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A tax imposed on a good will affect the supply curve of that good, since it artificially increases the cost of manfacturing that good. Therefore, the supply curve will shift left. This will push the price up. We need to determine how much of that price increase will be felt by the consumer and how much will be "absorbed" by the supplier.
We can determine this by looking at the demand curve:
The burden of the tax depends overall on the elasticity of the demand curve. The more inelastic the demand curve, the more of the tax will be borne by the consumer.
This is intuitive; remember that an inelastic good is one which the consumer is largely indifferent to price changes - they will continue to purchase their chosen quantity of the good, despite price changes. A tax is a form of price change.
(Diagrams from Tutor2U)
The price increase is borne by consumers and the rest of the tax (the gap between the supply curves) is borne by the producer.
For an elastic good, i.e. a good with quite a flat demand curve, we can see that the resulting consumer price: P1 to P2 is much smaller than the tax. Thus, the producer has absorbed a lot of the tax. It's worth noting that the fall in demand is still quite large.
For an inelastic good, the consumer price change is much larger: P1-P2.