<p>When solving this problem, it is important to notice that whenever you have a tax, there will be a difference between the price that the buyers pay and the price that the sellers will receive.</p>
<p>Let <span class="math-container">$p_D$</span> be the price that the buyers pay and let <span class="math-container">$p_S$</span> be the price that the sellers receive.</p>
<p>The price <span class="math-container">$p_D$</span> is the one that is relevant for the buyers, so it should enter the demand function, <span class="math-container">$D(p_D)$</span>.</p>
<p>The selling price <span class="math-container">$p_S$</span> is the only price that is relevant for the sellers, so it is the price that should enter the supply function, <span class="math-container">$S(p_S)$</span>.</p>
<p>At the moment you have two equations in three unknowns, the amount sold (or bought) <span class="math-container">$q$</span>, the price <span class="math-container">$p_D$</span> and the price <span class="math-container">$p_S$</span>. So you need an additional equation to solve the model.</p>
<p>The additional equation links the two prices <span class="math-container">$p_S$</span> and <span class="math-container">$p_D$</span>. In particular, the difference between the two prices is given by the tax. If the seller receives <span class="math-container">$p_S$</span> then the buyer pays <span class="math-container">$p_D = (1+t)p_S$</span>.</p>

CC BY-SA 4.0
2021-10-07T14:54:45.483Z
2021-10-07T14:54:45.483Z
tdm
<p>For Example:</p>
<p><span class="math-container">$D(p) = 50 - p$</span></p>
<p><span class="math-container">$S(p) = p/20$</span></p>
<p>The p* of this problem is <span class="math-container">$47.61$</span>, however, when I add a .1 proportional tax I get an answer of <span class="math-container">$43.29$</span> which does not make sense because that price is lower than the previous equilibrium price.</p>
<p>I am using the equations:</p>
<p><span class="math-container">$D(p) = 50 - (p + .1p) = (p + .1p)/20 = S(p)$</span></p>
<p>Am I dividing wrong? I suspect that I am getting a percentage change that is correct, it is just negative instead of positive. Any help would be appreciated.</p>

CC BY-SA 4.0
2021-10-06T22:19:14.487Z
Hint: Consider that the tax is only paid by buyers. Sellers don't receive any additional revenue from the proportional tax.
RegressForward
<microeconomics><demand><taxation><equilibrium>
When solving for a new equilibrium price after the institution of a tax, I keep getting a price that is lower than my previous equil price. Why?
maverick1054
# When solving for a new equilibrium price after the institution of a tax, I keep getting a price that is lower than my previous equil price. Why?

(Asked by: username_0 on 2021-10-06)

For Example:

$D(p) = 50 - p$

$S(p) = p/20$

The p\* of this problem is $47.61$, however, when I add a .1 proportional tax I get an answer of $43.29$ which does not make sense because that price is lower than the previous equilibrium price.

I am using the equations:

$D(p) = 50 - (p + .1p) = (p + .1p)/20 = S(p)$

Am I dividing wrong? I suspect that I am getting a percentage change that is correct, it is just negative instead of positive. Any help would be appreciated.

**Tags:** microeconomics, demand, taxation, equilibrium
> **Comments:**
> **username_1**: Hint: Consider that the tax is only paid by buyers. Sellers don't receive any additional revenue from the proportional tax.  

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## 1 answers

### Answer by username_2 on 2021-10-07. Score: 2

When solving this problem, it is important to notice that whenever you have a tax, there will be a difference between the price that the buyers pay and the price that the sellers will receive.

Let $p\_D$ be the price that the buyers pay and let $p\_S$ be the price that the sellers receive.

The price $p\_D$ is the one that is relevant for the buyers, so it should enter the demand function, $D(p\_D)$.

The selling price $p\_S$ is the only price that is relevant for the sellers, so it is the price that should enter the supply function, $S(p\_S)$.

At the moment you have two equations in three unknowns, the amount sold (or bought) $q$, the price $p\_D$ and the price $p\_S$. So you need an additional equation to solve the model.

The additional equation links the two prices $p\_S$ and $p\_D$. In particular, the difference between the two prices is given by the tax. If the seller receives $p\_S$ then the buyer pays $p\_D = (1+t)p\_S$.


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