Incentives and Behavior Prof. Dr. Heiner Schumacher KU Leuven 11. Exploiting Consumers Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 1 / 21
Introduction One of the most crucial general questions in behavioral economics is whether behavioral biases a¤ect market outcomes. If they do not, then they may be interesting psychologically, but of minor economic interest. In this lecture, we consider two examples how behavioral biases may a¤ect the trade between …rms and consumers. Both examples generate contract features that can be found in real-world contracts. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 2 / 21
Introduction Overview A simple two-period model A simple two-period model: Time-consistent agent A simple two-period model: Time-inconsistent, sophisticated agent A simple two-period model: Time-inconsistent, naive agent Shrouded attributes Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 3 / 21
A simple two-period model A consumer and a monopolistic …rm can trade a service. There are three periods t = 0 , 1 , 2. 1 In period 0, the …rm o¤ers a contract with a two-part tari¤ ( L , p ) . The consumer can accept or reject this contract. If she rejects it, she receives her reservation utility ¯ u in period 1 and there are no further transfers between …rm and consumer. Assume in the following that the consumer has accepted the contract. In period 1, the consumers pays L to the …rm. She then decides whether to consume ( C ) the good or not ( NC ). If she chooses C , she immediately incurs costs of consumption c , pays p to the …rm and receives bene…t b in period 2. If she chooses NC , her payo¤ is 0 and there are no more transfers between …rm and consumer. 1 This model is based on DellaVigna, Stefano, and Ulrike Malmendier (2004): “Contract Design and Self-Control: Theory and Evidence,” Quarterly Journal of Economics 119(2), 353–402. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 4 / 21
A simple two-period model In period 0, the …rm and the consumer do not know the exact value of c . We assume that c is distributed on [ 0 , 1 ] according to the distribution function F with strictly positive density f . The …xed costs of the …rm in period 1 are given by K . If the consumer chooses C , the …rm further incurs per-unit cost a � 0. The consumer’s intertemporal preferences in period t are given by ( β , δ ) -preferences: ∞ δ τ � t u τ , ∑ u t + β τ = t + 1 where u τ is her instantaneous utility in period τ . The consumer’s belief about her future present-bias is denoted by ˆ β . Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 5 / 21
A simple two-period model: Time-consistent agent Suppose that the agent is time-consistent ( β = 1). In period 1, she consumes the good if and only if δ b � c � p � 0 ( ) c � δ b � p . Thus, in period 0, her expected utility from the contract is δ b � p Z U TC = δ [ � L + δ b � c � pdF ( c )] . 0 The …rm therefore maximizes its pro…t δ b � p Z π ( L , p ) = δ [ L � K + p � adF ( c )] , 0 subject to the participation constraint U TC � δ ¯ u . Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 6 / 21
A simple two-period model: Time-consistent agent The participation constraint must be binding (why?). Thus, we can easily solve this problem by substituting the participation constraint into the objective function and maximizing over p . The optimal contract features p TC = a , i.e., the optimal price equals the marginal costs (“marginal cost pricing”). Thus, the total surplus is maximal. L TC is chosen so as to extract full consumer surplus. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 7 / 21
A simple two-period model: Time-inconsistent, sophisticated agent Now suppose that the agent has a self-control problem ( β < 1), but perfectly anticipates it ( ˆ β = β ). In period 1, she consumes the good if and only if δβ b � c � p � 0 ( ) c � βδ b � p . In period 0, her expected utility from the contract is βδ b � p Z U S = βδ [ � L + δ b � c � pdF ( c )] . 0 Note that the term under the integral is the same as under time-consistency! Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 8 / 21
