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Essay text:
For any p p, we can rewrite the Nash bargaining condition by using the
equations (1) to (4) and the free entry condition Uf = 0 such like:
w = arg max
w
( p??w
r+ ) (w??rUw
r+ )1?? (6)
And ?nd the F.O.C w.r.t , we get the wage equation:
w(p;Uw) = (1 ?? )p + rUw (7)
From equation (7), we can see that the reservation wage w = p = rUw.
Moreover, the modi?ed unemployed value for workers will be
rUw = b + w Z rUw
[Vw(w(p;Uw)) ?? Uw] dG (p)
Since
1
Vw(w(p;Uw)) = (1?? )p+ rUw+Uw
r+
We have the ?nal expression for the unemployed value is
rUw = b + (1?? ) w
r+ Z rUw
[p ?? rUw] dG (p)
Since
p(w;Uw) = w?? rUw
(1?? )
Therefore, the density function of wages is given by
f(w) =
(1?? )??1g(p(w;Uw))
1??G(p) w p
0 w < p
(8)
where g(p) = G0(p)
1...
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