A Commercial Gift for Charity

A Commercial Gift for Charity

Anouk Schippers

August 21, 2015

Abstract

Commercial firms are increasingly tying the sales of their products with donations to a charitable cause. Apart from a charitable motive, offering these hybrid bundles could be a strategic instrument for firms to increase profits. This paper addresses the latter perspective by investigating whether tying the sales of products to do-nations to charity increases profits net of the donation, and if so, which donation scheme is most profitable. The theoretical model shows that, given rational agents, complete markets, and absent transaction costs, selling hybrid bundles is not prof-itable, even not when accounting for consumer altruism. We expect, however, that offering hybrid bundles can be profit-increasing. Similar to the overweighing of small probabilities, consumers may overestimate the part of the sales price donated to charity when evaluating hybrid bundles. The model shows that if consumers suffer from such biases, offering hybrid bundles can be profit-increasing. The ten-tative experimental results indicate that selling hybrid bundles is indeed profitable. Surprisingly, donating a fixed amount rather than a percentage to charity seems to be the most profitable scheme.

JEL classification: D4, L2, L310.

1

Introduction

Over the last years, commercial firms have increasingly linked their products with dona-tions to charity, thereby offering a hybrid bundle. Firms differ in their disclosure as to how much of each sale is donated to charity as well as in the framing of the donation. Whereas IKEA donates e 1 for each soft toy of children’s book sold around Christmas, Dopper Foundation donates 5% of net sales revenue of its water bottle. Do these com-mercial firms tie the sales of their products with donations to a charitable cause because of pure charitable motives or is the charity being used as a strategic incentive to increase profits? The main objective of this paper is to address the latter perspective by investi-gating whether tying the sales of products to donations to charity increases profits net of the donation to charity and, if so, which donation scheme is most profitable.

the donation (a fixed amount in Frackenpohl and P¨onitzsch) and to the fractions donated (100% in 60% of the cases in Elfenbein and McManus).

We test a theoretical model that predicts that –given rational agents, complete markets and absent transaction cost– offering hybrid bundles is not profitable. Accounting for consumer altruism or warm-glow (Andreoni 1990) does not change this result. Consumers are willing to tick up their payment when purchasing hybrid bundles, but this increase does not exceed the amount donated to charity. However, the model proposes that firms may benefit from offering bundles if consumer biases are present. Similar to the overweighing of small percentages (Kahneman and Tversky 1979) consumers may overestimate the part that is donated to charity via purchasing the bundle. We believe that this kind of bias is especially prevalent when a scheme is adopted in which a percentage of the sales price is donated (instead of a fixed amount), and when the percentages donated are smaller. Hence, the model predicts that profits net of the donation to charity are higher in case the sale of a private product is tied to a (smaller) percentage donation of the sales price. Our experimental design aims to distinguish between the different donation schemes. In the control condition (Control), the seller offers only the private product. In the treatment conditions, the seller sells the hybrid bundle conisting of a private product and a donation to charity. This donation is 2% of the sales price in treatment Asym-2, 5% in treatment Asym-5, and a fixed amount of 0.43 ECU (Experimental Currency Units, 1 ECU equalse 2) in Asym-Abs. The tentative results of the experimental study seem to confirm the hypothesis that offering hybrid bundles is profitable. On average, positive profits are attained when donating 2%, 5% or a fixed amount of the sales price. Compared to offering the product without a donation to charity (average profits of 0.75 ECU), donating 5% increases profits by 0.59 ECU, while donating 2% generates slighly lower profits (average profits of 0.64 ECU). Surprisingly, and contrary to the predictions of the theoretical model, donating a fixed amount seems to be most profitable (average profits of 2.07 ECU).

al-located by the buyers in the dictator game, and self-reported charitable behaviour by the participants, do not differ significantly between the treatments. Buyers are also equally able to translate percentages into amounts, as the probability numeracy scores of the participants are not significantly different. As well, participants do not seem to dislike donations in percentages of the sales price, as both Asym-2 and Asym-5 generate pos-itive profits. Lastly, the share of buyers that buys from the live-seller does not differ significantly in Asym-2, which suggests that buyers do not believe that a 2% donation of the sales price is too small to have a meaningful impact.

Although it seems that offering hybrid bundles is a strategic instrument for firms to increase profits, we find suggestive evidence of crowding out behaviour of charitable donations. Buyers could make a private (direct) donation to the charity next purchasing the hybrid bundle. We find that average private donations are lower in the treatment conditions as compared to the control condition (although only significantly lower in Asym-Abs). Moreover, the average total contributions (private donations of the buyers plus the donations via the bundle) to charity are significantly lower in the treatment conditions. Finally, we note that average donations via the hybrid bundle are rather small in comparison with average private donations. Hence, although offering hybrid bundles may be a strategic instrument for firms, the effect on charitable donations seems less favourable.

2

Theoretical Framework

This section will summarize the theoretical model as provided in Soetevent et al. (2015), and list the research hypotheses that can be derived from the model.

2.1

Theoretical Model

This section will summarize the key findings of the theoretical model as developed by Soetevent et al. The model assumes that one of the firms (live-seller) either sells a hybrid bundle consisting of a private product and a donation to charity, or only the private product, while the other firm (computer-seller) sells the private product at marginal cost (pM C_).1 _{In treatment Control, the live-seller sells only the private product at price (p}U_).

