<p><strong>Model 1</strong>:</p>

<p>The tax rate $\tau$ which maximizes tax revenue equals $\frac{1}{1 + a\epsilon}$ where $\epsilon$ is the elasticity of how taxable income responds to changes in the tax rate across and $a$ is some parameter. See this paper: <a href="https://eml.berkeley.edu/~saez/saez-slemrod-giertzNBER09.pdf" rel="nofollow noreferrer">https://eml.berkeley.edu/~saez/saez-slemrod-giertzNBER09.pdf</a> (see page 6)</p>

<p>We can estimate $a$ to be about 1.5 and $\epsilon$ to be about 0.4 or less, hence the maximizing rate is about 60 % or more.</p>

<p><strong>Model 2:</strong></p>

<p>Tax revenue is $\tau Y(\tau)$ where $Y(\tau)$ is total production which depends on the tax rate. If we say that a 1 % increase in the tax rate leads to a 2.5 % decrease in total output, we get that $Y'(\tau) = -2.5Y(\tau)$. So, $Y(\tau) = Ce^{-2.5\tau}$. </p>

<p>So revenue is $\tau C e^{-2.5\tau}$. Maximizing this simple equation in $\tau$ gives a tax maximizing rate of 40 %.</p>

<hr>

<p>These two models give highly different results. Which one makes more "sense"? </p>

<p>Model 2 is simple to understand, but I have not read the paper which uses Model 1, it seems a bit advanced for me. </p>

CC BY-SA 3.0
2018-03-01T17:51:31.850Z
What context(s) are you considering? Model 1 seems to be based on micro-level household behavior, while Model 2 appears to be related to macro-level national income and tax variables.
Herr K.
CC BY-SA 3.0
2018-03-01T18:43:00.423Z
If the difference is due to the parameters, then question depends on those magic numbers too.  It seems $60\%=1.5\times 0.4$ and $40\% = \frac{1}{2.5}$
Henry
<taxation>
Which model produces the correct revenue-maximizing rate?
Makei
# Which model produces the correct revenue-maximizing rate?

(Asked by: username_0 on 2018-03-01)

**Model 1**:

The tax rate $\tau$ which maximizes tax revenue equals $\frac{1}{1 + a\epsilon}$ where $\epsilon$ is the elasticity of how taxable income responds to changes in the tax rate across and $a$ is some parameter. See this paper: <https://eml.berkeley.edu/~saez/saez-slemrod-giertzNBER09.pdf> (see page 6)

We can estimate $a$ to be about 1.5 and $\epsilon$ to be about 0.4 or less, hence the maximizing rate is about 60 % or more.

**Model 2:**

Tax revenue is $\tau Y(\tau)$ where $Y(\tau)$ is total production which depends on the tax rate. If we say that a 1 % increase in the tax rate leads to a 2.5 % decrease in total output, we get that $Y'(\tau) = -2.5Y(\tau)$. So, $Y(\tau) = Ce^{-2.5\tau}$.

So revenue is $\tau C e^{-2.5\tau}$. Maximizing this simple equation in $\tau$ gives a tax maximizing rate of 40 %.

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These two models give highly different results. Which one makes more "sense"?

Model 2 is simple to understand, but I have not read the paper which uses Model 1, it seems a bit advanced for me.

**Tags:** taxation
> **Comments:**
> **username_1**: What context(s) are you considering? Model 1 seems to be based on micro-level household behavior, while Model 2 appears to be related to macro-level national income and tax variables.  
> **username_2**: If the difference is due to the parameters, then question depends on those magic numbers too.  It seems $60\%=1.5\times 0.4$ and $40\% = \frac{1}{2.5}$  

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## 0 answers

