equilibrium with partial participation.
|
Partial consumer |
Full consumer parti- | |||
|
θ1 |
E [p] |
ρ |
E [P ] | |
|
J c |
↑ |
↑ |
J |
J |
|
↑ μ |
↑ |
- |
J |
J |
|
↑v |
↑ |
↑ |
_ |
_ |
|
↑N |
J |
_ |
↑ |
↑ |
Table 1: Summary of comparative statics results
a. The effects of a reduction in search cost c
The first result we want to emphasize is that a reduction in search cost leads to an increase in the
expected price in an equilibrium with partial consumer participation. This follows immediately
from the equilibrium condition v - E [p] - c = 0. To understand the intuition behind this result
let us point out that, as Figure 1 shows, the intensity with which non-shoppers search in this type
of equilibrium rises as c falls. Note further that these consumers are precisely those who do not
exercise price comparisons, and thus they are prepared to accept higher prices. Consequently, a
fall in c increases sellers’ incentives to charge higher prices more frequently, which in turn raises
the expected price.
When c decreases more, the equilibrium will change into one of full participation. Under full
participation, a decline in c results in a fall in the reservation price ρ (cf., Stahl (1989)). Inspection
of the equilibrium price distribution reveals that F increases as ρ decreases (see Proposition 1). As
a result, expected price decreases in c.
These observations regarding the influence of a reduction in search cost on expected price-to-
cost margins are gathered in Figure 2. In Figure 2(a) we have simulated an economy where the
number of informed consumers is large (μ = 0.8). This graph depicts expected price as a function
of relative search cost and illustrates the comparative statics analysis given above. When there
are few shoppers (μ = 0.1) expected price decreases in search cost for almost the entire parameter
region (cf., Figure 2(b)). This is because for this parameter constellation the economy is most likely
to be in an equilibrium with partial consumer participation.
b. The effects of an increase in the proportion of shoppers μ
We next consider the effects of an increase in μ. Under partial participation, a change in the number
of shoppers does not influence expected price-to-cost margins as nothing changes to the equilibrium
10