# Quantity supplied & demanded equation with tax

Here's the simple question I can't get my head around :(

QD= 120-P
QS= 2P-10
Tax= 25 euro per unit


How much does the government receive?

The government revenue is going to be 1500 euros. The tax shifts the supply or the demand curve vertically depending on wether the tax is charged to the consumer or the producer (turns out it doesn't really matter at the end you get the same government revenue).

Here you can find a graph representing the situation if the consumer is charged the tax.

https://www.desmos.com/calculator/8unflceczk The demand curve shifts from the $Q^{D}=120-P$ (red line) to $Q^{D,tax}=120-(P+25)$ (green line). The supply curve is unchanged (blue line).

The new equilibrium quantity is 60 (instead of 76.667 in the case with no tax), and the revenue is equal to the unit tax times the quantity $25\times60=1500$, which is equal to the area of the orange rectangle.

• thank you a lot, much love from the university of Amsterdam <3 – Hakan Bektas Jun 12 '18 at 17:35