Imitation in location choice

information is strictly positive, although strictly less than Firm 1’s demand for infor-
mation: 0 < θ⅛ < θ↑. In this case, Firm 2’s location choice rule can be described as
“partial imitation” because Firm 2 chooses a location near, although not exactly the
same, as Firm 1. Firm 2’s choice of location depends in part on its private signal x2.
Partial imitation implies that y2 and y1 are closer than they would be if both firm’s
relied only on private information.

Figure 1 shows individually profit-maximizing levels of information (i.e., θ↑ and
θ2 ), chosen by Firms 1 and 2 respectively, for the entire range of (inverse) information
costs. The figure also shows aggregate profit, π ₁(y↑, θ↑)+ π₂(y⅛, θ2), in the centralized
(topmost curve) and decentralized (second curve from the top) cases. The gap be-
tween the two aggregate profit curves, which varies nonmonotonically over the range
of information costs, provides one measure of the social cost of imitation. Comparison
of the this gap at the extremes versus middle of the range of information costs reveals
an interesting nonmonotonicity for the quadratic specification of C (θ): the social cost
of imitation is negligible in environments where information is either very scarce or
very abundant, and maximal in the intermediate range of information costs.

This result is different than what was reported above for the exponential cost
function. For exponential costs, the cost parameter was bounded from above and,
even for cost parameters where neither firm acquired information in the decentralized
case, the central planner would always demand a minimum of θ1 = 1/2. Thus,
the gap between centralized and decentralized aggregate profits was maximal where
information costs were highest. In contrast, for the case of quadratic costs, if the cost
parameter is high enough that neither firm demands information, then it does not
pay for the central planner to acquire any information either.

Another interesting feature of Figure 1 is nonmonotonicity of θ2. Whereas Firm
1 always demands more information as c falls, Firm 2’s demand for information

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