In the other treatments, the live-seller offers the hybrid bundle at price (pB_{). In treatment}

Asym-2, the seller donates 2% to charity. This part is 5% in treatment Asym-5 and an absolute amount of 0.43 ECU in treatment Asym-Abs.2

The model assumes that consumers have altruistic preferences. In our experiment, buyers have to make two choices: whether to buy from which seller (transaction decision) and whether to make a private donation (donation decision). Buyer’s utility can be represented by the following utility function that incorporates warm-glow for the charity (Andreoni 1990):

Ui(x − p − gU, gT, G) = x − p − gU + αi

p

gT ₍₁₎

In this function, x is the utility that the buyer derives from buying the private good. p denotes the price paid for the product, such that x − p is the buyer’s net consumption utility from buying the private good. αi

p

gT _{is the warm-glow utility that the buyer}

derives from giving a total amount of gT _{= g}B_(pB_{) + g}U _{to the charity. g}B_(pB_{) reflects the}

potential indirect donations via purchasing the bundle). Note that a term reflecting how much the buyer cares about the charity per se is absent (βi

√

G). Including such a term in the model leads to complete crowding out of donations of pure altruists. As crowding out is not expected to drive the results (subjects will not know the contributions by others), the model abstracts from pure altruism.

If both sellers offer only the private good (Control), the buyer will decide as follows: • Buy from the live-seller if pU _{≤ p}M C_.

• Buy from the computer-seller if otherwise.

If the live-seller offers the hybrid bundle and the computer-seller offers the private product (the Asymmetric treatments), the buyer will decide on making a separate donation to charity as follows:

• Buyers who do not buy the hybrid bundle optimally donate in a separate transaction: gU ∗ = max {α2_i/4, 0}.

• Buyer who do buy the bundle optimally donate in a separate transaction: gU ∗ ₌

max {α2_i/4 − gB(pB), 0}.3.

In case of strong warm glow (α2_i/4 > gB(pB) > 0), the buyer could do the following: • Purchase the hybrid bundle from the live-seller. Separate donations will be gU ∗ ₌

α2

i/4 − gB(pB). This leads to total utility of UB = x − pB+ gB(pB) + 14α 2 i.

• Purchase the private product from the computer-seller. Separate donations will be gU ∗ = α2_i/4. This leads to total utility of UA= x − pM C+ α2_i/4.

Combining the above gives the decision of the buyer: • Buy from the live-seller if pB_{− p}M C _{< g}B_(pB_).

• Buy from the computer-seller if otherwise.

This means that the buyer will only buy the hybrid bundle from the live-seller if the price premium pB− pM C _{is less than the donation g}B _{to the charitable cause. Hence, offering}

the hybrid bundle is not profitable when the buyer has strong warm-glow preferences. In case of moderate warm-glow (0 ≤ α2

i/4 ≤ gB(pB)), the buyer will not make a

separate donation on top of purchasing the hybrid bundle. The buyer’s total utility from buying the hybrid bundle from the live-seller equals: UB = x − pB + αipgB(pB). The

buyer’s utility from buying the private product from the computer-seller is the same as before. Hence, the buyer will decide from which seller to buy as follows:

• Buy from the live-seller if pB_{− p}M C _{≤ α}

ipgB(pB) − α2i/4.4

• Buy from the computer-seller if otherwise.

A buyer with moderate warm-glow preferences is only willing to buy the hybrid bundle from the live-seller if the price premium does not exceed the donation to the charity. Hence, we have the following result:

Result 1. Buyers with altruistic preferences (α > 0) will never buy the hybrid bundle if the premium pB _{− p}M C _{for the hybrid bundle exceeds the indirect donation g}B_(pB_{) made}

to the charitable cause.

In our experimental design, the live-seller competes with a computer-seller. Apart from the donation to charity, the marginal cost (M C) of sellers is constant and identical. We distinguish between the following cases:

• The live-seller offers the private product. This is a case of Bertrand competition with homogeneous goods. Theory predicts that: pU = pM C; π = 0.

4_{Note that the maximum value of the right-hand side of the inequality is g}B_(pB_{), by setting α} iequal

to its upper bound 2pgB_(pB_{). Inserting the upper bound value for α}

• The live-seller offers the hybrid bundle, consisting of a private product and a dona-tion to charity. The total marginal cost of the live-seller increases by gB_(pB_{). Hence,}

this is a case of Bertrand competition with asymmetric cost. Theory predicts that: pB = pB_{W T A} = M C + gB(pB_{W T A}); π = 0.

Our experimental design distinguishes between the following treatments: Control, in which the live-seller offers the private product; Asym-2, in which the live-seller offers the hybrid bundle, consisting of a private product and a 2% donation to charity; Asym-5, in which the live-seller donates 5% of the sales price to charity; and Asym-Abs, in which the seller donates a fixed amount of the sales price. In 2, 5 and Asym-Abs, the donation takes the form of a percentage τ of the sales price. The live-seller’s willingness to accept equals: pB_{W T A} = M C + τ pB_{W T A} ⇒ pB

W T A = M C1−τ. In Asym-Abs,

the donation is a lump-sum T , such that the live-seller’s willingness to accept equals: pB

W T A = M C + T.

Thus far, the theoretical model has shown that offering the hybrid bundle is not profit-increasing for the seller. Tying the sale of a product with donations to charity can become profitable if consumers have a biased perception of the part of revenues that is donated to charity via purchasing the bundle. Similar to the overweighing of small probabilities (Kahneman and Tversky 1979), consumers may overestimate the part donated via purchasing the hybrid bundle. As the relation between the amount paid and the donation is less straightforward if the part donated is framed as a percentage, buyers are more likely to overestimate their contribution to the charity when the part donated is framed as a percentage. As a result, buyers may misperceive their donation via purchasing the bundle, leading to an increase in the willingness to pay for the hybrid bundle. Hence, profits are expected to be larger when donating a percentage of the sales price rather than a fixed amount of the sales price.

