Pay-What-You-Want Pricing Schemes
A Self-Image Perspective
G.A. Kahsay1
M. Samahita2
1 Department
of Food and Resource Economics
University of Copenhagen
2 Department
of Economics
Lund University
Microeconomics Seminar, 10 February 2014
Outline
1 Introduction
PWYW Examples
Previous Literature
Motivation
2 The Model
Specifications
Solving the Model
3 Results
PWYW vs FP
Comparative Statics
Welfare Analysis
4 Summary
Margaret Samahita, Department of Economics, Lund University
PWYW Examples
I
Food industry
I
I
I
I
Margaret Samahita, Department of Economics, Lund University
One World Community
Cafes (US)
Der Wiener Deewan
(Austria)
Lentil as Anything
(Australia)
Terra Bite Lounge (US)
I
Music industry: Magnatune,
Moshpit Tragedy Records
I
Travel industry: NH-Hoteles
(Belgium, the Netherlands),
“free” walking tours
I
Service industry: Google
Answers, tipping
I
...
Empirical Studies and Field Experiments
I
Kim et al. (2009): restaurant, cinema, cafe
I
Regner and Barria (2009), Regner (2010), Regner and Riener
(2012): Magnatune
I
Gneezy et al. (2010), Gneezy et al. (2012), Riener and Traxler
(2012): theme park, tour boat, Der Wiener Deewan restaurant
Table 1: Tour boat experiment results (Gneezy et al., 2012)
Purchase rate
Average price
FP $5
FP $15
PWYW
64%
$5
23%
$15
55%
$6.43
Margaret Samahita, Department of Economics, Lund University
Empirical Studies and Field Experiments
Table 2: Theme park experiment results (Gneezy et al., 2010, 2012)
Purchase rate
Average price
FP
PWYW
PWYW + Charity
0.50%
$12.95
8.39%
$0.92
4.49%
$5.33
Observation 1
Individuals pay a positive PWYW amount
Observation 2
The PWYW amount exceeds the fixed price
Observation 3
PWYW purchase rate is lower than in fixed-price setting
Margaret Samahita, Department of Economics, Lund University
Previous Literature
Conditions for PWYW
I Chen et al. (2009): PWYW profitable in industries with
existence of fair-minded consumers, low marginal costs, high
concentration of low willingness-to-pay consumers and a
competitive marketplace. Suggest posting a minimum price.
I Fernandez and Nahata (2009): if customers have positive
valuation, not all will free-ride in equilibrium, and in some
cases all will pay. If social cost is considered, customers may
opt-out. May be more attractive than fixed pricing.
I Mak et al. (2010): self-interested customers - PWYW
profitable if firm threatens to switch to fixed price.
I Isaac et al. (2010): PWYW sustainable given a social norm
regarding minimum contributions, reduces dead-weight loss
relative to fixed-price scheme.
I Schmidt et al. (2012): social preferences and desire to keep
seller in market. PWYW more successful in isolation than in
competition with fixed-price seller.
Margaret Samahita, Department of Economics, Lund University
Previous Literature
Consumers’ preferences
I
Selfish: want to keep seller in business
I
Altruism
I
Reciprocity
I
Guilt
I
Social norms
I
Fairness
By themselves explain positive amount paid, but not lower purchase
rate and higher amount paid relative to fixed-price schemes.
Margaret Samahita, Department of Economics, Lund University
Motivation
I
Gneezy et al. (2012): self-image as an explanation
I
Self-image in behavioral economics
Self-signaling through
I
I
I
purchasing
opting out
Margaret Samahita, Department of Economics, Lund University
The Model
Utility of buying:
Ui (c) =
u (x) − c
| i {z }
net material utility
+ fi (c, r )
| {z }
c, r ≥ 0
self-image
I
x is a vector of the good’s characteristics, ui (x) is the good’s
consumption utility
I
c is amount paid, equals posted price in fixed-price schemes or
chosen by individual in PWYW
Margaret Samahita, Department of Economics, Lund University
Self-Image
I
I
Self-image = fi (c, r )
Derived from fair payment to seller:
I
I
f (c, r ) = 0 whenever c = r
Monotonically increasing:
I
fc > 0, fcc < 0, fr < 0
Reservation utility of not buying is normalized to zero
Margaret Samahita, Department of Economics, Lund University
Seller’s Fair Price
The seller’s fair price is determined differently in PWYW and
Fixed-Price schemes.
Under PWYW:
r = v R c.
Under a fixed-price scheme:
r = p = c.
Hence, self-image is zero in a fixed-price scheme.
Margaret Samahita, Department of Economics, Lund University
Heterogeneity
I
Heterogeneous in ui (x) ∈ R+
I
Heterogeneous in image-sensitivity
Relative Image Sensitivity
An individual j is referred to as globally more image-sensitive than i
if:
∂fj
∂fi
(c, r ) >
(c, r )
∀c
∂c
∂c
Margaret Samahita, Department of Economics, Lund University
Solving the Model
Backward induction:
1. Utility maximization - find c ∗
2. Compare U(purchase) with U(no purchase) - decide to buy or
not to buy
Margaret Samahita, Department of Economics, Lund University
Step 1: Finding c ∗
FOC:
∂fi
(c, v ) = 1
∂c
If j is more sensitive than i, ci∗ < cj∗ .
