I have a small problem, I have a situation where we have a perfectly inelastic offer and a normal demand, then there is a tax that is paid by the supplier who supports the totality of the charges ? Is it not the buyer ? Since the supplier can just lower his production ? I need some explanation om this thanks and sorry for my bad english.
If "supply is perfectly inelastic" it cannot be the case that the supplier can "just lower his production". The point of "perfectly inelastic supply", is exactly to represent the case, where the supplier will offer a specific quantity at whatever price, even zero. The classic case here is a good that is it deteriorates quickly in terms of quality or even consumption safety (say fresh foods).
The equilibrium price is then determined by demand. If the state appears and wants to take a chunk out of the price by imposing a tax, the tax will fully burden the supplier.
Of course this is the static approach. In a dynamic setting, such a situation may for example create incentives for an unofficial market, where the supplier tries to hide sales from the state in order to reduce the tax burden.