The model captures this idea by denoting the buyer’s perceived total donation to charity as ˆgT_(gU_{, g}B_{) = g}U _{+ ˆg}B_{. It means that the separate donation to charity (g}U_{) is}

The bias increases the utility from buying the bundle for all individuals with α ≥ 0. The model predicts some crowding out, as less individuals will make a private donation next to buying the hybrid bundle: only individuals with α > ˆα = 2pˆgB_(pB_{) will do so. These}

buyers will buy the bundle instead of the private good if: pB− pM C _{≤ ˆg}B_(pB_{). Hence, if}

the bias is larger than the actual donation to charity, the seller is able to make positive profits. Buyers who will not make a private donation next to buying the bundle (α ≤ ˆα), will buy the bundle instead of the private good if: pB− pM C _{≤ αpˆg}B_(pB_{) − α}2_{/4. Sellers}

are able to gain positive profits if the right-hand side of the equation is larger than the actual donation to charity. The model assumes the following functional form for the bias:

f (gB) = gB+ C 1 + φgBI(g

B _{> 0) (2)}

with C, φ > 0 and I(·) an indicator function. _1+φgC B represents the total biased estimate

of the donations via purchasing the bundle. C measures how severely small donations are overestimated and φ represents how quickly this bias disappears for increasing actual donations. As the bias decreases in gB, the estimate will be larger for smaller actual donations. This implies that the biased estimate will be larger in 2 than in Asym-5. Net profits are thus expected to be larger in the former treatment.

2.2

Research Hypotheses

Hypothesis 1. Selling the hybrid bundle is expected to generate positive profits net of the donation to charity.

Hypothesis 2. Net profits are expected to be larger when the donation is framed as a percentage rather than as a fixed amount, and when the percentage donated is smaller:

πASY M −2> πASY M −5> πASY M −ABS > πCON T ROL= 0,

3

Experimental Design

3.1

Charity Market Game

Each buyer is matched with one seller, together they constitute a ‘market’. Next to that, a computer-seller is active in each market. As in Abrams et al. (Abrams, Sefton and Yavas 2000), the buyer’s valuation for the private good is common knowledge. Buyers do not know the marginal cost of supplying a unit of the private good, but it is common knowledge that – apart from the donation to charity – these unit costs are constant across periods. In all treatments, this cost is set at 8 Experimental Currency Unit (ECU) per unit provided.5

Whether or not part of the price goes to charity is exogenously determined in order to prevent sellers from using the charity as a signalling device to get higher prices. The percentage donated to charity and the fact that this percentage is imposed on sellers will be known to buyers. The charity selected for this experiment is the Red Cross, because it is an internationally renowned charity with the mission to protect human life and health. A letter signed by the Red Cross was provided to participants to increase the credibility that any donations by the participant will be transferred to the Red Cross.

The live-seller’s task is to set a price between zero and an imposed maximum (15) with increments of 0.01 ECU. The computer-seller will set a price equal to the marginal cost of the live-seller in all periods. In the benchmark condition, both types of sellers sell the private product and they do not donate to the Red Rross. In the treatment conditions, the live-seller offers the hybrid bundle consisting of the private product and a donation to charity, while the computer-seller does not donate to charity. This difference between the sellers in the treatment conditions is known to buyers. Buyers will also be notified which seller is the live-seller and which one is the computer-seller. Comparing the control and the treatment conditions enables us to detect the effect of tying the sale of a product with a donation to charity.

5_{The unit cost is set at a strictly positive level to ensure that in equilibrium, the total cost of providing}

After the sellers have set their prices, the buyer’s decision task in each period is twofold:

• Buying decision: Whether to buy from the live-seller or the computer-seller.

• Donation to the Red Cross: Buyers can make a separate donation to the Red Cross. In each period, buyers receive an endowment of 15 ECU, which is the maximum they can spend in total on the purchase of the product and on the donation. Buyers can at most buy 1 unit of the product. In each period, after making the buying decision, buyers can make a private donation to the Red Cross by typing in the amount they would like to donate. This donation is on top of potential indirect donations via purchasing the bundle. The transaction costs of the private donation to the Red Cross can be regarded as (close to) zero, because the effort buyers need to make in order to make this donation is minimal. Potential private donations will be donated to the Red Cross by the experimenters immediately after the experiment has ended.

The payoffs of the buyers and the sellers depends on the purchasing decision of the buyer. If the buyer buys from the live-seller, the payoffs are as follows:

• Buyer’s payoff: Total surplus gained from the transaction minus potential donations to the Red Cross (15 minus the price paid and the donation).

• Seller’s payoff: Price received minus marginal cost and potential donations to the Red Cross.

3.2

Treatments

For this study, the following treatments were run: Control, Asym-2, Asym-5, and Asym-Abs. Table 1 shows the parameter choices of the experiment and the equilibrium predictions of the experimental design. All prices stated are multiples of 0.01 Experimental Currency Units (ECU). The table shows the characteristics of the buyers and the live-sellers for each treatment. The marginal costs (MC) for the live-sellers are set at 8 in each treatment. The donations (a fraction τ and a lump-sum T ) differ per treatment: the seller does not donate to charity (Control), the seller donates 2% of the price received (Asym-2), 5% of the price (Asym-5), or a fixed sum of 0.43 ECU (Asym-Abs). The buyer’s maximum amount to spend in each period (x ) is 15 ECU for each treatment.

Table 1: Parameter choices and equilibrium predictions. Prices are in ECU. Treatment Control Asym-2 Asym-5 Asym-Abs

Seller characteristics MC 8 8 8 8 τ – 0.02 0.05 – T – – – 0.43 Buyer characteristics x 15 15 15 15 Equilibrium predictions pS 8 – – – pB _{- 8.17 8.43 8.43} πS 0 – – – πB – 0 0 0

The equilibrium predictions are that – given rational consumers, absent transaction costs and with complete markets – sellers are not able to make profits in any of the treatments. In Control, competition with the computer-seller will drive the price of the separate product (pS) to marginal cost, such that no profits (πS) are earned. In the treatments where the live-seller needs to donate part of the price received to the Red Cross, we expect buyers to increase their willingness to pay for the bundle (pB_{). However, this increase}

3.3

Procedure

Set up

In June 2015, the study was run with the treatments Control, Asym-2, Asym-5 and Asym-Abs. The experimental sessions were conducted in the GrEELab of the University of Groningen. As Table 2 shows, a total of 60 participants participated in our experiment. On average, participants were 22.68 years old and 61% was female.6 One session consisting of 15 trading periods was scheduled for each treatment, except for treatment Asym-5, which was run with two sessions. Upon arrival in the lab, participants were placed in cubicles and randomly allocated the role of buyer or seller of the product. They kept this role for the entire experiment as we wish to study consumer biases and switching roles would distort the analysis. No rematching between sellers and buyers takes place, as the seller’s motive for collusion is not present in the single live-seller design.

