《工业组织》（英文版）Advertising and price elasticity （dorfman-Steiner result Demand function

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

Extending the Dorfman-Steiner Result: Conjectural Variations For 'small numbers, oligopoly firms have to make their decisions taking into account their rivals' reactions (mutual interdependence ) So the demand facing an individual firm is of the form: q= q(p,A,A) where Ar refers to the average advertising of the firms rivals. The effect aa can not be neglected. It measures the extend to which I conjecture my advertising to affect that of other firms Profits are thus I =p q(p,A,A)-C[q(p,A,A)J-A The firm maximises with respect to her own advertising, which leads to the F,0.C 歌p歌-如歌“欲“(-)款-1=0 (p-MC) (12) Multiplying the above by A/q p)(a合a全÷)-A 可 =m>0 elasticity of demand w.r.t. own advertising. m< 0 elasticity of demand w.r.t. the firms rivals advertising aA elasticity of the firm's rivals advertising w.r.t. the frm’ s own advertising So(12)becomes (p-MC)(n,+ n dividing both sides by p 二 A Here, advertising is an instrument of oligopolistic competition. We expect that when n, is negative and in absolute terms large (small numbers oligopoly), and interdependence in adverstising is high (a large n. then advertising/sales ratio will be small