Advertising and price elasticity ( dorfman-Steiner result Demand function q(p, A) c(q): cost function A: advertising expenditure Profit function I=pq(p,A)-clq(p, A)]-A (1) Two choice variables: the price p and a dC.ag=0(2〕 an aap aa-da aa-aa=0 (3) Take (3),multiply by A/q and rearrange P款令“出合(4) advertising expenditure ., the elasticity of demand with respect to note that dc So (4)becomes divide both sides by p note that pq =r (revenue PPMA (7) Take (2), multiply by p/q dqp p dc aq dq ap Note that the price elasticity of demand -n)+p-Mc(-n)=0(9) Substituting (11)into (7) So the firms's optimal level of advertising intensity (A/R) is equal to the ratio of its advertising elasticity 'of demand to the price elasticity of demand it faces. The important implication of this demonstration is that the level of advertising is chosen simul taneously with the level of price there is no cause and effect relationship between these two variables 1