<p>I apologise for the poor formatting and such, this is one of my first posts so please let me know if anything needs improvement (including, possibly, the correctness of my answer!).</p>

<p>For part a.), I'm assuming that a per unit tax of $2q$ is levied on the consumer in this market. The inverse demand function and inverse supply function are given by $p = \frac{393}{2} - \frac{q}{2}$ and $p = 4q + 48$ respectively. Thus, a per unit tax of $T = 2q$ will result in the inverse demand function being $p + 2q = \frac{393}{2} - \frac{q}{2} \iff p = \frac{393}{2} - \frac{5q}{2}$. Equating supply and demand, we find that the new equilibrium quantity is $q = 22.846$, the price that consumers pay is $185.077$ and the price producers receive is $139.385$.</p>

<p>For part b.), I'm assuming that a tax of $20$% of revenue is levied on the producer in this market. The inverse demand function and inverse supply function are given by $p = \frac{393}{2} - \frac{q}{2}$ and $p = 4q + 48$ respectively. Thus, a tax of $20$% of revenue will result in the inverse supply function being $p - 0.2p = 4q + 48 \iff p = 5q + 60$. Equating supply and demand, we find that the new equilibrium quantity is $q = 18.2$, the price that consumers pay is $187.4$ and the price producers receive is $120.8$.</p>

<p>I hope this makes sense (and is correct)! Feedback would be great!</p>

CC BY-SA 3.0
2016-01-10T04:38:06.107Z
2016-01-10T04:38:06.107Z
user6834
<p>Given that demand for a good X is equal to $q_D=393-2p$ and market supply is $q_S=p/4-12$. Find equilibrium price and quantity, consumer and producer surplus and draw a diagram illustrating the situation. Given that:</p>

<p>a) $T=2q$, every single item sold is taxed.</p>

<p>b) $T=20\% TR$ total revenue is taxed</p>

<p>Obviously i have calculated the equilibrium price and quantity before taxation that is $p=180,q=33$.But i have no idea how to caculate those two values after taxation.</p>

CC BY-SA 3.0
2016-01-10T17:29:34.700Z
Please refer to the site's policy on homework and homework-like questions : http://meta.economics.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions. In particular, see http://meta.economics.stackexchange.com/questions/1458/announcement-new-policy-on-homework-questions on questions with numbers.
Martin Van der Linden
CC BY-SA 3.0
2016-01-13T06:24:50.370Z
Hint: think about how taxes change the demand/supply equations.
Herr K.
<microeconomics><mathematical-economics><government>
Government's intervention question
mkropkowski
# Government's intervention question

(Asked by: username_0 on 2016-01-09)

Given that demand for a good X is equal to $q\_D=393-2p$ and market supply is $q\_S=p/4-12$. Find equilibrium price and quantity, consumer and producer surplus and draw a diagram illustrating the situation. Given that:

a) $T=2q$, every single item sold is taxed.

b) $T=20\% TR$ total revenue is taxed

Obviously i have calculated the equilibrium price and quantity before taxation that is $p=180,q=33$.But i have no idea how to caculate those two values after taxation.

**Tags:** microeconomics, mathematical-economics, government

> **Comments:**
> **username_1**: Please refer to the site's policy on homework and homework-like questions : http://meta.economics.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions. In particular, see http://meta.economics.stackexchange.com/questions/1458/announcement-new-policy-on-homework-questions on questions with numbers.  
> **username_2**: Hint: think about how taxes change the demand/supply equations.  

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## 1 answers

### Answer by username_3 on 2016-01-10. Score: 1 | Accepted answer

I apologise for the poor formatting and such, this is one of my first posts so please let me know if anything needs improvement (including, possibly, the correctness of my answer!).

For part a.), I'm assuming that a per unit tax of $2q$ is levied on the consumer in this market. The inverse demand function and inverse supply function are given by $p = \frac{393}{2} - \frac{q}{2}$ and $p = 4q + 48$ respectively. Thus, a per unit tax of $T = 2q$ will result in the inverse demand function being $p + 2q = \frac{393}{2} - \frac{q}{2} \iff p = \frac{393}{2} - \frac{5q}{2}$. Equating supply and demand, we find that the new equilibrium quantity is $q = 22.846$, the price that consumers pay is $185.077$ and the price producers receive is $139.385$.

For part b.), I'm assuming that a tax of $20$% of revenue is levied on the producer in this market. The inverse demand function and inverse supply function are given by $p = \frac{393}{2} - \frac{q}{2}$ and $p = 4q + 48$ respectively. Thus, a tax of $20$% of revenue will result in the inverse supply function being $p - 0.2p = 4q + 48 \iff p = 5q + 60$. Equating supply and demand, we find that the new equilibrium quantity is $q = 18.2$, the price that consumers pay is $187.4$ and the price producers receive is $120.8$.

I hope this makes sense (and is correct)! Feedback would be great!


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