Imitation in location choice

can go in either direction in response to a drop in the cost of information. When
information is very expensive, neither firm acquires much information and both locate
near the unconditional mean μ_a. Because Firm 1’s information reduces the marginal
benefit of Firm 2’s information in all cases, Firm 2 acquires even less information than
Firm 1, weighting Firm 1’s location more than its own signal. At the other extreme
when information is very cheap, Firm 1 acquires so much of the available information
about good locations that Firm 2 receives little marginal benefit from its own private
information. In this case, the reduction in Firm 2’s marginal benefit of information
dominates its increase in demand owing to lower acquisition costs.

The variable θ; provides one natural (inverse) measure of the magnitude of imita-
tion, because it represents the extent to which Firm 2 collects private information (i.e.,
not imitating Firm 1). Alternatively, the magnitude of imitation could be quantified
by the squared distance between the firms’ locations:

( y2 - y ; )2 = [⁽1 I θ 1θθ 2 ]²( x 2 - θ 1 x 1)2.                        (29)

which, in expectation, equals:

E[(y2 - y2)²] = θ2(1 - θ 1)2σ²2/(1 - θ 1 θ2)•                     (30)

The distance between the firms’ locations is small when θ2 is near zero or θ1 is near
1. The expected distance given by the square root of the expression in (30) reaches a
maximum of 30 percent of the standard error σa. If σa is interpreted as the average
distance of the ideal location from its unconditional mean, then with this parameteri-
zation, firms will on average be closer to each other than the ideal location is from its
mean. Another point of interest not directly observable in Figure 1 is that the central
planner’s solution always prescribes more total information than in the decentralized
case. That is, the sum of quantities of information, θ1 + θ2, chosen by the planner
is always greater than in the decentralized economy, with a maximum difference of

18

<<   17   18   19   20   21   22   23   >>

More intriguing information