<p>Implementing @dismalscience comment suggestion, the unit tax burdens the suppliers. So the demand schedule is not affected, only supply. How? Since the tax is fixed per unit sold (and not a percentage charge), then the slope of the supply curve should not change. Therefore what remains is an upwards shift, that will lead to increased equilibrium price-decreased equilibrium quantity. The algebra should lead one to</p>

<p><a href="https://i.sstatic.net/FZFex.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/FZFex.png" alt="enter image description here"></a></p>

<p>One could see this as a fixed shift in overall (not just production) <em>marginal</em> cost: the quantity has the same production marginal cost as before -but now "$2" is added as an obligation per unit, to cover the tax.</p>

CC BY-SA 3.0
2015-10-14T21:30:07.897Z
2015-10-14T21:30:07.897Z
Alecos Papadopoulos
<p>Suppose the supply of a good is given by the equation $Q_S = 360*P_S - 720$. And the demand for a good is given by $Q_D = 960 - 120*P_D$. The government decides to levy a tax of \$2 per unit on the good, to be paid by the seller.</p>

<p>And I must find the equilibrium quantity of the curves, after the \$2 tax has been taken into account for. I know the equilibrium quantity is 540 before the tax based on the following calculations:</p>

<ol>
<li>$Q_S=Q_D$</li>
<li>$360P-720 = 960-120P$</li>
<li>$480P = 1680$</li>
<li>$P = 3.5$</li>
<li>If we sub in 3.5 into both equations ($Q_S$ and $Q_D$) then we get 540.</li>
</ol>

<p>Therefore, the equilibrium quantity is 540 before taxes have been taken into account. However, I am unsure how to figure out the equilibrium quantity after the tax.</p>

<p>Does anyone know how to go about solving this issue?</p>

<p>All help is appreciated.</p>

CC BY-SA 3.0
2015-10-13T23:41:56.013Z
Hi! We prefer you type in the information from the pictures. There are several reasons for this. meta.economics.stackexchange.com/questions/1365/ Additionally, you should show what you've tried so far, otherwise this will be closed as a homework question with no effort shown.
dismalscience
CC BY-SA 3.0
2015-10-14T00:06:53.173Z
So how would you represent the tax in this system of equations? A \$2 per-unit tax is equivalent to the seller receiving 2 fewer dollars per unit, right? First, which equation should change? Second, how should that equation change?
dismalscience
CC BY-SA 3.0
2015-10-14T00:11:23.960Z
The supply equation (Qs) should change, I think. I have tried (360(1.5) - 720 = -180), since 3.5-2 = 1.5. But, I don't think that the new equilibrium quantity is a negative.
Kelsey
CC BY-SA 3.0
2015-10-14T00:19:21.517Z
Ah! I see your problem. You've written it as though the price will decrease by 2. Why should the price decrease by two? Perhaps instead the supplier will ask for a higher price to offset the tax, and the buyers will pay some of the increased price, resulting in a new price and quantity? Remember that the consequence of a tax is that the supplier is now receiving $2 less than the demander is paying. Consider inserting a new equation to reflect this: Ps=Pd-2, and rearrange the equations for the supply and demand curves so that you you're solving for price, rather than quantity.
dismalscience
<supply-and-demand><taxation><general-equilibrium>
How Do I Calculate the After-Tax Equilibrium Quantity of a Supply and Demand Graph?
Kelsey
# How Do I Calculate the After-Tax Equilibrium Quantity of a Supply and Demand Graph?

(Asked by: username_0 on 2015-10-13)

Suppose the supply of a good is given by the equation $Q\_S = 360\*P\_S - 720$. And the demand for a good is given by $Q\_D = 960 - 120\*P\_D$. The government decides to levy a tax of \$2 per unit on the good, to be paid by the seller.

And I must find the equilibrium quantity of the curves, after the \$2 tax has been taken into account for. I know the equilibrium quantity is 540 before the tax based on the following calculations:

1. $Q\_S=Q\_D$
2. $360P-720 = 960-120P$
3. $480P = 1680$
4. $P = 3.5$
5. If we sub in 3.5 into both equations ($Q\_S$ and $Q\_D$) then we get 540.

Therefore, the equilibrium quantity is 540 before taxes have been taken into account. However, I am unsure how to figure out the equilibrium quantity after the tax.

Does anyone know how to go about solving this issue?

All help is appreciated.

**Tags:** supply-and-demand, taxation, general-equilibrium
> **Comments:**
> **username_1**: Hi! We prefer you type in the information from the pictures. There are several reasons for this. meta.economics.stackexchange.com/questions/1365/ Additionally, you should show what you've tried so far, otherwise this will be closed as a homework question with no effort shown.  
> **username_1**: So how would you represent the tax in this system of equations? A \$2 per-unit tax is equivalent to the seller receiving 2 fewer dollars per unit, right? First, which equation should change? Second, how should that equation change?  
> **username_0**: The supply equation (Qs) should change, I think. I have tried (360(1.5) - 720 = -180), since 3.5-2 = 1.5. But, I don't think that the new equilibrium quantity is a negative.  
> **username_1**: Ah! I see your problem. You've written it as though the price will decrease by 2. Why should the price decrease by two? Perhaps instead the supplier will ask for a higher price to offset the tax, and the buyers will pay some of the increased price, resulting in a new price and quantity? Remember that the consequence of a tax is that the supplier is now receiving $2 less than the demander is paying. Consider inserting a new equation to reflect this: Ps=Pd-2, and rearrange the equations for the supply and demand curves so that you you're solving for price, rather than quantity.  

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## 1 answers

### Answer by username_2 on 2015-10-14. Score: 2 | Accepted answer

Implementing @dismalscience comment suggestion, the unit tax burdens the suppliers. So the demand schedule is not affected, only supply. How? Since the tax is fixed per unit sold (and not a percentage charge), then the slope of the supply curve should not change. Therefore what remains is an upwards shift, that will lead to increased equilibrium price-decreased equilibrium quantity. The algebra should lead one to

[![enter image description here](https://i.sstatic.net/FZFex.png)](https://i.sstatic.net/FZFex.png)

One could see this as a fixed shift in overall (not just production) *marginal* cost: the quantity has the same production marginal cost as before -but now "$2" is added as an obligation per unit, to cover the tax.


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