Table 2: Summary of the treatments.

Treatment Name Donation to charity Nr. rounds Nr. participants

I Control 0 15 10

II Asym-2 2% 15 14

III Asym-5 5% 15 24

IV Asym-Abs 0.43 ECU 15 12

Total 60 60

Charity Market Game

The experiment started after participants had carefully read the instructions and correctly answered the control questions. In each period, participants assigned the role of seller had to indicate their pricing decision, while participants assigned the role of buyer had to indicate their buying and donation decisions. We let subjects play this experimental charity market game for 15 periods. The conversion rate was: 1 ECU=e 2.

6_{Table 5 in Appendix A provides an elaborate summary of participant’s statistics. There are no}

Dictator Game

After participants finished the 15 trading rounds, the altruistic preferences of the par-ticipants were measured using the dictator game.7 _{This game consists of two players: a}

dictator and a receiver. The dictator has to divide a sum of 10 ECU between himself and the receiver. The receiver has no impact on the decision of the dictator: the allocation as determined by the dictator will be executed. Each participant was assigned the role of dictator. Simultaneously, each participant was assigned the role of receiver. For their payment, subjects were randomly matched with another participant. They received the allocation they decided upon as well as the allocation determined by the other player. The conversion rate was: 1 ECU=e 0.50.

Questionnaire

After the participants indicated their allocation in the dictator game, they filled in a questionnaire about demographic variables, their charitable behaviour, and they answered a question about probability numeracy. Finally, the participants were thanked and paid out one random period in the market game and their allocations of the dictator game. Any donations made to the Red Cross on behalf of the participants in the selected payment period were transferred to the Red Cross by the experimenters immediately after the experiment finished.

4

Experimental Results

4.1

Non parametric analysis

Table 3 below provides the descriptive statistics of the data per treatment and in total. The subsections below each discuss the variables in depth.

7_{We are aware of the limitations of using the dictator game to measure altruism, e.g. behaviour}

Table 3: Descriptive statistics

Control Asym-2 Asym-5 Asym-Abs Total Market Price Mean 5.80 8.72 8.39 9.97 8.51 SD 3.61 0.59 2.79 1.32 2.59 Minimum 0.00 8.10 0.10 7.50 0.00 Maximum 9.00 10.50 13.00 12.43 13.00 Observations 15 29 68 29 141 Market Price (when Price ≥ MC) Mean 8.75 8.82 9.83 10.50 10.02 SD 0.42 0.59 1.05 0.91 1.72 Minimum 8.00 8.17 8.50 8.44 8.00 Maximum 9.00 10.50 13.00 12.43 13.00 Observations 6 25 48 23 102 Profits Mean -2.20 0.55 -0.03 1.54 0.18 SD 3.61 0.58 2.65 1.32 2.48 Minimum -8.00 -0.06 -7.91 -0.93 -8.00 Maximum 1.00 2.29 4.35 4.00 4.35 Profits (when Price ≥ MC) Mean 0.75 0.64 1.34 2.07 1.30 SD 0.42 0.57 1.00 0.91 1.00 Minimum 0.00 0.00 0.07 0.01 0.00 Maximum 1.00 2.29 4.35 4.00 4.35 Bundle Donations Mean - 0.17 0.42 0.43 0.37 SD - 0.01 0.14 0.00 0.15 Minimum - 0.16 0.01 0.43 0.01 Maximum - 0.21 0.65 0.43 0.65 Observations - 29 68 29 126 Private Donations Mean 1.37 1.12 1.35 0.90 1.21 SD 1.43 1.59 1.59 1.17 1.50 Minimum 0.00 0.00 0.00 0.00 0.00 Maximum 6.00 7.00 7.00 5.00 7.00 Observations 75 105 180 90 450

4.1.1 Sales transactions

In the experiment, 450 sales transactions are recorded (30 buyers making 15 transactions). The main interest is in the sales transactions of the live-seller. Recall, the live-seller offers the hybrid bundle in the Asymmetric treatments, but only the private product in the control condition. The computer-seller sells the private product. In total, 141 transactions (31.33% of total transactions) with the live-seller are observed. The bundle was sold 68 times (over two sessions) in Asym-5, and 29 times in both Asym-2 and in Asym-Abs. The live-seller sold the product in 15 cases in Control.

Figure 1: Live-seller’s sales transactions as a share of total transactions.

The sales transactions with the live-seller as a share of total sales transactions is shown in Figure 1. The dark blue bar (Market price) shows the sales transactions in which the buyer has bought from the live-seller as a percentage of the market transactions (141 transactions in total). As can be seen from the graph, a larger share of buyers buys from the live-seller when the sale of a product is bundled with a donation to charity (p=0.03).8 8_{The p-values reported in this subsection are obtained from the Fisher’s exact test, because of the}

small sample. The Bonferroni correction is applied for the pairwise comparisons. The correction on the significance level is (with α = 0.05) 0.05

Compared to Control, the share of buyers purchasing from the live-seller is considerably higher in Asym-5 (p=0.006), but does not differ significantly in Asym-2 (p=0.292) and in Asym-Abs (p=0.081).

