(a) μ = 0.8
(b) μ = 0. 1
Figure 2: The influence of lower search cost c on expected price (N = 2)
condition v - E [p] - c = 0. To understand the underlying economic forces of this result, we first
note that an increase in μ has in principle a pro-competitive effect. Keeping the search intensity
of non-shoppers constant, firms would tend to charge lower prices with higher probability as there
are relatively more shoppers. However, a change in μ also affects θ 1. To see this, one can apply the
implicit function theorem to equation (14) to obtain
which means that an increase in μ results in an increase in the search intensity of the non-shoppers
θ1 . This is obviously due to the fact that more informed consumers in the market makes searching
more attractive for the non-shoppers, as the former buyers put pressure on firms to reduce prices.
A higher search intensity of non-shoppers in turn gives firms incentives to increase prices, since
non-shoppers do not compare prices. Interestingly, these two opposite forces offset each other so
that expected price remains constant.
dθ ι
dμ
N f 1 (1 -y ) N -1
(1 — μ)2θ 1 0 1 I Nμ(1 -y)N-1 2
1+ θ 1(1 -μ )
Nμ Γ1 (1—y ) N -1
-(1 -μ)θ2 0 1 , Nμ(1 -y)N-1 2
1+ θ 1(1 -μ )
μ (1 ^^ μ ) ’
(15)
If non-shoppers search for one price for sure, the pro-competitive effects of an increase in μ
mentioned above are strengthened by the fact that the reservation price ρ decreases in μ and thus
expected prices fall (cf., Stahl (1989)). These remarks are gathered and illustrated in Figure 3.
Figure 3(a) simulates an economy where product’s valuation is relatively low compared to search
cost (c/v = 0.5). The figure depicts expected price-to-cost margins as a function of μ. As Φ(1; μ; N)
is decreasing in μ ,it easily follows that for a given N and c/v, there is a unique b such that inequality
11
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