Imitation in location choice

however, chooses a substantially larger quantity of information for Firm 1:
θ 1 = 1 - ¹ c∕σ_a² = ¹ + ¹ θ↑.                         (23)

¹         2 ^a 2    2¹

The expression above relates the central planner’s optimal value of θ1 to Firm 1’s own
choice in the decentralized regime, showing that the central planner always chooses
a larger value. This increase in information raises aggregate profits above the level
achieved in the decentralized case by the amount c(1+ log(1/2)). To gauge how large
a change in aggregate profits this would be in percentage terms, one needs to refer
to aggregate profit in the decentralized case: 2π0 — 2c + clog(c∕σ2}. Thus, the per-
centage change depends on the magnitude of c relative to π0, which can be adjusted
to achieve arbitrarily large percentage changes, provided c> 0, although only as a
possibility claim without compelling motivation. These formulas show that the level
of change in aggregate profits, as a measure of inefficiency based on the thought ex-
periment of moving from decentralized to centralized regimes, is proportional to the
cost-of-information parameter c. Therefore, inefficiency is most severe when informa-
tion acquisition is expensive, and least severe when it is cheap. This claim depends
critically on specification of C (θ), as the next section shows aggregate efficiency to
be nonmonotonic in c when the cost function is quadratic.

2.4 Quadratic cost of information

While the case of absolute imitation nicely represents the real-world phenomenon
of imitation and the complete absence of any cost-benefit analysis of unoccupied
locations, the intermediate case is interesting as well, where Firm 2 conditions on
Firm 1’s location but also acquires private information. The remaining analysis in
the paper relies on the following quadratic specification of the cost-of-information
function:

C(θ) = cθ²∕2.                                   (24)

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