From both WTP and chosen quantities, we expand our analysis computing the variation in demand for beef coming from providing information. Since the market for soy burgers is still small, we do not account for any market adjustments related to plant-based products. As seen by Foster and Just (1989), the value of information is a welfare estimation related to the demand shift. The methodology we apply is an extension of the one developed by Marette, Roosen, and Blanchemanche (2008) and Lusk and Marette (2010), and it only takes into account the relative variation of WTP. Differently from previous works on estimating the value of information, we take into account two effects for calibrating the demand shifts: the relative variations of WTP and the relative variations of quantities. We consider the following simple demand for beef by a representative consumer *i*, namely

${q}_{i}^{D}(p,I)=A[Id+(1-I+Iz)\times p{]}^{\u03f5}$(2)

where: *p* is the price of beef; $\u03f5$ the direct-price elasticity; *A, d* and *z* are parameters; *I* represents the level of information. If the consumer *i* is not aware of messages/characteristics at the time of the purchase, then *I* = 0. Conversely, *I* = 1 means that the consumer is aware of the characteristic(s) and this awareness affects his consumption choice. The inverse demand is given by:

$p\left({q}_{i},I\right){=}^{\left({\left[{q}_{i}/A\right]}^{1/}-Id\right)}{/}_{\left(1-I+Iz\right)}$(3)

The demand function (2) can be calibrated with market variables, such that it represents the per capita average monthly demand of beef burger. As a proxy of the equilibrium price, we used the average market price *P*_{R} observed in several supermarkets in Lombardy at the time of the experiment. More precisely, we use the average value of observed prices for a beef burger (as in Figure 1) using a sample of 20 prices collected at different points of sale. We estimate the average per capita monthly consumption of ground beef *E(q)* using the values declared by participants in the exit questionnaire.^{5} Using *P*_{R} we first calibrate the demand ${q}_{i}^{D}\left(p,I\right)$ under the assumption *I* = 0, meaning when no additional messages, as the ones provided during the experiment, are revealed to consumers. This calibrated demand ${q}_{i}^{D}\left(p,I\right)$ represents the average monthly consumption per participant of ground beef *E*(*q*). With *E*(*q*), *P*_{R} and $\u03f5$ introduced in eq. (2) and with *I = 0*, the parameter *A* is calibrated for satisfying eq. (2) and is equal to $E\left(q\right)=A{\left[{P}_{R}\right]}^{\u03f5}$.

The parameters *d* and *z* are estimated with the variations in WTP and chosen quantities estimated in the lab. We restrict our estimation to a Marshallian approximation of demand variations.^{6} First, let us consider values $\text{WTP}i1$ and $\text{WTP}i2$ indicating participant *i*'s WTP before and after the complete revelation of information, namely after round #5. The relative variation in average WTP provides a first measure of the inverse demand shift, $\omega =\left[E(\text{WTP}2)-E(\text{WTP}1)\right]/E(\text{WTP}1)$, where *E*(.) denotes the overall expected value considering all participants. The WTP represents the maximum amount of money that a consumer is ready to pay for one unit of product, which means that from eq. (3), WTP gives information about *p*(*1,I*_{i}), namely when one unit is purchased (i. e. *q*_{i} = 1). The relative variation of WTP coming from the revelation of information in the lab gives an estimation of the relative variation of the price *p*(*1,I*_{i}) related to the information. In eq. (4) introduced below, the price under the absence of information is equal to *p*(*1,0*), and the price with complete information is equal to *p*(*1,1*), with *p*(*q*_{i},I_{i}) given by (3).

The relative variation in average chosen quantities is $\delta =\left[E(X2)-E(X1)\right]/E(X1)$, where values ${\text{X}}_{\text{1}}^{i}$ and ${\text{X}}_{\text{2}}^{i}$ indicates participants *i*'s quantity choice of a product before and after the complete revelation of information. We assume that, when making quantity choices, consumers perceive the average price *P*_{R} as the market and equilibrium price of beef (see Appendix B). This relative shift in quantities represents the possible demand shift given by (4) at the equilibrium price *P*_{R}. From eq. (2), the purchased quantity at the price *P*_{R} and under the absence of information is equal to ${q}_{i}^{D}\left({P}_{R},0\right)$, and the purchased quantity with information is equal to ${q}_{i}^{D}\left({P}_{R},1\right)$. The values *d* and *z* are given by solving the following system of eq. (4), accounting for both the relative variations of prices and quantities due to the revelation of messages:

$\{\begin{array}{c}\frac{p(1,1)-p(1,0)}{p(1,0)}=\omega \\ \frac{{q}_{i}^{D}\left({P}_{R},1\right)-{q}_{i}^{D}\left({P}_{R},0\right)}{{q}_{i}^{D}\left({P}_{R},0\right)}=\delta \end{array}$(4)

Figure 3 shows the demand shift related to equations of the system (4) when information about beef and soy is revealed. Following the standard convention, price is measured on the vertical axis and quantity on the horizontal axis. The equilibrium price is represented by ${P}_{R}^{}$. The initial demand is represented by the line *p*(*q*_{i},0). For *I* = 0, the purchased quantity by a consumer *i* is ${q}_{i}^{D}\left({P}_{R},0\right)=E\left(q\right)$, where $E\left(q\right)$ is the average monthly consumption of ground beef used for the calibration. The information leads to a decline of the demand from *p*(*q*_{i},0) to *p*(*q*_{i},1). This demand shift is calibrated with eq. (4) and is detailed in Figure 3 where parameters *ω* and *δ* are represented.

Figure 3: Beef demand shift and the value of information.

From Figure 3, we are interested on estimating these two values: (a) the price premium *μ* at the equilibrium point, where *μ* most likely differs from the WTP variation for a unit quantity; (b) the value of information, given by the area *FEG*, that represents the welfare gain from being informed and shifting consumption from ${q}_{i}^{D}\left({P}_{R},0\right)$ to ${q}_{i}^{D}\left({P}_{R},1\right)$ (Foster and Just 1989).

presents the data we use for the estimation and the results. More precisely, the top of provides the market parameters and some results coming from the lab experiment. The relative variations $\omega $ and *δ* indicated in Figure 3 and in eq. (4) come from the revelation of all messages in the lab, namely between stage #1 and stage #5, as indicated at the top of .

Table 7: Parameters for calibrating the welfare variation in Italy.

Results are presented in the bottom panel of . These results related to Figure 3 are computed with a *Mathematica®* program given in Appendix C. The negative premium for beef at the initial equilibrium point of the demand function is quite significant with $\mu /{P}_{R}$ equal to –0.280; this value is much higher than the relative variation of the WTP for one unit of product (ω = −0.015) as presented in Figure 3. The value of information is relatively low, since it represents 3.49% of the initial expenditure for beef, computed as the product of price and purchased quantity. Moreover, as also suggested by Figure 3, the value of information strongly depends on the shape of the demand function. The value of information (*FEG)* can eventually be generalized and extrapolated to the whole Italian population. Knowing the value of information for the whole Italian population can be helpful to carry out a cost-benefit analysis comparing it to the cost of revealing information.

Even if the value of information equal to €0.287 in is relatively low, it is still higher than the alternative value that could be computed by omitting the relative changes in the chosen quantity $\delta $, as presented in (3). Omitting $\delta $, once the parameter *z* = 0 in eqs. (2) and (3), and with only the first line of eq. (4), the estimated value of information would be 11 times lower. In other words, abstracting from the relative changes in the chosen quantity $\delta $ would lead to a significant underestimation of the value of information, with consequences for cost-benefit analyses.

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