Assume that the price received is given by P_S and the price paid is P_D = P_S(1 + t), where t is the ad valorem tax rate (e.g. with tax rate of 5%, t = 0.05, the price paid by demanders is 1.05P_S). The supply function is given by Q_S = S(P_S) and the demand function by Q_D = D(P_D)

Show that for a small ad valorem tax t, dlnP_S/dt e_D/(e_S - e_D), and dlnP_D/dt e_S/(e_S - e_D), where e_S; e_D are the price elasticity of supply and demand.