Effects of Taxes on Sale of Goods:

An important application of our theory is to tax incidence, i.e., how the burden of a tax on goods is shared by producers and consumers. We will see that this depends on the relative sizes of the price elasticity’s of supply and demand.

A specific tax is a tax expressed in absolute amounts of money per unit of goods sold (or bought), for example a tax on a bottle of beer may be τ = 1kr. An ad valorem tax is a tax expressed as a fraction, α, (or percentage) of the price, the value added tax is such a tax. If the price (including the tax) that consumer’s pay is p, the price that suppliers receive is: ps=(1 − α).p, the tax revenue, per unit sold, is therefore T = α . p. In the case of a specific tax the price that suppliers receive is ps = p − τ.

Any tax, whether specific or ad valorem, is determined by a political authority (democratic or autocratic as the case may be) and can therefore be considered to be exogenous, or an environmental variable which cannot be controlled by either side of the market. In practice taxes are paid by suppliers (because this is much more efficient than if consumers were required to pay them), and we can therefore think of taxes as a factor which shifts down the supply curve, or shifts up the inverse supply curve. From the suppliers point of view it is just another cost of supplying a good, a fee that must be paid to the tax authority. Returning to our old supply function for a liter of beer, we now write it as:

Q^S = 20 + 3p − τ

The inverse supply curve now becomes,

Hence, the slope of the supply curve is the same, but it has shifted up by the (specific) tax.

If the specific beer tax is τ = 2kr, the direct supply curve will shift down to Q′^S = 18+3. p, and we have already solved such a case and found that the price increases to p′ = 10.4 (and quantity demanded decreases to Q′^D = 49.2. The price that beer suppliers receive is p′^s = 8.4 and tax revenue is T = 49.2 x 2 = 98.4

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