The dark-blue bar incorporates the transactions with the live-seller at market prices. However, in 39 sales transactions with the live-seller (27.66% of total transactions with the live-seller), the price was set below marginal cost. Correcting for below marginal cost pricing results in the light-blue bar (Market price ≥ 8) for Control and in the purple bar (Market price ≥ MC) for the Asymmetric treatments.9 _{The graph shows that}

especially in Control, sellers priced below marginal cost: live-sellers have incurred losses in around half of the transactions in that treatment. We clearly observe larger shares of buyers buying from the live-seller at market prices above marginal cost in the Asymmetric treatments (p<0.015). The graph also reveals that the bundles are bought at prices at least equal to marginal cost, such that offering the bundle seems profitable. 10

4.1.2 Market prices

We find suggestive evidence of a larger share of buyers buying from the live-seller when this seller offers a hybrid bundle. We now turn to the market prices that the live-seller sets for the bundle in the Asymmetric treatments and for the private product in the control condition. Figure 2 shows the average market prices conditional on buyers buying from the live-seller. 11

In the figure, the dark-blue bar (Market price) shows the market price of the trans-actions with the live-seller (141 transtrans-actions in total). The average market prices differ

9

The marginal cost of the live-seller in Control is equal to eight, but it is raised by the donation to charity in the Asymmetric treatments.

10

Figure 2: Live-seller’s average market prices (in ECU).

significantly (One-Way-ANOVA p=0.000), and are higher in the Asymmetric treatments (p< 0.002).12 _{This implies that buyers increase their willingness to pay for the private}

product if it is coupled with a donation to charity. The market price is significantly below marginal cost (eight) in Control (p=0.017).13

Correcting for below marginal cost pricing results in the light-blue bar (Market price ≥ 8) for Control, and in the purple bar (Market price ≥ MC) for the Asymmetric treatments.14 _{The graph reveals that especially for Control and Asym-5, live-sellers}

engage in below marginal cost pricing. Average market prices differ significantly (One-Way-ANOVA p=0.005). Compared to Control, average market prices are higher in Asym-5 and in Asym-Abs (p<0.008), but are not significantly different in Asym-2 (p=0.789). Among the Asymmetric treatments, market prices are higher in Asym-Abs (p<0.006), and in Asym-5, as compared to Asym-2 (p=0.000).15

12_{The p-values reported in this subsection are obtained from unpaired t -tests, unless reported otherwise.} 13

As the sample consists of 5 buyers and 5 sellers in Control, deviant –or irrational– pricing behaviour of an individual sellers may affect the average market price to a large extent.

14_{For the Asymmetric treatments, the donation to charity via the bundle should be taken into account}

in computing the marginal cost.

15

4.1.3 Profits

Figure 3 shows the average profits net of the donation to charity of the live-seller per treatment. The dark-blue bar (Average profits) takes into account all market transactions with the live-seller. Average profits differ significantly (One-Way-ANOVA p=0.000) and are larger in the Asymmetric treatments (p<0.005).16 _{Donating an absolute amount}

seems to be the most profitable scheme, while donating 5% of the sales price causes small losses. Substantial (and significant) losses are incurred in Control (p=0.017).

Figure 3: Live-seller’s average profits (in ECU).

Excluding market prices below marginal cost results in the light-blue bar (Average prof-its: P ≥ 8) for Control, and in the purple bar (Average profprof-its: P ≥ MC) for the Asymmetric treatments. The graph shows that especially in Asym-5 and Control, sellers price below marginal cost. Significant differences in average profits when market prices are at least equal to marginal cost are observed between the treatments (One-Way-ANOVA p=0.008). Compared to Control, the graph indicates that average profits are

higher in Asym-5 (p=0.080) and in Asym-Abs (p=0.001), but not significantly differ-ent in Asym-2 (p=0.669). Hence, compared to selling only the private product, offering the bundle seems profitable when donating 5% of the sales price (average profits of 1.34 ECU) or donating an absolute amount of 0.43 ECU (average profits of 2.07 ECU). Do-nating 2% of the price received is least profitable (average profits of 0.64 ECU) and not profit-increasing compared to Control (average profits of 0.75 ECU). Donating a fixed amount of the sales price results in higher profits as compared to donating 2% or 5% (p<0.002). Donating 5% is also more profitable than donating 2% (p=0.001).17

4.1.4 Charitable donations

This section discusses the implications for the charity in terms of donations via the bun-dle and private donations of buyers. Does offering hybrid bunbun-dles crowd out private donations, such that total donations to the charity decline?

Figure 4: Share of buyers making a private donation.

Figure 4 shows the share of buyers making a private donation to the Red Cross. The

17_{Average profits of the live-seller (taking into account all market prices) are higher in session 2 of}

dark-blue bar (All buyers) depicts the share of buyers that makes a private donation to the charity, regardless of whether they have bought the bundle from the live-seller or from the computer-seller (450 observations in total).18 _{In total, 65.56% of the buyers makes a}

private donation. In each treatment, around 60% of the buyers makes a private donation to the Red Cross (no significant differencens, p=0.532).19

In the Asymmetric treatments, a total of 126 bundles are bought, on top of which 77 private donations are made (61.11% of the bundle-buyers made a private donation). In Figure 4, the purple bar (Bundle buyers) shows the buyers who made a private donation on top of their indirect donation via the bundle as a share of the buyers that bought the bundle (126 observations in total). The share of bundle buyers that makes a private donation to charity does not differ between the Asymmetric treatments (p=0.113, pairwise t -tests, (p>0.067).20

The average donations in ECU are shown in Figure 5 below. The dark-blue bar (Average Bundle Donations) presents the average amount donated to charity via bundle purchases. The average bundle donations are significantly different (One-Way-ANOVA p=0.000). Average bundle donations are highest in Asym-Abs (0.43 ECU) but do not differ significantly from Asym-5 (0.42 ECU) (p=0.689). Average bundle donations are significantly lower in Asym-2 (0.17 ECU) (p=0.000).

