By Yoram Weiss, Gideon Fishelson

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**Extra resources for Advances in the Theory and Measurement of Unemployment**

**Example text**

Also, it can be seen that the (2,2) type receives a higher payoff. Indeed UI (Jt 4 Ib) + oVo (2,2) = ~ [1+ov o (2,2) -OEVf] > w(1,0) The solution for the bargaining problem with t types of player 1 may be obtained by investigating the above solution. Notice that the best feasible outcome for all types of player 1 is which is implemented by Jt I (or by having player 1 pay oEvf and player 2 pay 1-0Evf independently of the state). Also, the best feasible outcome for the firm (for E sufficiently small) is {O, 0, ...

2 Let {Vo(k)}k~O' vo(k)E [0,1] for every k, be given. Then, Vf has a unique solution. 9) we may obtain vf(k) = A(k) p(k)y - A(k). 11) where A(k) = 1/[y+ l-yO(I-p(k) )-0], and A(k) = A(k)yo [vo(k) (l-p(k»v o(k+l)]. 12) Now, yA(k) is increasing in 0, and, at 0=1, yA(k) = 1/p(k). Therefore, yA is bounded by 1/p(a). Also, since vo(k)E [1,0] for every k, then A(k) is bounded by b/p(a). It thus follows that: E, { Also, Ee ~ 9, A(k)yp(k)] } < E, { ~ 9, [ ~~~; I} {~ad -A(k)]} < O/p(a). 12). D. For any value of Vf we have unique values for vo(k), and for every sequence {vik)} we have a unique solution for Vf.

11) 8,p(t, O)}. By substituting for A we may obtain A' = A = [1 - OEe{L 8t (l-p(t, O))} - (0/2)a]-1 (I-A) - (0/2)a , Now, Ee , 8, (l-p(t, {~ O))} = Ee {~, 8t} - a =1- a. '=----1-0+(o/2)a It is easy to see that a = Ee {~8tp(t, O)} ~ Ee {~8t} = 1. Hence, A' is 44 Search Unemployment: Theory and Measurement positive and bounded. Also, since 0 < I-cwo (t+ 1,1) < 1, then Eo {~ at p(t, 0) ~ [1-0vo (t+ 1, I)]} < 1, and, therefore, EVf has a well defined, unique solution. D. 1 There exist unique equilibrium values (Ev~, {v~(t, j)}~.