Question

Question #2 (L02, LO3, LO7 For the sake of developing the optimal rate of advertising for a business firm, Dorfman-Steiner model has been developed. Set the objective function of the model? 1- Set the first-order conditions for the optimization? 2- 3- Discuss the main model results which are relevant guiding indicators of a business firm for its advertising spending based on the following main relations: (P-MC) E= E £E, = %AP A Ed PQ P %AA Managerial Economics 8e AND Business Strategy MICHAEL R. BAYE JEFFREY T. PRINCE

Answer 1

The objective tmctron the model is TCeAeCA, P- [aG) A fime maximi3e peafit Cumetin e(PA2 uartity uhih is Th ot s rofito P & A are ametin f4 P Pice. REP,A) A Renl of advertising. conditions tinst rder are - 2. The 1 P+ P a c 2a P uwi manipulate abone expaesson it in tuma elastici tyo dem baing le Q P P ed MC ed

&ed Mc is M C ed Magin a P cast & ed M C ed t P MC ed ed + Mc ed-ed = 1 MC P Ed P 1 Cp - M. C ed pinast second in wea Wse which is er dez Conditien A 2c 20-1 0 A

1/20 Cest CM Manginal |*Ne wil convert it inte dif eret a boenn ohere which is elastia ty Neaput to Advetsing reA ide introdue eA we Out put uith A MC./a 2 A A Q P.Q A 1-+ MC. eA. A total ravenue Call P R I MC. KA R P X eA. R eA P- Mc P A MC ReA R P T colro

Uaing O, ne kmow P- MC や2. n Sutstitute t CA A ed) A R. eA Pxa) ed whe A s A dueutising Aperding, Ri Reueue ea+ larti aty t demand with iespet to ddwectisng ed- euce elasticty o demand 313 T I

Two aspects of this result:

1. More elastic the demand curve, the lower will be advertising to sales ratio. For the extreme case where ed is infinite we can verify that A/R will be close to 0.

2. Greater the advertising elasticity, higher will be A/R ratio. That is, firms will spend more on advertising relative to Sales.