By Yoram Weiss, Gideon Fishelson
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Extra resources for Advances in the Theory and Measurement of Unemployment
Indeed, if \\u\\oo ~ M, then I\Tul\oo ~ M+l-&vf. , if u~ w then Tu ~ Tw) and, for any constant r, T(u+r) ~ Tu + &r. This follows from the fact that (l-p(k) )& . 7). 7). 8) is well defined. Let wm(k) = ~ L p(i)(&/ay-k IT m . i~k [1-p(j)], mE (k,k+l, ... ). j~k-l Now, wm(k) is monotonically increasing in m and is bounded. a < ~~ l~k (. 8). 7), so it is a solution. By the previous part of the proposition we know that it is the unique bounded solution. D. 8) satisfies the property vo(k) ::;; 1 - oV f which is required for the problem to be well defined (the set S to be non-void).
The firm assign probability 1 to the worker to be of this type). 7) Under equilibrium (*), this situation holds in general. When the firm sees a worker of type t, it makes the conjecture that he has failed all his tests because, otherwise, he would not have been in the market. Therefore, the firm believes that a worker of type t is, in fact, a worker of type (t, 0), and this expectation is fulfilled by the worker's behaviour. 8) To show that strategies (*) indeed form an equilibrium, and to investigate some of its properties, we have to describe the properties of the term Va (t+ 1, 1), the market value of a successful worker.
This level of complication is beyond the scope of the paper. 3 Under assumption 2 ('decreasing learning'), w is strictly decreasing in k (for 0 < y < 00). 8) we have vo(k) = ~ [ 1 p(k) a + 6(I-p(k) )p(k+ 1) ap(k) + 6 2 (I-p(k) )(P-(k+ 1) )p(k+2) a 2p(k) + + ... j It can be seen that assumption 2 implies, in our model, that p(k+ 1) p(k+2) p(k+i) p(k+ 1+i) . p(k) < p(k+ 1) , and, also, p(k) < p(k+ 1) for every l. Therefore, term by term, vo(k+ 1)/p(k+ 1) is bigger than vo(k)/p(k). It thus follows that vo(k)/p(k) is strictly increasing in k (strictly decreasing in p(k».