<p>There is nothing wrong with the formula.</p>
<p>According the textbook (McAfee Introduction to Economic Analysis pp 72) this is not tax on quantity supplied but ad valorem tax on supply. Hence;</p>
<p><span class="math-container">$$\underbrace{T}_{\text{total  tax revenue}}=\underbrace{t}_{\text{tax rate}}\underbrace{q^∗}_{\text{quantity sold}}\underbrace{c(q^∗)}_{\text{cost of one unit}}$$</span></p>
<p>This formulation makes perfect sense for ad valorem tax.</p>
<p>The total revenue government gets is the tax rate applied to the value of production times the number of products produced.</p>

CC BY-SA 4.0
2024-09-09T12:03:13.700Z
2024-09-09T12:03:13.700Z
1muflon1
<p>The authors state that the tax revenue is
<span class="math-container">$$T = tq^{*}c(q^{*})$$</span>
, where <span class="math-container">$t$</span> being the tax percentage, <span class="math-container">$c$</span> being the total cost function based on the quantity supplied <span class="math-container">$q^{*}$</span>.<br />
This is not quite right since the tax per unit should be <span class="math-container">$c'(q^{*})t$</span>, which is the product of marginal cost and the tax percentage.<br />
This formula comes from the book &quot;Introduction to economic analysis&quot; by <strong>Preston McAfee</strong> page 72. The formula for <span class="math-container">$c(q)$</span> is in page 18.</p>
<p>How is the authors' formula correct? I can't explain this!</p>

CC BY-SA 4.0
2024-09-09T15:33:29.230Z
On [page 72](https://my.uopeople.edu/pluginfile.php/57436/mod_book/chapter/37625/ECON1580RecommendedTextbook.pdf#page=72) the author does say: "To start, we will denote the **marginal cost** of the quantity $q$ by $c(q)$"
Herr K.
<microeconomics><mathematical-economics>
What is wrong with this tax revenue formula?
Duck Gia
# What is wrong with this tax revenue formula?

(Asked by: username_0 on 2024-09-09)

The authors state that the tax revenue is
$$T = tq^{\*}c(q^{\*})$$
, where $t$ being the tax percentage, $c$ being the total cost function based on the quantity supplied $q^{\*}$.  
This is not quite right since the tax per unit should be $c'(q^{\*})t$, which is the product of marginal cost and the tax percentage.  
This formula comes from the book "Introduction to economic analysis" by **Preston McAfee** page 72. The formula for $c(q)$ is in page 18.

How is the authors' formula correct? I can't explain this!

**Tags:** microeconomics, mathematical-economics
> **Comments:**
> **username_1**: On [page 72](https://my.uopeople.edu/pluginfile.php/57436/mod_book/chapter/37625/ECON1580RecommendedTextbook.pdf#page=72) the author does say: "To start, we will denote the **marginal cost** of the quantity $q$ by $c(q)$"  

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## 1 answers

### Answer by username_2 on 2024-09-09. Score: 2 | Accepted answer

There is nothing wrong with the formula.

According the textbook (McAfee Introduction to Economic Analysis pp 72) this is not tax on quantity supplied but ad valorem tax on supply. Hence;

$$\underbrace{T}\_{\text{total tax revenue}}=\underbrace{t}\_{\text{tax rate}}\underbrace{q^∗}\_{\text{quantity sold}}\underbrace{c(q^∗)}\_{\text{cost of one unit}}$$

This formulation makes perfect sense for ad valorem tax.

The total revenue government gets is the tax rate applied to the value of production times the number of products produced.


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