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Policy multiplier in binary choice: model 2

More realistically, consider the following model. A total of N agents adopt one of two production technologies. One produces y* per agent, and the other y per agent per period, where y < y*. The total output per period is

where x = n/N is the fraction of agents which chose the more efficient technology. Stochastically one of (N — n) agent changes its choice at the rate

or one of n agents changes its choice at the rate

where щ (x) = exp( fg (x)) and щ2 = 1 — щ1. Here g(x) is the policy multiplier. Policymaker wants to persuade agents to switch to using the high-yielding technique.

In Aoki and Yoshikawa (2007, s. 4.2) it is shown that the parameter b is к/ф(x), к >0, which is a constant, where ф(х) is the standard deviation associated with this binary choice situation. Changing to g (x) to g (x)+h (x) by policymaker has the multiplier

is shown where the coefficient of variation is СУ(ф) = o-(x) /g(x).

As the CV grows, the fraction x tends to 1/2, that is, no policy effects in attempting to increase output.

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