Donations via the bundle are rather small in comparison with the average private donations shown in the light-blue bar (Average Private Donations). Average private donations are significant across treatments (One-Way-ANOVA p=0.007). Compared to Control, average private donations do not differ significantly in 2 and in

Asym-18_{Note that 30 buyers participated in this experiment, each making 15 private donation decisions.}

Hence, the percentages reflect the share of trading rounds in which the buyer made a private donation. For convenience, we have called this ‘the share of buyers’.

19_{The p-values for comparisons of shares reported in this subsection are obtained from the Fisher’s exact}

test, because of the small sample. For pairwise comparisons, the Bonferroni correction is applied, assuming a 5% significance level. As three pairwise comparisons are made, the correction on the significance level is: 0.05

3 = 0.0167. For average amounts in ECU, the reported p-values are obtained from unpaired t -tests, unless stated otherwise.

20

Figure 5: Average donations (in ECU).

5 (p>0.269), but are lower in Asym-Abs (p=0.011).21 The average private donations are higher in Asym-5 compared to Asym-Abs (p=0.010).

The purple bar (Average Total Donations) shows the average total donations for the Asymmetric treatments.22 _{Average total donations are significantly different between}

the treatments (One-Way-ANOVA p=0.000), and lower in the Asymmetric treatments (p<0.001). Hence, offering the bundle seems to crowd out private donations and leads to lower average total donations to the charity.23 _{The crowding out effect is least severe in}

Asym-5, as average total donations are highest in that treatment (p<0.06).24

21

In Asym-Abs, the seller had to donate 0.43 ECU. As this was known to buyers, it might have created a reference point for the private donation. Indeed, buyers have donated an amount of 0.43 ECU in eight cases (8.89% of total private donations), and donated eight times an amount of 0.4 ECU (8.89%). In the other treatments, these two amounts were not observed.

22

Note that the bar for Control depicts the average private donations as well as the average total donations, because, by design, hybrid bundles were not offered by the live-seller.

23

Average profits and average market prices are highest in Asym-Abs, but average private donations are lowest. Figure 4 also shows that the share of buyers that both bought the bundle and made a private donation is lowest in Asym-Abs. In Asym-Abs, buyers make on average significantly lower private donations (except for Asym-2), and conditional on buying the bundle, fewer buyers make a private donation in Asym-Abs (although not significant).

24

4.2

Regression Analysis

Table 4 presents the estimation results of the regression analysis. The dependent variable in models I and II is profits of the live-seller net of the donation to charity. The dependent variable in models III and IV is the price paid by the the buyer to the live-seller. Models I and III take into account all market prices, whereas model II and IV consider only market prices set at or above marginal cost.

Table 4: Estimation Results

Net Profits Price Paid by Buyer Model (I) Model (II) Model (III) Model (IV) Constant 2.14 3.72∗∗∗ 0.73 8.55∗∗∗ (1.86) (0.89) (1.90) (1.15) Asym-2 1.86∗∗ –0.70 1.99∗∗∗ 0.29 (0.4) (0.44) (0.74) (0.47) Asym-5 2.15∗∗∗ 0.53 2.47∗∗∗ 1.39∗∗∗ (0.76) (0.43) (0.64) (0.43) Asym-Abs 2.76∗∗∗ 1.19∗∗∗ 3.65∗∗∗ 1.78∗∗∗ (0.69) (0.37) (0.73) (0.47) Age –0.20∗∗∗ –0.14∗∗∗ 0.20∗∗∗ 0.02 (0.07) (0.04) (0.07) (0.04) Gender –0.63 0.28 –1.98∗∗∗ 0.29 (0.49) (0.21) (0.44) (0.24) Probability 1.34∗∗ 0.31 1.68∗∗ –0.49 Numeracy (0.53) (0.26) (0.57) (0.37) F-statistic 10.48 12.24 10.21 9.13 Prob. F-statistic 0.000 0.000 0.000 0.000 Adjusted R2 0.29 0.40 0.28 0.33 Observations 141 102 141 102

In model I, the dependent variable is mean profits net of the donation to charity. In model II, the dependent variable is mean profits net of the donation when sellers have priced at or above marginal cost. In model III, the dependent variable is the price paid by buyers to the live-seller. In model IV, the dependent variable is the price paid by buyers to the live seller when the price is at least equal to the marginal cost of the live-seller. In all models, the independent variables are the treatments Asym-2, Asym-5 and Asym-Abs, where Control is the benchmark. The control variables are the age, gender and a probability numeracy dummy (equal to one if the participant answered the question correctly). Three stars (∗∗∗_{), two stars (}∗∗∗_{) and one star (}∗_{) indicate significance at the}

Comparing models I and II, the dependent variable is the profits of the live-seller net of the donation to charity. The significance of the coefficients for Asym-2 and Asym-5 disappears when excluding market prices below marginal cost. This confirms the finding of section 4.1.3 that average profits in Asym-2 do not differ significantly from Control, but not the finding that profits in Asym-5 are significantly different. For Asym-Abs, excluding below marginal cost pricing results in a lower, but still significant, coefficient. Hence, compared to selling only the private product, offering one extra hybrid bundle with a fixed amount donation to charity seems to increase net profits by 0.53 ECU. Offering a hybrid bundle with a donation of 2% or 5% of the sales price seems not profit-increasing as compared to the benchmark treatment. Age seems to have a significant negative impact on profits of the live-seller, but gender does not influence profits. Probability numeracy does affect profits if considering all market prices, but becomes insignificant if prices set below marginal cost are excluded.25

In Model IV, the dependent variable is the price paid by the buyer when the live-seller has priced at or above marginal cost. The coefficients for Asym-5 and Asym-Abs are significant at 1%, while the coefficient for Asym-2 is not significant. Hence, offering the private product with a donation of 5% or an absolute amount to charity seems price-increasing relative to not donating part of the product price to charity. Donating a fixed amount increases the market price by the most (1.78 ECU). This result seems to confirm the findings of section 4.1.1, that market prices are significantly higher in Asym-5 and Asym-Abs compared to Control. Age, gender, and probability numeracy become insignificant when excluding prices paid by buyers that are below the marginal cost of the live-seller.

