Suppose an ad valorem (or value tax) 0 (in units of a numeraire) is imposed on good . Denote the price the seller gets after tax as . Therefore, the price the consumer pays after tax is (1 + ) Let () and () denote the aggregate demand and supply functions of the good respectively. () is continuous and non-increasing at all at all > 0 and is strictly decreasing at any < max (0) where ( ) is the marginal utility of consumer at good 's quantity level . () is continuous and non-decreasing at all at all > 0 and is strictly increasing at any > min (0) where () is the marginal cost of firm at good 's quantity level . Also assume max (0) > min (0) and () and () are differentiable. i) Find the effect of the tax on market price i.e. () ( denotes the equilibrium price). [3 points]. ii) Prove that when the aggregate supply is perfectly inelastic () = 1+