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I am reading the lecture note in labor economics by Acemoglu and Autor. In the chapter of basic search model, they assume capital is perfectly reversible, and argue that "Perfect reversibility implies that $w$ does not depend on the firm's choice of capital ... Suppose $k$ is not perfectly reversible then suppose that the worker captures a fraction $\beta$ all the output in bargaining. Then the wage depends on the capital stock of the firm, $w(k)=\beta A f(k)$ ;$A f^{\prime}(k) =\frac{r+\delta}{1-\beta}$ capital accumulation is distorted." (page 241.)

I don't understand how is the reversibility of capital related to the determination of wage?

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  • $\begingroup$ Could you please provide page so people interested in answering can also check the source for more context? $\endgroup$
    – 1muflon1
    May 24 at 21:35
  • $\begingroup$ @1muflon1 I feel that I have answered the question by myself but I am not 100% sure about my answer. What should I do in this case? $\endgroup$ May 24 at 21:51
  • $\begingroup$ You can just write an answer yourself and see if other people upvote it or if other answers are forthcoming. You are allowed to answer your own questions if you genuinely later found answer. $\endgroup$
    – 1muflon1
    May 24 at 21:54
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I think I get the answer but I am not 100% sure. Any comment would be welcome.

I realized that this is related to the search-matching nature of the model (comparing to competitive labor market), so that if capital is not perfectly reversible the worker can bargain with the firm. Note that even with perfect reversibility, given the match-specific surplus, the wage is still determined by a Nash Bargaining. However the firm's choice of capital would be independent to this Nash Bargaining and be efficient ($f^{\prime}(k)=r+\delta$).

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