25_{Probability numeracy is the ”ability to understand and process probabilistic concepts” (Dillingh,}

5

Altruistic Preferences

5.1

Dictator Game

We find that the average market price and average profits (when the market price is set at or above marginal cost) are highest when the live-seller donates a fixed part of the sales price received. This is a surprising result, as it is contrary to the predictions of the theoretical model. It could be that buyers in Asym-Abs are willing to pay a higher price because they are more altruistic than the buyers in the other treatments. We tested the altruistic preferences of buyers by letting them play a dictator game after the charity market game.26 All participants were assigned the role of dictator. Half of the dictators were assigned the role of ‘buyers’ in the charity market game, and half of the dictators were sellers in the main experiment. Dictators could divide a sum of 10 ECU between themselves and the receiver.

Figure 6 below shows the average amounts in ECU that the dictators allocated to the receivers in the dictator game per treatment and over all observations in the column ‘Total’.27 We are mainly interested in the degree of altruism of the buyers, and whether it can explain the surprising result that average profits (when market prices are at least equal to marginal cost) are highest in Asym-Abs. On average, buyers assigned the role of dictator have allocated 3.40 ECU to the receiver, with the highest amount observed in Asym-Abs (3.64 ECU) and the lowest amount in Control (3.20 ECU). The differences between the four treatments are not significant (One-Way-ANOVA p=0.919).28 _{The graph}

shows that the average allocation to the receiver is higher in the Asymmetric treatments, but not significantly higher (p>0.742). The average amounts allocated to the receiver also do not differ significantly among the Asymmetric treatments (p>0.684).29 _Hence,

26_{The exact procedure of this game can be found in Section 3.3.}

27_{Table 5 in Appendix B summarizes the descriptive statistics of the allocations to the receiver.} 28_{In this subsection, the reported p-values obtained from unpaired t -tests, unless stated otherwise.} 29_{On average, participants allocated a sum of 2.94 ECU to the receiver. This amount was highest in}

we cannot find evidence that, based on the allocations in the dictator game, buyers in Asym-Abs are more altruistic than the buyers in the other treatments.

Figure 6: Average Allocations in the Dictator Game (in ECU).

5.2

Self-Reported Charitable Behaviour

The charitable behaviour of the participants was also measured by including a question-naire at the end of the experiment.30 _{The percentage of participants who donate to}

different charities and to the Red Cross specifically on an annual basis is shown in Figure 7. In total, 28.33% does not donate to charity, with the highest share of participants not donating in Asym-5 (33.33%) and the lowest share in Asym-2 (21.43) (no significant differences among the four treatments, p=0.979).31 More than half of the participants who do donate to charities, donate to one or two charities on an annual basis (no signif-icant differences, p=1.000). In Asym-2, the share of participants donating to three to

The differences between the treatments are not significant (One-Way-ANOVA p=0.803). Compared to Control, average amounts given to the receiver are significantly lower in Asym-Abs (p=0.094). Among the Asymmetric treatments, the average amount allocated to the receiver is significantly lower in Asym-Abs compared to Asym-5 (p=0.067).

six different charities per year is larger than in Asym-Abs, but not significantly different (p=1.000). The share of participants donating to the Red Cross on an annual basis is largest in Asym-Abs (no significant differences between the treatments, p=0.447). Also, no significant differences are found among the Asymmetric treatments (p>0.253).

Figure 7: Share of participants donating to charities.

Figure 8 below shows the participant’s average scores on how much the Red Cross deserves their donation (0=not at all, 10=completely) and on how they would rank the Red Cross in terms of reputation (0=very bad, 10=excellent). The dark-blue bar (Red Cross deserves donations) presents the average score of the Red Cross on deserving the participant’s donation. The average scores do not differ significantly, neither compared to Control (One-Way-ANOVA p=0.227) nor among the Asymmetric treatments (p>0.593).32 _The

Figure 8: Average score of the Red Cross.

6

Discussion

in itself. A donation of 2% is, however, not profit-increasing relative to not donating to charity. It could be that buyers believe that a 2% donation of the sales price is too small, such that the sellers might as well not donate to charity. In this case, the bias leads to underestimation instead of overestimation of the part donated. However, the percentage of buyers purchasing the bundle (around 60%) in Asym-2 is not significantly lower. The average price set by the live-seller in Asym-2 does not deviate much from the the prices set in the other Asymmetric treatments, and is less volatile over the 15 trading periods (see Figures 9 and 10 in Appendix B). Hence, outliers do not seem to drive the results in Asym-2.

7

Conclusion

Commercial firms are increasingly tying the sales of their products with donations to charity. Apart from a charitable motive, offering hybrid bundles could be a strategic instrument for these firms to increase profits. The theoretical model shows that – given rational agents, complete markets and absent transaction cost – positive profits cannot be gained when selling a hybrid bundle, even not when accounting for consumer altruism (Andreoni 1990). We, however, hypothesize that consumers may suffer from a bias when evaluating hybrid bundles. Similar to the overweighing of small probabilities, consumers may overestimate the part donated to charity when purchasing hybrid bundles. We ex-pected that this bias would be larger when the percentages donated are smaller. Also, we expected a larger overestimation bias when the donation is framed as a percentage rather than as a fixed amount, as the relation between the amount paid and the part donated is less straightforward in that case.

