Microeconomics Tax incident: unit tax imposed to consumer or producer

Question

I come up with a thought that if there is any difference in term of imposing a tax to consumer or producer, I searched for the answer and there is some logic messing up..

let Pd be the consumer price; and Ps be the producer price Suppose the Unit Tax imposes to consumer, so in equilibrium: Pd=Ps+t since the consumer now is paying extra t dollars than the producer receive.

On the other hand, Suppose the unit tax imposes to producer, so in equilibrium: Ps+t=Pd since the producer now is paying extra t than its originally pay

Now the question is, why two formulas are identical? So is there any difference impose unit tax in terms of consumer or producer? ...or I did something wrong with my logic?

Thanks!

Answer 1

The two formulas should be the same. If the consumer pays the tax, he pays Pd to the producer and t to the government, so as you say Ps=Pd+t. If the producer pays the tax, he collects Ps from the consumer and remits t to the government, giving Ps-t=Pd. Why should it be any different? The government is collecting t either way.