Eliciting Non-hypothetical Willingness-to-pay for Novel Products: An Application to Cultured Meat

Abstract

Estimating the demand for greener products may be challenging when these products are not yet on the market. We design an experiment to elicit the willingness-to-pay (WTP) for a novel product in a non-hypothetical way, despite the fact that the product is not marketed and thus cannot be delivered to participants. We consider a cultured meat product which is presented to participants using the producer’s advertising. The basic experimental device consists in eliciting (i) how much a participant is willing to pay for the product under uncertainty about product delivery, and (ii) her beliefs about the probability that the product will be actually delivered. In our sample of 158 French students, under 20% of participants never want to buy the product, and below 10% assign a probability of zero that the product will be delivered if purchased. The average WTP is fairly low, at about 3 Euros per 100 g. A number of factors increase (e.g., education and low meat consumption) or decrease (e.g., neophobia and disgust) this WTP. The simple exposure to the new meat substitute during this experiment reduces subjects’ pro-meat justifications. We investigate the external validity of our results using a hypothetical survey on a representative sample (N = 1200). We also discuss methodological issues such as deception and incentive compatibility.

Appendix: Theory background and methodology

1.1 Eliciting the WTP for a new product

The object of the experiment is to elicit a subject’s WTP for a new product. The subject receives income w for her participation in the experiment, and can use that income to buy the product. The originality of the experiment is that the WTP is elicited under uncertainty about whether the product will be delivered. That is, there are two scenarios: either the product is delivered or it is not. One scenario was selected before the experiment, but the subject does not know which. We assume that the subject is an expected-utility maximizer, and that she holds a subjective probability p regarding the product-delivery scenario.

In the first step, the subject faces a list of prices at which the product can be bought or not, given that only one price will be randomly selected. Under expected utility, this decision problem amounts to report a cutoff value so that the subject buys the product if and only if the price is below that value (Karni and Safra 1987). Therefore, when facing a sequence of binary choices as in our experiment, the subject conditionally agrees for each choice to buy the product if and only if the drawn price is below this cutoff value. Formally, a price c is drawn from a distribution F(.), the subject reports a cutoff value v, and she buys the product at price c if $v>c$; otherwise she does not buy the product. If the product is not bought, the utility of current income is $u_{0}(w)$; otherwise it is $u_{1}(w-c)$. We assume that both utilities $u_{1}$ and $u_{0}$ are strictly-increasing and twice-differentiable. Crucially, this value is elicited under delivery contingency. That is, the subject knows that the product may not be delivered even if she "buys" it. As such, under the non-delivery scenario, the subject does not pay anything and does not receive the product, even if $v>c$.

The subject’s problem is then given by choosing the value v maximizing expected utility:

$$\begin{aligned} \max _{v}p\left[\int ^{v}u_{1}(w-c)dF(c)+\int _{v}u_{0}(w)dF(c)\right]+(1-p)u_{0}(w), \end{aligned}$$

which, under $p>0$, has the following first-order condition (FOC):

$$\begin{aligned} u_{1}(w-v^{*})=u_{0}(w), \end{aligned}$$

so that revealing the true WTP $v^{*}$ for the product is the best strategy for the subject despite the uncertainty about product delivery. Note also that $v^{*}$ does not depend on F(.), as is well known. If the subject holds subjective beliefs $p>0$, the WTP elicitation mechanism is incentive compatible in a "strict" sense; i.e. the subject strictly prefers to report the true value $v^{*}$ than anything else.

Hence, for incentive compatibility, we only require that the subjective probability of delivery is strictly positive. Note that if this probability is replaced by a nondegenerate random variable and ambiguity attitude toward this probability is introduced, this should not change that prediction (and thus the incentive compatibility property) for common smooth ambiguity aversion theories.

1.2 Eliciting the Probability that the Product will be Delivered

We now want to elicit the participant’s subjective probability p. In a second step, namely after $v^{*}$ has been elicited, and after the price c has been drawn and revealed to the subject, we use a scoring rule to elicit the subject’s beliefs about the probability of the (non)delivery scenario.

The scoring rule provides financial payments Sj, with $j=0,1$ contingent on the realization of each scenario. The subject reports a probability $\alpha$ that the product will be delivered; this corresponds to the proportion of tokens chosen by the subject in the experiment. Formally, the subject receives $S_{1}(\alpha )$ if the product is delivered and $S_{0}(\alpha )$ otherwise. The subject’s problem is then to maximize her expected utility over $\alpha$ in [0, 1]:

$$\begin{aligned} pv(w+S_{1}(\alpha ))+(1-p)u_{0}(w+S_{0}(\alpha )), \end{aligned}$$

where the utility function v(w) is either $u_{1}(w-c)$ or $u_{0}(w)$, depending on whether the product was purchased in the first step. Note that since $u_{1}(.)$ or $u_{0}(.)$ are strictly increasing, so is v(.).

