Experimental Evidence of Risk Aversion in Consumer Markets: The Case of Beef Tenderness

list L_k = (p₁^k,..., p_T^k) with p_t^k ≥ 0 ∀t and ∑_ι pt = 1, where pt is the probability of tenderness t
occurring in lottery k.

Quality V can be viewed as a simple lottery or as a compound lottery. A compound lottery, L^C,
is the risky alternative that yields the simple lottery Lt with probability αt. Quality V may be described
as a compound lottery of the simple lotteries A, B, and C or LV = ( LA, LB, LC;a_A,a_B,a_C) with
α_k ≥ 0 ∀k and ∑ α_k = 1. The compound lottery LV can be reduced to the simple

lottery L_V = (p₁^V,...,p_T^V) , with the same ultimate distribution of tenderness probabilities. That is, the
probability of outcome t in the reduced lottery is p_t^V = α_A p_t^A + α_B p_t^B + α_C p_t^C . Whether the
probabilities of various outcomes arise as a result of a simple lottery or of a more complex compound
lottery has no significance, i.e., the simple lottery LV is equally good as the compound lottery
L^C_V= (L_A,L_B,L_C;0.25,0.50,0.25) .

Assuming that a participant’s preferences are represented by a von Neumann-Morgenstern
utility function, the expected utility of the simple lottery LV, EU(LV), is

(1)            EU ( L_v) = EU ( LV) = 0.25 ∙ U ( LA) + 0.50 ∙ U ( LB) + 0.25 ∙ U ( LC).

The first equality states that the simple lottery is equally good as the compound lottery and the second
equality states that the expected utility is equal to the weighted average of the utilities of the simple
lotteries LA, LB, and LC with the probabilities of these lotteries as weights.

The certainty equivalent of a lottery, CE(L), is the amount of money obtained with certainty
that gives the same expected utility as the lottery. In an incentive compatible auction, a participant’s
bid for a lottery equals his or her CE of the lottery, or

(2)            Bid(k) = CE(L_k).

The expected value of a lottery is the weighted average of the monetary values associated with
the possible outcomes using the probability of each outcome as weights. In our case, the expected
value of quality V, EV(L_V),is the weighted average of the CEs for the qualities A, B, and C using the
probabilities of each quality as weights

(3)           EV(L_V)=EV(L^C_V)=0.25∙CE(L_A)+0.50∙CE(L_B)+0.25∙CE(L_C).

A risk-averse participant will bid less for a lottery than the expected value, a risk-neutral
participant will bid the expected value, and a risk-seeking participant will bid more than the expected
value. We calculate two measures of risk aversion. First, we calculate each participant’s risk premium
for the uncategorized generic beef by subtracting his or her bid for V from the expected value of V:
(4)           Risk premium = EV(L_V ) - Bid(V).

Second, we calculate each participant’s risk ratio by dividing his or her bid for V by the
expected value of V:

(5)           Risk ratio=Bid(V)/EV(L_V).

A risk ratio of less than one implies risk aversion, a ratio equal to one implies risk neutrality and a
ratio larger than one implies risk-seeking behavior (Di Mauro and Maffioletti, 2004).

Results

Tenderness

Table 2 presents the mean bids and their standard deviations. Columns H1 and H2 present the results
of the two hypothetical auction trails. Columns R1 and R2 present the results of the non-hypothetical
real trials conducted before tasting, while columns R3 and R4 present the results of the real trials
conducted after tasting.

As expected, participants are willing to pay more for tender beef. In R1 and R2, the mean bid
for A was 17% higher and the mean bid for C was 24% lower than the mean bid for B. In the two trials
after the tasting, the mean bid for A was 21% higher and the mean bid for C was 19% lower than the
mean bid for B. Furthermore, the mean bid for A, B, and C was 31%, 12%, and -15%, respectively,
higher than the mean bid for V in R1 and R2, and 27%, 6%, and -14% higher in R3 and R4. All these

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