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Grossman Helpman (2001) - Special Interest Politics Chapters 4 And 5 (view source)
Revision as of 22:01, 26 April 2010
, 22:01, 26 April 2010→One Lobby - Continuous States
:<math>\theta_2 \ge 2\theta_1 +4\delta - \theta_{min}\,</math>
If the truth is in <math>\theta_2\,</math>, then the SIG would prefer to report this rather than <math>\theta_1\,</math> iif: :<math>(\theta_2 + \delta) - \frac{(\theta_1 + \theta_2)}{2} \le (\theta_1 + \delta) - \frac{(\theta_{min} + \theta_1)}{2}\,</math> This solves to: :<math>\theta_2 \le 2\theta_1 +4\delta - \theta_{min}\,</math> Putting these two together we have that: :<math>\theta_2 = 2\theta_1 +4\delta - \theta_{min}\,</math> Or more generally: :<math>\theta_j = 2\theta_{j-1} +4\delta - \theta_{j-2}\,</math> There are two boundaries where <math>\theta_n = \theta_{max}\,</math> and <math>\theta_0 = \theta_{min}\,</math>, which can be used together to solve the general solutions for <math>\theta_j\,</math>: :<math>\theta_j = \frac{j}{n}\theta_{max} +\frac{n-j}{n}\theta_{min} -j(n-j)\delta\,</math> Considering that <math>\theta_1 > \theta_{min}\,</math> it must be the case that: :<math>2n(n-1)\delta < \theta_{max} - \theta_{min}\,</math>
