1. Signaling unobservable quality choice through price and advertising: The case with competing firms
Speaker: Wu Fulan
3rd August,2009

2. Outline
Motivation
The model
Results
Conclusions

3. Motivation
Literature on price and/or advertising as signals of firms’ unobservable quality
Exogenous quality literature
Endogenous quality literature
Examples of exogenous quality literature
Kihlstom and Riordan (1984), Milgrom and Roberts (1986), and Bagwell and Roirdan (1991)
Examples of Endogenous quality literature
Klein and Leffler (1981), Sharpiro (1983), Wolinsky (1983), Riordan (1986), Bester (1998) and more recently Rasmussen (2008)
In and Wright (2009)

4. The monopoly model setup
There are four stages
In stage 1, each firm chooses its quality from
In stage 2, each firm chooses a price and an advertising expenditure
In stage 3, a representative consumer observes these choices but not the quality level and decides whether to buy from the firm or not
In stage 4, if the consumer buys, it observes the firm’s true quality, and with probability decides whether to repurchase or not

5. The monopoly model setup (continued)
is strictly concave, increasing
The firm and consumer discount the last period payoffs by
Consumers wishing to buy in a period, buy a single unit, receiving utility from the good of type t
The unit cost of production is for the good of type t
Assume

6. Reordering invariance refinement by In and Wright (2009)
Multiple perfect Bayesian equilibria for the game we consider
Equilibrium refinement “reordering invariance” in In and Wright (2009)
Reordered variant of the original game
This game shares the same reduced normal form as the original game.
A unique pure strategy subgame perfect Bayesian equilibrium

7. Analysis of the monopoly model
Assume
The minimum level of advertising is
A high quality equilibrium in which

8. The duopoly model setup
There are two firms that are maximally differentiated in the standard Hotelling fashion.
The timing here is the same as before, except now consumers choose one firm in stage 3 based on their location on the unit interval, and in stage 4 decide whether to repurchase
Stage 3 is divided into two sub stages: stage 3a and stage 3b
Suppose a measure 1 of consumers are uniformly distributed on the interval
Let a consumer located at on get an additional firm- specific utility of from firm 1 and from firm 2, where v measures competition intensity

9. The duopoly model setup (continued)
The bigger , the more intense is competition
This additional utility is obtained by shopping at firm i at stage 3a regardless of whether the consumer buys anything at firm i in stage 3b.
However, consumer can only shop at one firm and must buy from where they choose to shop
This specification ensures that the market will be covered, with all consumers buying from one and only one firm , but also at the same time avoiding the possibility that a firm can charge above vv and still make some sales.

10. The duopoly model setup (continued)
Thus if both firms charge a price at or below , all consumers will want to shop at one of the firms to get the added utility from shopping, and will just be willing to buy the good from the firm they choose if they think it is high quality.
This implies if firm which is thought to be high quality price above , consumers very close to that shop may still shop there, but they will not buy anything, and they know that when they make their choice of where to shop.
Thus, although the consumer makes two decisions, given the assumption that consumers can only buy from where they shop, they actually can make two decisions together, which is where to buy from.

11. Necessary conditions for a high quality equilibrium
An equilibrium in which both firms chooses high quality
If both firms charges price above , all consumers will want to shop at the firms, but they will not buy anything
If , then
Quality ensuring condition

12. Necessary conditions for a high quality equilibrium (continued)
Further,
A consumer at is indifferent between firm 1 and firm 2 if
Firm 1’s demand function
Firm1’s profit function is

13. Necessary conditions for a high quality equilibrium (continued)
Maximize firm 1’ profit
subject to
then set

14. A high quality equilibrium
A high quality equilibrium in which the two firms choose high quality,

15. A numerical example Consider a example with and
This assumption implies that
If we further assume that
The monopoly solution has A=0.14, P=1, and profit=0.86
Now we extend the example to consider competition. Assume
The solution has A1=A2=0.21, P1=P2=0.74
Each firm’s profit is 0.16

16. Check the proposed equilibrium for high quality
Check a firm can not do better by deviating and choosing a lower price and advertising level, such that it will want to set low quality
If firm 1 did this, then its demand function is

17. Check the proposed equilibrium for high quality (continued)
Substitute into the demand function
gives P1=0.2, and its resulting profit is 0.04(<0.16)

18. Results
Pure strategy equilibrium exists when , but there is no pure strategy equilibrium when
The case of monopoly corresponds to in the high quality equilibrium
When the competition effect is weak, the monopoly price and advertising level remains an equilibrium outcome.
As the competition effect gets stronger, the high quality firms lower their prices and raise their advertising levels as shown in figure 1.

19. Results: relationship between price, advertising and competition( )
Note: A and p1 are advertising and price level respectively in the proposed high quality equilibrium

20. Conclusions The high quality equilibrium outcome under monopoly
Price and advertising level
Profit and social welfare
Social welfare with a ban on advertising
The high quality equilibrium outcome under duopoly
Social welfare owing to the price and advertising

21. Thank you
The End