21.10 Advertising Models
Three types of advertising:
- Informative Advertising: increase overall demand of your brand
- Persuasive Advertising: demand shifting to your brand
- Comparison: demand shifting away from your competitor (include complementary)
n customers distributed uniformly along the Hotelling’s line (more likely for mature market where demand doesn’t change).
\[ U_A = V - p_A - tx \\ U_B = V - p_B - t(1-x) \]
For Persuasive advertising (highlight the value of the product to the consumer):
\[ U_A = A_A V - p_A - tx \]
or increase value (i.e., reservation price).
\[ U_A = \sqrt{Ad_A} V - p_A - tx \]
or more and more customers want the product (i.e., more customers think firm A product closer to what they want)
\[ U_A = V - p_A - \frac{tx}{\sqrt{Ad_A}} \]
Comparison Advertising:
\[ U_A = V - p_A - t\sqrt{Ad_{B}}x \\ U_B = V - p_B - t \sqrt{Ad_A}(1 - x) \]
Find marginal consumers
\[ V - p_A - t\sqrt{Ad_{B}}x = V - p_B - t \sqrt{Ad_A}(1 - x) \]
\[ x = \frac{1}{t \sqrt{Ad_A} + t \sqrt{Ad_B}} (-p_A + p_B + t \sqrt{Ad_A}) \]
then profit functions are (make sure the profit function is concave)
\[ \pi_A = p_A x n - \phi Ad_A \\ \pi_B = p_B (1-x) n - \phi Ad_B \]
where
\(\phi\) = per unit cost of advertising (e.g., TV advertising vs. online advertising in this case, TV advertising per unit cost is likely to be higher than online advertising per unit cost)
t can also be thought of as return on advertising (traditional Hotelling’s model considers t as transportation cost)
Equilibrium prices conditioned on advertising
\[ \frac{d \pi_A}{p_A} = - \frac{d}{p_A} () \\ \frac{d \pi_B}{p_B} = \frac{d}{p_B} \]
Then optimal pricing solutions are
\[ p_A = \frac{2}{3} t \sqrt{Ad_A} + \frac{1}{3} t \sqrt{Ad_B} \\ p_B = \frac{1}{3} t \sqrt{Ad_A} + \frac{2}{3} t \sqrt{Ad_B} \]
Prices increase with the intensities of advertising (if you invest more in advertising, then you charge higher prices). Each firm price is directly proportional to their advertising, and you will charger higher price when your competitor advertise as well.
Then, optimal advertising (with the optimal prices) is
\[ \frac{d \pi_A}{d Ad_A} \\ \frac{d \pi_B}{d Ad_B} \]
Hence, Competitive equilibrium is
\[ Ad_A = \frac{25 t^2 n^2}{576 \phi^2} \\ Ad_B = \frac{25t^2 n^2}{576 \phi^2} \\ p_A = p_B = \frac{5 t^2 n }{24 \phi} \]
As cost of advertising (\(\phi\)), firms spend less on advertising
Higher level of return on advertising (\(t\)), firms benefit more from advertising
With advertising in the market, the equilibrium prices are higher than if there were no advertising.
Since colluding on prices are forbidden, and colluding on advertising is hard to notice, firms could potential collude on advertising (e.g., pulsing).
Assumption:
- Advertising decision before pricing decision (reasonable because pricing is earlier to change, while advertising investment is determined at the beginning of each period).
Collusive equilibrium (instead of using \(Ad_A, Ad_B\), use \(Ad\) - set both advertising investment equal):
\[ Ad_A = Ad_B = \frac{t^2 n^2}{16 \phi^2} > \frac{25t^2 n^2}{576 \phi^2} \]
Hence, collusion can be make advertising investment equilibrium higher, which makes firms charge higher prices, and customers will be worse off. (more reference Aluf and Shy - check Modeling Seminar Folder - Advertising).
Combine both Comparison and Persuasive Advertising
\[ U_A = V - p_A - tx \frac{\sqrt{Ad_B}}{\sqrt{Ad_A}} \\ U_B = V - p_B - t(1-x) \frac{\sqrt{Ad_A}}{\sqrt{Ad_B}} \]
Informative Advertising
- Increase number of n customers (more likely for new products where the number of potential customers can change)
How do we think about customers, how much to consume. People consume more when they have more availability, and less when they have less in stock (Ailawadi and Neslin 1998)
Villas-Boas (1993)
- Under monopoly, firms would be better off to pulse (i.e., alternate advertising between a minimum level and efficient amount of advertising) because of the S-shaped of the advertising response function.
Model assumptions:
- The curve of the advertising response function is S-shaped
- Markov strategies: what firms do in this period depends on what might affect profits today or in the future (independent of the history)
Propositions:
- “If the loss from lowering the consideration level is larger than the efficient advertising expenditures, the unique Markov perfect equilibrium is for firms to advertise, whatever the consideration levels of both firms are.”
Nelson (1974)
Quality of a brand is determined before a purchase of a brand is “search qualities”
Quality that is not determined before a purchase is “experience qualities”
Brand risks credibility if it advertises misleading information, and pays the costs of processing nonbuying customers
There is a reverse association between quality produced and utility adjusted price
Firms that want to sell more advertise more
Firms advertise to their appropriate audience, i.e., “those whose tastes are best served by a given brand are those most likely to see an advertisement for that brand” (p. 734).
Advertising for experience qualities is indirect information while advertising for search qualities is direct information . (p. 734).
Goods are classified based on quality variation (i.e., whether the quality variation was based on searhc of experience).
3 types of goods
experience durable
experience nondurable
search goods
Experience goods are advertised more than search goods because advertisers increase sales via increasing the reputability of the sellers.
The marginal revenue of advertisement is greater for search goods than for experience goods (p. 745). Moreover, search goods will concentrate in newspapers and magazines while experience goods are seen on other media.
For experience goods, WOM is better source of info than advertising (p. 747).
Frequency of purchase moderates the differential effect of WOM and advertising (e.g., for low frequency purchases, we prefer WOM) (p. 747).
When laws are moderately enforced, deceptive advertising will happen (too little law, people would not trust, too much enforcement, advertisers aren’t incentivized to deceive, but moderate amount can cause consumers to believe, and advertisers to cheat) (p. 749). And usually experience goods have more deceptive advertising (because laws are concentrated here).
Iyer, Soberman, and Villas-Boas (2005)
Firms advertise to their targeted market (those who have a strong preference for their products) than competitor loyalists, which endogenously increase differentiation in the market, and increases equilibrium profits
Targeted advertising is more valuable than target pricing. Target advertising leads to higher profits regardless whether firms have target pricing. Target pricing increased competition for comparison shoppers (no improvement in equilibrium profits). (p. 462 - 463).
Comparison shoppers size:
\[ s = 1 - 2h \]
where \(h\) is the market size of each firm’s consumers (those who prefer to buy product from that firm). Hence, \(h\) also represents the differentiation between the two firms
See table 1 (p. 469).
\(A\) is the cost for advertising the entire market
\(r\) is the reservation price
Yuxin Chen et al. (2009)
Combative vs. constructive advertising
Informative complementary and persuasive advertising
Informative: increase awareness, reduce search costs, increase product differentiation
Complementary (under comparison): increase utility by signaling social prestige
Persuasive: decrease price sensitivity (include combative)
Consumer response moderates the effect of combative adverting on price competition:
It decreases price competition
It increases price competition when (1) consumers preferences are biased (firms that advertise have their products favored by the consumers), (2) disfavor firms can’t advertise and only respond with price. because advertising war leads to a price war (when firms want to increase their own profitability while collective outcome is worse off).