
v
t
(1.0,1.0)
(1.0,1.5) (3.0,1.5)
(3.0,1.0)
(a) Example (A) Product Types, s = 0.4
v
t
(1.0,1.0)
(1.0,1.1) (3.0,1.1)
(3.0,1.0)
(b) Example (B) Product Types, s = 0.2
Figure 3: Numerical Examples: Product Types
product prices are solved from equations 13, 14, and 15. Specifically, y
00∗
= 0.627 in example (A) and y
00∗
=
1.515 in example (B); the prices of the four product types (p
∗
v,t
, p
∗
v,t
, p
∗
v,t
, p
∗
v,t
) = (0.686,0.936,1.686,1.936)
in example (A) and (p
∗
v,t
, p
∗
v,t
, p
∗
v,t
, p
∗
v,t
) = (0.243, 0.293, 1.243, 1.293) in example (B). So in terms of price
the ordering of the four types in both examples is (v,t) > (v,t) > (v,t) > (v,t), as shown in the price panels
of Figure 4 and Figure 5. Further, the conditional probability of choosing each of the four product types
can be calculated using equations 16 and 17: (q
∗
v,t
,q
∗
v,t
,q
∗
v,t
,q
∗
v,t
) = (0.343,0.312,0.843,0.645) in example
(A) and (q
∗
v,t
,q
∗
v,t
,q
∗
v,t
,q
∗
v,t
) = (0.121,0.133,0.621,0.588) in example (B). Note that the expected sales are
proportional to these conditional probabilities, so the ordering of the four product types in terms of sales is
(v,t) > (v,t) > (v,t) > (v,t) for example (A) and (v,t) > (v,t) > (v,t) > (v,t) for example (B). We illustrate
these orderings in the sales panels of Figure 4 and Figure 5 respectively.
Consider product selection for recommendation. For each of the four product types, we calculate the
expected industry profit and consumer surplus when a product of that type is recommended by the plat-
form. In example (A), the expected industry profits with recommendation are (1.216, 1.319, 1.656, 1.779)
and the expected consumer surpluses are (0.345,0.373,0.938,0.852). In example (B), the expected indus-
try profits with recommendation are (0.990,0.987,1.186,1.211) and the expected consumer surpluses are
(1.329,1.334,1.701,1.694). Thus, if the objective is to maximize total producer profits, the ordering of the
product types is (v,t) > (v,t) > (v,t) > (v,t) for example (A) and (v,t) > (v,t) > (v,t) > (v,t) for example
(B). These orderings are shown in the producer profit panels of Figure 4 and Figure 5. If the objective is
to increase expected consumer surplus, the ordering of the product types is (v,t) > (v,t) > (v,t) > (v,t) for
both examples. These orderings are shown in the consumer surplus panels of Figure 4 and Figure 5.
Two observations demonstrate our theoretical results in the previous section. First, as is shown in the
lower panels of Figure 4 and Figure 5, when conditioning on quality, which taste dispersion type is better for
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