If an excise tax reduces economic surplus why does the government impose the tax?

To discourage the sale of certain goods known to be HARMFUL and HAZARDOUS to the people and environment. Government's also make some money from the imposed taxes.

Explanation: Excise taxes are legislated taxes which are imposed by Government to discourage the sale of certain substances or Product,Products such as TOBACCO, GASOLINE, ALCOHOL etc. This tax is often imposed within the Businesses within the country,the Government also sometimes makes money through this increased taxes,as the excise taxes are imposed on Businesses thy inturn increase the price of the goods affected.

u = 30

continuing your method

= +

subtract from both sides

= - thus

= -

= ⇒ u = 30