A simple two-period model: Time-inconsistent, sophisticated agent The …rm maximizes its pro…t βδ b � p Z π ( L , p ) = δ [ L � K + p � adF ( c )] , 0 subject to the participation constraint U S � βδ ¯ u . We substitute the participation constraint into the objective function and maximize over p . Observe that the …rm essentially maximizes the joint surplus of the …rm and self-0! The optimal price equals p S = a � δ b ( 1 � β ) . Thus, the price is below marginal costs! This lower price solves the agent’s self-control problem and thereby increases her willingness to pay. The …rm’s contract is a commitment device! Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 9 / 21
A simple two-period model: Time-inconsistent, naive agent Finally, suppose that the agent has a self-control problem ( β < 1), and is partially naive about it ( ˆ β > β ). In period 1, she consumes the good if and only if δβ b � c � p � 0 ( ) c � βδ b � p . However, in period 0, the consumer expects to consume it if and only if δ ˆ ) c � ˆ β b � c � p � 0 ( βδ b � p . Thus, she overestimates the probability with which she uses the good (und thus overvalues the contract). In period 0, her expected utility from the contract is ˆ βδ b � p Z U N = βδ [ � L + δ b � c � pdF ( c )] . 0 Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 10 / 21
A simple two-period model: Time-inconsistent, naive agent The …rm maximizes its pro…t βδ b � p Z π ( L , p ) = δ [ L � K + p � adF ( c )] , 0 subject to the participation constraint U N � βδ ¯ u . We substitute the participation constraint into the objective function so that the maximization problem becomes ˆ βδ b � p βδ b � p Z Z max δ [ δ b � c � pdF ( c ) � K + p � adF ( c ) � ¯ u ] p 0 0 ˆ βδ b � p βδ b � p Z Z = max δ [ δ b � c � adF ( c ) � K + δ b � c � pdF ( c ) � ¯ u ] . p 0 βδ b � p The …rst term is real surplus, while the second term is “…ctitious surplus”. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 11 / 21
A simple two-period model: Time-inconsistent, naive agent For cost realizations in the interval βδ b � p < c < ˆ βδ b � p self-0 believes that it will consume in period 1, but actually this will not be the case. We calculate that the optimal price for the monopolist is β ) δ bf ( ˆ f ( βδ b � p N ) � F ( ˆ βδ b � p N ) βδ b � p N ) � F ( βδ b � p N ) p N = a � ( 1 � ˆ . f ( βδ b � p N ) Thus, we again have below marginal cost pricing. Note that the second term captures the commitment e¤ect and the third term the naiveté e¤ect. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 12 / 21
A simple two-period model: Time-inconsistent, naive agent The naive agent is exploited to the extent that she ends up with less utility than her outside option is worth. The monopolist exploits naiveté, not time-inconsistency (this is a general result). The model is also applicable to leisure goods with immediate bene…ts and delayed costs (e.g. unhealthy food choices). We then have above marginal cost pricing. A number of industries have these pricing features (health clubs, credit cards, gambling casinos, phone contracts). Unfortunately, the predictions for sophistication and naiveté are the same in this model. This, however, is not a general result (in a richer environment, there are di¤erences between contracts for sophisticated and naive consumers). Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 13 / 21
Shrouded attributes An important question for economic policy is whether competition between …rms eliminates the negative consequences of consumer mistakes. Suppose the answer is yes: The policy maker then only has to ensure that there is enough competition; no need to use regulation or consumer protection. In the following, we describe a market where competition between …rms is not enough to ensure e¢cient outcomes. 2 2 This model is based on Gabaix, Xavier, and David Laibson (2006): “Shrouded Attributes, Consumer Myopia, and Information Suppression in Competitive Markets,” Quarterly Journal of Economics 121(2), 505–540. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 14 / 21
Shrouded attributes There are two …rms i = 1 , 2. Each …rm o¤ers a “base good” and an “add-on” service/good. Examples: Printers and ink, hotel room and mini bar, bank account and overdraft fees. Production costs are normalized to zero. Firm i charges p i for the base good and ˆ p i for the add-on. Each …rm also decides whether to reveal (unshroud) or conceal (shroud) the fact that an add-on service may be necessary. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 11. Exploiting Consumers 15 / 21
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