Suppose that workers value their time anywhere between $0/hour and $50/hour, wit

Question

Suppose that workers value their time anywhere between $0/hour and $50/hour, with every value between 0 and 50 being equally likely. A worker will take a job only if the wage is above the value of his time. Suppose that if a worker takes a job, he will generate revenue equal to 1.5 times the amount he values his time -- that is, a worker who values his time at $20/hour will generate $20(1.5) = $30 revenue for a rm each hour. Firms cannot how productive workers are before hiring them; all workers look identical. a. Is there an equilibrium in which all workers are hired? If so, describe it (what wages are paid, which workers work). If not, is there an equilibrium in which any workers are hired? b. What is the name for this economic phenomenon studied in this question? c. Suppose workers become more productive, so that now when a worker is hired, he increases a rm's revenue by X times the amount he values his time (that is, a worker who values his time at $20/hour will generate $20X dollars for a rm each hour). Would you get a dierent answer to part a if X were much larger? Explain why.

Explanation / Answer

Is there an equilibrium in which all workers are hired? If so, describe it (what wages are paid, which workers work). If not, is there an equilibrium in which any workers are hired?

No; if all workers were to be hired, the max wage a rm would be willing to pay is $37.50, but the best workers will not work at this wage. Similar to the used car example from the lecture of Tuesday, October 11, this market will completely unravel, and no workers will work for rms.

b. What is the name for this economic phenomenon studied in this question?

Adverse selection or market collapse.

c. Suppose workers become more productive, so that now when a worker is hired, he increases a rm’s revenue by X times the amount he values his time (that is, a worker who values his time at $20/hour will generate $20 X dollars for a rm each hour). Would you get a dierent answer to part a if X were much

Yes, you would get a dierent answer. Suppose all workers work. Then, a rm is willing to pay a wage no higher than average productivity, which is 25X. So, as long as X > 2, there is an equilibrium in which all workers work, and adverse selection is not a problem.

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