Could you explain the distribution of the incidence of a tax and why it may fall differently on consumers and producers?

Firstly it would be useful to define terms and state that the majority of the time the tax in question will be a tax on a good or service for example the tax on cigarettes (tobacco). The reason that this question can even be asked is because the tax is actually, in technical terms, on the seller who is faced with a choice. The seller can either pay the tax himself and not raise the price of the goods, or can pass some (or in fact all) of the tax onto the consumers in the form of higher prices. This is referred to as the incidence of tax, which is the distribution of the tax burden between consumers and producers. 

The determining factor in determining the incidence of tax is the elasticity of demand for the good or service being taxed. If demand is elastic (at this point draw a graph) then the incidence of tax would not be placed to heavily on the consumer because there demand for the good is particularly responsive to price changes. Suppliers would stand to lose out overall if they raise the price of the good too much and they would be better off absorbing the cost. Conversely if the good or service demand is price inelastic (at this point also draw a graph), that is the price can be raised but people will still demand the good without much change, then the incidence of tax can fall more greatly on to the consumer.