# 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 щ_{2} = 1 — *щ _{1}.* 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.