A Note on Costly Sequential Search and Oligopoly Pricing (new title: Truly Costly Sequential Search and Oligopolistic Pricing,)

Figure 3: The influence of μ on expected price (N = 2).

(10) holds with equality. Therefore, the market equilibrium exhibits partial participation when μ
lies in the interval (0,μ) and it exhibits full participation when μ lies in the interval (b, 1). It
is straightforward to see that, starting from an equilibrium with full consumer participation, as
μ → 0 the economy eventually moves into an equilibrium with only partial participation so the
Diamond result cannot arise in our model. In Figure 3(b) we have simulated an economy where
search cost is relatively low (c/v = 0.05). The only difference is that the region of parameters for
which consumers search for one price with probability 1 is much larger than before.

c. The effects of an increase in the value of the purchase v

We next briefly focus on changes in v . For convenience we shall graph expected price against c/v .
The main difference with the (reverse) effects of a change in c, is that under full participation c
affects ρ, whereas v does not affect ρ. So, the only difference with case a. is that now when buyers
search for one price for sure, an increase in v does not alter the reservation price of the non-shoppers
ρ so expected margins remain unchanged.

The graphs of Figure 4 show the influence of an increase in v on expected prices. Figure 4(a)
simulates an economy where search costs and the number of informed consumers are relatively high
(c = 0.5 and μ = 0.8). When c/v lies in the interval (Φ(1), 1), non-shoppers do not participate
in the market surely. In this parameter area, the expected margin rises as v increases. When c/v
is between 0 and Φ(1), non-shoppers search for one price with probability 1. For this region of
parameters expected margins are unaffected by a change in v. Figure 4(b) shows the case of an
economy with relatively few shoppers.

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