TA said this was wrong. What am I missing here?

**Tags:** macroeconomics, mathematical-economics, gdp, interest-rate

> **Comments:**
> **username_1**: In your final equation for r, it looks like you've divided by A rather than a. Could this be the error?  
> **username_0**: Of course! That must have been it, because I can't see any other error.  
> **username_2**: what assumptions you can make about I, I^C and S^C? are they exogenous?  

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## 0 answers

