Persuasive advertising Equating equations(11.5)with(11. 7) yields M BAcA-p,+T PQM, where Q=Q(M). (11.8 Equation (11. 8)is known as the Dorfman-Steiner(1954)condition. Therefore Proposition 11.7 A monopoly's profit-maximizing advertising and price levels should be set so that the ratio of advertising expenditure to revenue equals the(absolute value of the) ratio of the advertising elasticity to price elasticity. Formally Thus, a monopoly would increase its advertising-to-sales ratio as the demand becomes more elastic with respect to the advertising(eA is close to 1), or less elastic with respect to price(pl is close to zero
Persuasive Advertising
Persuasive advertising 11. 1. 2 Too much or too little persuasive advertising? Persuasive advertising was defined as a method of information transmission that boosts the demand for the advertised product. Thus, persuasive advertising makes the good attractive to consumers and therefore has the potential to increase welfare. This does not imply that persuasive advertising must be truthful. All that persuasive advertising does is to provide an image for the product that would induce the consumer to purchase the product in order to identify with the message or people portrayed in the ads Dixit and Norman(1978) have proposed an extremely simple method for evaluating the welfare effect of persuasive advertising. Consider a simplified version of the demand function(11. 1)where B=64, EA=0.5, and ep=-2. For this case, we assume that 8a1 1/2 (119) Taking the unit production cost to equal c= 1, the monopolist chooses p and aM to maximize r(A,p)=pQ-1Q-A=64A/2p-1-64A4/p-2-A.(1.10)
Persuasive Advertising
Persuasive advertising The first-order condition with respect to p is given by 0 ar(A,p)-64√A,128VA p (111) implying that p 16VA. Since the demand function has a constant elasticity the monopoly price is independent of the level of advertising. The first-order condition with respect to a is given by 0 8(A, p) 6 64 8A 2vAp 2vAp2 Implying that AM=64 and hence Q=16 64=128 In order to check whether the monopoly advertises at the socially optimal level we first need to calculate the consumer surplus associated with each advertising level. The shaded area in Figure 11. 1 shows the consumer surplus associated with a given advertising level a and the monopoly price pM=2. Hence, for a given advertising level A, the consumer surplus is given by 16VA CS(A)= dQ-2x16VA (1113) 2×8VAQ 32VA=32VA
Persuasive Advertising
Persuasive advertising 2 16A igure I1.1 F1 Consumer surplus for a given persuasive-advertising level Assuming a monopoly price of p-2, the firms profit level as a function of the level of advertising is given by r(A,2)=2Q(4)-Q(4)-A=32A-16A-A=16A-A.(1140
Persuasive Advertising
Persuasive advertising The social planner takes the monopoly price p-2 as given and chooses an advertising level Ato maxW(A)=CS(A)+*(A, 2)=48VA-A (1115) The first-order condition is given b 0=o(4) 1.1 aA Hence the socially optimal advertising level is A*=242>64=A. Notice that this social optimum is not a"first-best"optimum, since a first-best optimum requires marginal cost pricing. Hence Proposition 11.2 Given a monopoly market structure, the equilibrium level of persuasive advertising is below the socially optimal level
Persuasive Advertising