A lab experiment was conducted to find out whether offering a hybrid bundle would lead to positive profits net of the donation to charity, and if so, which donation scheme would be most profitable. The experimental design aimed to distinguish between the different donation schemes. Whereas the seller offered only the private product in the control condition (Control), the hybrid bundle was offered in the treatment conditions. The treatment conditions differed in the amount and framing of the donation: a donation of 2% of the sales price (Asym-2), a donation of 5% of the sales price (Asym-5), and a donation of a fixed amount of 0.43 ECU (Asym-Abs).

are not more altruistic than in the other treatments. Average allocations by buyers to the receiver in the dictator game do not differ significantly between the treatments. As well, no differences in self-reported charitable behaviour can be found. A second reason for the higher profits in Asym-Abs could be that buyers dislike percentages or the effort they have to induce in order to translate percentages into amounts. However, the probability numeracy scores of the participants show that the subjects are equally able to understand and process probabilistic concepts. Moreover, positive profits gained in both Asym-2 and in Asym-5 seem to suggest that buyers do not dislike percentages in itself. A third reason could be that buyers believe that a donation of 2% of the sales price is too small, such that sellers could as well not donate. This would lead to an underestimation of the part donated to charity. However, the results indicate that the percentage of buyers purchasing from the live-seller does not differ between the treatments.

Although offering hybrid bundles thus seems a strategic instrument for firms to increase profits, average donations via the bundle are rather low in comparison with average private donations that buyers could make to the charity. Moreover, suggestive evidence is found that offering hybrid bundles causes crowding out behaviour of private donations: average private donations as well as total contributions to the charity are lower in case a hybrid bundle is sold to buyers.

References

Abrams, Eric, Martin Sefton, and Abdullah Yavas, “An Experimental Comparison of Two Search Models,” Economic Theory, 2000.

Andreoni, James, “Impure Altruism and Donations to Public Goods: A Theory of Warm-Glow Giving,” The Economic Journal, 1990.

and A. Abigail Payne, “Is crowding out due entirely to fundraising? Evidence from a panel of charities,” Journal of Public Economics, 2011.

Ariely, Dan, Anat Bracha, and Stephan Meier, “Doing Good or Doing Well? Image Motivation and Monetary Incentives in Behaving Prosocially,” The American Economic Review, 2009.

Dana, Jason, Roberto A. Weber, and Jason Xi Kuang, “Exploiting moral wiggle room: experi-ments demonstrating an illusory preference for fairness,” Economic Theory, 2007.

Davis, Douglas D. and Charles A. Holt, Experimental Economics, Princeton University Press, 1992. Dillingh, Rik, Peter Kooreman, and Jan Potters, “Probability Numeracy and Insurance Purchase.” Elfenbein, Daniel W. and Brian McManus, “A Greater Price for A Greater Good? Evidence that Consumers Pay More for Charity-Linked Products,” American Economic Journal: Economic Policy, 2010.

Frackenpohl, Gerrit and Gert P¨onitzsch, “Bundling Public with Private Goods,” 2013.

Gneezy, Ayelet, Uri Gneezy, Gerhard Riener, and Leif D. Nelson, “Pay-What-You-Want, Identity and Self-Signaling in Markets,” Proceedings of the National Academy of Sciences of the United States of America, 2012.

Kahneman, Daniel and Amos Tversky, “Prospect Theory: An Analysis of Decision under Risk,” Econometrica, 1979.

Smith, Scott M. and David S. Alcorn, “Cause marketing: a new direction in the marketing of corporate responsibility,” Journal of Consumer Marketing, 1991.

A

Participant’s Summary Statistics

Table 5: Participant’s summary statistics.

Control Asym-2 Asym-5 Asym-Abs Total

Demographics

Female (in %) 80 50 50 81.82 61.02

Observations 10 14 24 11 59

Age (in years)

Mean 22.60 22.50 23.00 23.27 22.86 SD 2.07 3.18 3.30 2.90 2.96 Minimum 19 18 18 20 18 Maximum 26 27 30 31 31 Observations 10 14 24 11 59 Charitable Behaviour Donate to different charities (in %)

Zero 30.00 21.43 33.33 25.00 28.33

One to Two 70.00 64.29 66.67 58.33 65.00

Three to Six 0.00 14.29 0.00 8.33 5.00

Six or More 0.00 0.00 0.00 8.33 1.67

Observations 10 14 24 12 60

Donate to Red Cross (in %) 0.00 7.14 4.35 20.00 7.14

Observations 9 14 23 10 56

Reputation Red Cross

Mean 7.70 7.86 7.58 7.75 7.70

SD 1.34 1.35 2.21 2.77 2.00

Minimum 5.00 5.00 0.00 0.00 0.00

Maximum 10.00 10.00 10.00 10.00 10.00

Observations 10 14 24 12 60

Red Cross deserves donation

Mean 7.00 7.71 7.29 7.25 7.33

SD 3.06 1.68 2.63 2.86 2.52

Minimum 0.00 4.00 0.00 0.00 0.00

Maximum 10.00 10.00 10.00 10.00 10.00

Observations 10 14 24 12 60

Probability Numeracy (in %) 50.00 100.00 79.17 58.33 75.00

Observations 10 14 24 12 60

B

Average Prices of the Live-Seller

Figure 9 shows the average price set by the live-seller in each period. Figure 10 depicts the average price set by the live-seller per period conditional on the buyer buying from the live-seller.

Figure 9: Average price of the live-seller.

C

Dictator Allocations

Table 6: Dictator’s allocation to the receiver (in ECU). Control Asym-2 Asym-5 Asym-Abs Total Buyers Mean 3.20 3.57 3.25 3.64 3.4 SD 2.17 1.72 1.76 2.14 1.81 Minimum 0.00 0.00 0.00 0.00 0.00 Maximum 5.00 5.00 5.00 5.00 5.00 Observations 5 7 12 6 30 Sellers Mean 3.20 1.93 3.08 1.33 2.48 SD 2.17 1.54 2.24 2.16 2.11 Minimum 0.00 0.00 0.00 0.00 0.00 Maximum 5.00 4.00 5.00 5.00 5.00 Observations 5 7 12 6 30 Total Mean 3.20 2.75 3.17 2.49 2.94 SD 2.04 1.78 1.98 2.38 2.00 Minimum 0.00 0.00 0.00 0.00 0.00 Maximum 5.00 5.00 5.00 5.00 5.00 Observations 10 14 24 12 60