Observation
∂fj
∂fi
(v , v ) < 1 ≤
(v , v ) ⇐⇒ ci∗ < v ≤ cj∗
∂c
∂c
Absolute Image Sensitivity
In this case, i is image-insensitive and j is image-sensitive.
Margaret Samahita, Department of Economics, Lund University
Step 2: Purchase Decision
I
Do not buy if ui (x) − c ∗ + fi (c ∗ , v ) < 0:
I
I
Buy if fi (c ∗ , v ) > c ∗ − ui (x):
I
I
consumption utility too low to justify paying c ∗
self-image gain of paying a high c is higher than material loss
Or if ui (x) − c ∗ > −fi (c ∗ , v )
I
self-image loss of paying a low c is lower than material benefit
Margaret Samahita, Department of Economics, Lund University
PWYW vs FP
Proposition 1
The purchase rate is weakly higher under PWYW than a fixed-price
scheme at price p ≥ v .
Proof.
Ui (ci∗ ) = ui (x) − ci∗ + fi (ci∗ , v )
≥ ui (x) − v + fi (v , v )
= ui (x) − v
≥ ui (x) − p
∀p ≥ v
= Ui (p)
Margaret Samahita, Department of Economics, Lund University
PWYW vs FP
Proposition 1
The purchase rate is weakly higher under PWYW than a fixed-price
scheme at price p ≥ v .
Intuitive:
I
Image-insensitive: free-ride.
I
Image-sensitive: gain self-image.
PWYW weakly increases purchase rate.
Margaret Samahita, Department of Economics, Lund University
PWYW vs FP
Proposition 2
The purchase rate is weakly lower under PWYW than a fixed-price
scheme at price p ≤ ci∗ − fi (ci∗ , v ) (≤ v ) ∀i.
Proof.
p ≤ ci∗ − fi (ci∗ , v ) =⇒ ui (x) − p ≥ ui (x) − ci∗ + fi (ci∗ , v )
=⇒ Ui (ci∗ ) ≤ Ui (p)
Margaret Samahita, Department of Economics, Lund University
PWYW vs FP
Proposition 2
The purchase rate is weakly lower under PWYW than a fixed-price
scheme at price p ≤ ci∗ − fi (ci∗ , v ) (≤ v ) ∀i.
I
Image-insensitive: consider image loss.
I
Image-sensitive: high optimal price.
PWYW weakly decreases purchase rate
With enough purchase by image-sensitive individuals, average
PWYW price exceeds fixed price.
Margaret Samahita, Department of Economics, Lund University
PWYW vs FP
Table 3: Tour boat experiment results (Gneezy et al., 2012)
Purchase rate
Average price
FP $5
FP $15
PWYW
64%
$5
23%
$15
55%
$6.43
Margaret Samahita, Department of Economics, Lund University
Comparative Statics: ↑ v
Proposition 3
An increase in v results in a weakly lower purchase rate.
Proof.
Ui (c ∗ (v )) = ui (x) − c ∗ (v ) + fi (c ∗ (v ), v )
∂U(c ∗ (v ))
dc ∗ (v )
=−
+
∂v
dv
∂f
=
<0
∂v
∂f dc ∗ (v ) ∂f
·
+
∂c ∗
dv
∂v
Margaret Samahita, Department of Economics, Lund University
Comparative Statics: ↑ v
Proposition 3
An increase in v results in a weakly lower purchase rate.
I
From fv < 0, ↑ v requires ↑ c to maintain self-image
I
Such ↑ c results in ↓ U
∗
A higher average price requires the extra condition ∂c
∂v > 0 and a
sufficiently high number of image-sensitive individuals still making a
purchase.
Margaret Samahita, Department of Economics, Lund University
Comparative Statics: ↑ v
Table 4: Theme park experiment results (Gneezy et al., 2010, 2012)
Purchase rate
Average price
FP
PWYW
PWYW + Charity
0.50%
$12.95
8.39%
$0.92
4.49%
$5.33
Margaret Samahita, Department of Economics, Lund University
Welfare Analysis
Assumptions:
I
Ui (c) = ui (x) − c + µi (c − v ) − 12 (c − v )2
v +1
I
n = 10, 000, 1 ≤ v ≤ 10, p = v ± 1, zero marginal cost
I
1
ui (x) ∼ U(0, 2v ), µi ∼ U( 1+v
,1 +
(a) Price
Margaret Samahita, Department of Economics, Lund University
µi > 0; c <
v
1+v )
(b) Purchase rate
Welfare Analysis
(a) Utility
(b) Profit
(c) Total welfare
Margaret Samahita, Department of Economics, Lund University
Summary
Given v , and the fixed price p,
I
I
If p ≥ v , PWYW (naturally) leads to a weakly higher purchase
rate.
If p ≤ v and the sufficiency condition is satisfied, individual
behavior may deviate from SET:
I
I
Higher average price
Lower purchase rate
I
An increase in the fair price v may reinforce both effects.
I
PWYW has the potential to increase welfare relative to a good
sold at a high fixed price.
Thank you!
Margaret Samahita, Department of Economics, Lund University