From Armantier and Treich (2013), we know that for any "proper" scoring rule (including the quadratic scoring rule we used here), the derivative of the objective above is

$$\begin{aligned} p(1-\alpha )v'(w+S_{1}(\alpha ))-(1-p)\alpha u_{0}'(w+S_{0}(\alpha )). \end{aligned}$$

It is immediate from this last expression that $p=0$ if and only if $\alpha =0$. Indeed, when $p=0$, this expression is always negative and the objective is thus maximized at $\alpha =0$. Moreover, when $\alpha =0$ this last expression is always positive, weakly so when $p=0$, implying that $\alpha =0$ cannot maximize the objective unless $p=0$. This simple result, which generalizes Proposition 3 in Harrison et al. (2017), thus predicts that if we observe $\alpha >0$ in the experiment then $p>0$, and in turn the WTP elicitation mechanism is incentive-compatible. This is our main theoretical prediction.

1.3 Methodological Discussion: Risk Preferences and Stakes

In Sect. 5, we discuss the possibility that risk preferences and stakes increase the number of zero-token participants, i.e. those who report $\alpha =0$. We note first that, in theory, risk preferences and stakes should not affect the main prediction above, which holds for any proper scoring rule and any increasing utility functions. However, this is not the case in practice as the scoring rules implemented in the lab are typically discrete. In our experiment, subjects bet tokens: Since betting only one token on the delivery scenario corresponds to a 0.1 probability, subjects may rationally make a zero-token choice when they hold sufficiently-small subjective probabilities. Moreover, the point that we emphasize below is that this zero-token choice can be more attractive under some forms of risk preferences and some types of stakes.

We first discuss the impact of risk preferences. Assume that the product is not delivered, i.e. $v(w)=u_{0}(w)$, so that utility and income are the same in each scenario, meaning that the subject has no stake. We then know from Proposition 4 in Harrison et al. (2017) that the subject reports more-central (respectively more-extreme) beliefs than p if she is risk-averse (risk-loving). Importantly, this implies that risk aversion cannot inflate the number of zero-token participants, as we state in the main text. However, risk loving leads to a bias with beliefs being reported toward the extremes, including $\alpha =0$ possibly under a discrete scoring rule, even for fairly intermediate subjective probabilities p. A numerical example is sufficient to illustrate. Assume that the quadratic scoring rule is used as in our experiment, and that $u_0(w)=(k+w)^2$ with $k>0$, so that risk loving $u_0''(w)/u_0'(w)=1/(k+w)$ falls with k. It is then easy to see that the optimal reported probability tends to zero as k tends to zero provided that $p<1/3$.²⁷

We now discuss the impact of stakes. Assume that the subject has bought the new product, i.e. $v(w)=u_{1}(w-c)$, so that utility is state-dependent and the subject has a stake. To illustrate the discussion, we will consider two specific forms of utility functions. First, assume quasi-linear utility $u_{1}(w-c)=u_0(w-c)+k$, where $u_0$ is the utility of income and k the hedonic utility derived from buying the product. In this case, the FOC is

$$\begin{aligned} p(1-\alpha )u_0'(w-c+S_{1}(\alpha ))-(1-p)\alpha u_{0}'(w+S_{0}(\alpha ))=0, \end{aligned}$$

implying that c plays exactly the role of a financial stake. Hence, we know from Armantier and Treich (2013) that the optimal reporting strategy $\alpha$ always increases with c under risk aversion. This is because the scoring rule serves as an insurance to compensate for the loss of income due to the payment of the product. This implies that the presence of stakes cannot increase the number of zero-token participants, and instead risk aversion distorts belief-reporting in favor of the product-delivery scenario.²⁸

Second, assume $u_{1}(w-c)=u_0(w-c+k)$, so that the benefit of buying the product is commensurable with income and has a monetary value of k for the subject. Moreover, note that the subject has a stake in the belief-elicitation task only if she buys the product at the current price, implying $k>c$. Again, we know from Armantier and Treich (2013) that this implies that buying the product strictly increases income and thus reduces marginal utility in the delivery scenario, thus providing an incentive to reduce $\alpha$ under risk aversion. Moreover, if this effect is strong enough a risk-averse subject facing a discrete scoring rule may rationally report $\alpha =0$ for hedging motives even if she holds a strictly positive subjective probability $p>0$. In this case, the effect of a stake can thus potentially inflate the number of zero-token subjects.

To sum up, we have illustrated theoretically a number of cases where the number of zero-token participants may, or may not, increase under a discrete scoring rule due to risk preferences and stakes. As a result, and in particular when the number of zero-token participants is high, it may be a good idea for the analysis of the experimental outcomes to further explore statistically the role of risk preferences and stakes, as we propose in Sect. 5.