Consider the problem of a firm deciding between two applicants. Make the following assumptions:
• Two types of unemployed workers: – High productivity (z = H) who exit unemployment with probability p H = 0.5 each period.
– Low productivity (z = L) who exit unemployment with probability p L = 0 each period.
• Unemployment lasts for two periods: d = 1 and d = 2 (after which job seekers exit the labor force).
• Firms would rather hire the more-productive H-type. • Firms cannot observe the job seeker’s type (z = H or z = L) directly.
• Half of all newly unemployed workers are H-type; half are L-type.
Using this information, answer the following questions:
(a) Suppose the firm cannot observe either of the two applicants’ unemployment durations (that is, it cannot see if d = 1 or d = 2) so the applicants are observationally identical for the firm. Compute the probability (from the firm’s perspective) that the applicants are H-types. [Hint: Because the firm knows nothing about either applicant, this is an unconditional probability that will be the same for both applicants.]
(b) Now suppose the firm can observe both applicants’ unemployment duration (that is, it knows if d = 1 or d = 2). Moreover, suppose that Applicant 1 is short-term unemployed (d = 1) and Applicant 2 is long-term unemployed (d = 2). Compute the probability that each applicant is an H-type conditional on the applicant’s known unemployment duration. [Hint: This is asking you to compute two conditional probabilities which you can do using Bayes rule!]
(c) If the firm can observe a worker’s unemployment duration but not a worker’s type, would it rather hire a short-term or long-term unemployed job seeker. Why?
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