Question

6. b. Use profit-maximization to mathematically derive the optimal advertising to sales ratio.

Answer 1

conditions of imperfect competition, both the producer and the traders are advertising to inform and influence or persuade consumers. The producer may, however, fix the price both to the traders and to consumers, and hence also the traders’ margin. Having this control the producer may be in a better position to pursue a co-ordinated marketing policy. The aim of this paper is to define the “optimal” marketing policy and compare it with the actual policy of the three largest firms (responsible for well above 70% of total sales) producing passenger cars in Australia. The traders’ sales promotion efforts in the industry under consideration increase with the value of the margin. This paper aims to find out whether higher margins increase traders’ efforts (partly because the higher remuneration attracts more efficient people) or merely lead *I am grateful to Garnsey Clemenger Pty. Ltd., Marketing and Consultants, Brisbane and to all firms which cooperated in supplying the data required for this study. I am also indebted to my colleagues: A. Andersen, H. Higgs, H.U. Tamaschke and G. West for their valuable comments. to the establishment of a number of new firms and hence higher distribution costs. The question, therefore, is whether the producer intensifies his advertising campaigns or increases the value of the mark-up to the traders. The following model is used to derive an optimal mark-up/advertising coefficient. Let: V= v = P= X= W= Y’ k= the cost of the producer’s advertising campaigns directed at consumers advertising costs as a fraction of total revenue price to consumers quantity demanded the cost of the trader’s advertising campaigns directed at consumers price to trader (or agent) trader’s margin (mark up) as a percentage of the price paid by consumers We have: v = vpx k = (P-Y)/P Let the demand function be x = x(p,v,W) and the producer’s profit 7r = p(1 -k-1,)x-c (1) (2) (3) (4)