Incentives and Behavior Prof. Dr. Heiner Schumacher KU Leuven 11. - - PowerPoint PPT Presentation

Incentives and Behavior

• Prof. Dr. Heiner Schumacher

KU Leuven

• 11. Exploiting Consumers
• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 11. Exploiting Consumers

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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

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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

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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.

1This 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

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A simple two-period model

In period 0, the …rm and the consumer do not know the exact value

• f 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: ut + β

∞

∑

τ=t+1

δτtuτ, where uτ 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 δb c p 0 ( ) c δb p. Thus, in period 0, her expected utility from the contract is UTC = δ[L +

δbp

Z

δb c pdF(c)]. The …rm therefore maximizes its pro…t π(L, p) = δ[L K +

δbp

Z

p adF(c)], subject to the participation constraint UTC 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

• ver p.

The optimal contract features pTC = a, i.e., the optimal price equals the marginal costs (“marginal cost pricing”). Thus, the total surplus is maximal. LTC is chosen so as to extract full consumer surplus.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 11. Exploiting Consumers

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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 δβb c p 0 ( ) c βδb p. In period 0, her expected utility from the contract is US = βδ[L +

βδbp

Z

δb c pdF(c)]. 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 π(L, p) = δ[L K +

βδbp

Z

p adF(c)], subject to the participation constraint US 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 pS = a δb(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 δβb c p 0 ( ) c βδb p. However, in period 0, the consumer expects to consume it if and only if δˆ βb c p 0 ( ) c ˆ βδb 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 UN = βδ[L +

ˆ βδbp

Z

δb c pdF(c)].

• 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 π(L, p) = δ[L K +

βδbp

Z

p adF(c)], subject to the participation constraint UN βδ¯ u. We substitute the participation constraint into the objective function so that the maximization problem becomes max

p

δ[

ˆ βδbp

Z

δb c pdF(c) K +

βδbp

Z

p adF(c) ¯ u] = max

p

δ[

βδbp

Z

δb c adF(c) K +

ˆ βδbp

Z

βδbp

δb c pdF(c) ¯ u]. 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 βδb p < c < ˆ βδb 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 pN = a (1 ˆ β)δbf (ˆ βδb pN) f (βδb pN) F(ˆ βδb pN) F(βδb pN) f (βδb pN) . 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

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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

2This 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

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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 pi for the base good and ˆ pi 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

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Shrouded attributes

There is a unit mass of consumers. The combination of base good and add-on has value v for them. The maximum willingness to pay for the add-on is ¯ p. A fraction 1 α of consumers is sophisticated and forms correct beliefs about the shrouded add-on price. A fraction α of consumers is naive and ignores the add-on price. If both …rms shroud the add-on price, they are unaware of it. If one …rm unshrouds the add-on price, all naive consumers become sophisticated. By expending costs e sophisticated consumers have the opportunity to substitute the add-on (print less, bring own drinks to the hotel, transfer money to avoid overdraft,...).

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 11. Exploiting Consumers

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Shrouded attributes

The timing of the model is as follows. In period 1, …rms simultaneously choose pi, ˆ pi and a shrouding decision. In period 2, consumers observe pi (and ˆ pi if at least one …rm unshrouds) and choose a …rm. In period 3, sophisticated consumers decide whether to substitute the add-on or not. Naive consumers have to buy the add-on from their …rm at price ˆ pi.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 11. Exploiting Consumers

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Shrouded attributes

Sophisticated consumers hold belief ˆ pE

i about the expected add-on

• price. In equilibrium, this belief must be correct.

They substitute in period 3 if e < ˆ pE

i . Thus, in period 2, they

purchase from …rm i if pi minfe, ˆ pE

i g > pi minfe, ˆ

pE

ig.

Myopic consumers are unaware of the add-on price and purchase from …rm i if pi > pi. We assume that if consumers are indi¤erent between …rms, they choose each …rm with equal probability.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 11. Exploiting Consumers

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Shrouded attributes

We can show the following result.

1

If α e

¯ p , there is a symmetric equilibrium in which both …rms shroud.

Equilibrium prices are then given by p

i = α¯

p and ˆ p

i = ¯

p; sophisticated consumers substitute the add-on.

2

If α < e

¯ p , there is a symmetric equilibrium in which …rms do not

• shroud. Equilibrium prices are then given by

p

i = e and ˆ

p

i = e.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 11. Exploiting Consumers

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Shrouded attributes

To verify the result in (1.) we show that (i) no …rm wants to change prices while maintaining shrouding, and (ii) no …rm wants to unshroud and change prices. The veri…cation of the result in (2.) is similar (you can do it as an exercise). What is the intuition behind this result? Shrouding creates pro…ts from naive consumers and losses from sophisticated consumers. Given the rival’s subsidized price for the base good, the …rm has to

• ¤er a relatively low price to attract any consumers. If the share of

naive consumers is su¢ciently large, this price would be negative. Unshrouding would hurt the rival, but the …rm would not gain from it.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 11. Exploiting Consumers

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Shrouded attributes

The equilibrium is ine¢cient because sophisticated consumers engage in costly substitution of the add-on (which could be provided at zero cost). The base good is subsidized by the revenues from naive consumers on the add-on. Naive consumers are exploited at the expense of sophisticated ones.

• Prof. Dr. Heiner Schumacher (KU Leuven)

Incentives and Behavior

• 11. Exploiting Consumers

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