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# mathsperts6 - Economics for Mathsperts VI The following...

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Economics for Mathsperts VI The following describes the shirking model of unemployment. Suppose each month an unemployed worker gets a job with probability p while an employed worker loses his/her job with probability s: Suppose unemployed workers receive b wage w: In a baby model we assume steady state so that nothing changes over time at the aggregate level. 1. Let V u describe expected discounted earnings while unemployed, V E de- scribe expected discounted earnings while employed and so are given by: V u = b + 1 1 + r [ pV E + (1 p ) V U ] V E = w + 1 1 + r [ sV U + (1 s ) V E ] : Solve for V U ; V E : 2. People are lazy and will only work hard if the value of being employed is su¢ ciently high; i.e. V E V U ± k where k describes the disutility of having to w to the point where V E V U = k: Solve for this wage w and show: w = b + r + s + p 1 + r k: Explain why this wage mark-up increases with
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