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fix(post): fix folding

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Barrett Ruth 2024-06-26 22:43:25 -05:00
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posts/economics/models-of-production.html
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@ -211,50 +211,61 @@
\bar{A}^\frac{1}{1-\alpha}(\frac{\bar{s}}{\bar{d}})^\frac{\alpha}{1-\alpha})\]
</p>
</div>
<div class="fold"><h3>analysis</h3></div>
<p>
Using both mathematical intuition and manipulating the visualization
above, we find that:
</p>
<ul style="list-style: unset">
<li>
\(\bar{A}\) has a positive relationship with steady-state output
</li>
<li>
Capital is influenced by workforce size, TFP, and savings rate
</li>
<li>
Capital output share's \(\alpha\) impact on output is twofold:
<ol>
<li>Directly through capital quantity</li>
<li>Indirectly through TFP</li>
</ol>
</li>
<li>
Large deviations in capital from steady-state \(K^*\) induce net
investments of larger magnitude, leading to an accelerated
reversion to the steady-state
</li>
</ul>
<p>
Lastly (and perhaps most importantly), exogenous parameters
\(\bar{s}, \bar{d}\), and \(\bar{A}\) all have immense ramifications
on economic status. For example, comparing the difference in country
\(C_1\)&apos;s output versus \(C_2\)&apos;s using the Solow Model,
we find that a difference in economic performance can only be
explained by these factors: \[
\frac{Y_1}{Y_2}=\frac{\bar{A_1}}{\bar{A_2}}(\frac{\bar{s_1}}{\bar{s_2}})^\frac{\alpha}{1-\alpha}
\]
</p>
<p>
We see that TFP is more important in explaining the differences in
per capital output
(\(\frac{1}{1-\alpha}>\frac{\alpha}{1-\alpha},\alpha\in[0,1)\)).
However, the Solow Model does not give any insight in to how to
alter what it considers to be the most important predictor of
output.
</p>
<div class="fold">
<h3>analysis</h3>
</div>
<div>
<p>
Using both mathematical intuition and manipulating the
visualization above, we find that:
</p>
<ul style="list-style: unset">
<li>
\(\bar{A}\) has a positive relationship with steady-state output
</li>
<li>
Capital is influenced by workforce size, TFP, and savings rate
</li>
<li>
Capital output share's \(\alpha\) impact on output is twofold:
<ol>
<li>Directly through capital quantity</li>
<li>Indirectly through TFP</li>
</ol>
</li>
<li>
Large deviations in capital from steady-state \(K^*\) induce net
investments of larger magnitude, leading to an accelerated
reversion to the steady-state
</li>
<li>
Economies stagnate at the steady-state \((K^*,Y^*)\)&mdash;this
model provides no avenues for long-run growth.
</li>
</ul>
<p>
Lastly (and perhaps most importantly), exogenous parameters
\(\bar{s}, \bar{d}\), and \(\bar{A}\) all have immense
ramifications on economic status. For example, comparing the
difference in country \(C_1\)&apos;s output versus \(C_2\)&apos;s
using the Solow Model, we find that a difference in economic
performance can only be explained by these factors: \[
\frac{Y_1}{Y_2}=\frac{\bar{A_1}}{\bar{A_2}}(\frac{\bar{s_1}}{\bar{s_2}})^\frac{\alpha}{1-\alpha}
\]
</p>
<p>
We see that TFP is more important in explaining the differences in
per capital output
(\(\frac{1}{1-\alpha}>\frac{\alpha}{1-\alpha},\alpha\in[0,1)\)).
<!-- TODO: poor phrasing -->
Notably, the Solow Model does not give any insights into how to
alter the most important predictor of output, TFP.
</p>
</div>
<h2>romer</h2>
<!-- TODO: transition talking about "Romer model does, though" -->
<!-- TODO: say the romer model provides avenue for LR growth -->
<!-- TODO: dynamics?????? -->
<h2>romer-solow</h2>
</article>
</div>