A firm hires two kinds of workers, alphas and betas. One can’t tell a beta from

Question

A firm hires two kinds of workers, alphas and betas. One can’t tell a beta from an alpha by looking at her, but an alpha will produce $3000 worth of output per month and a beta will produce $2,500 worth of output in a month. The firm decides to distinguish alphas from betas by making them pass an examination. Suppose that for each question that they get right on the exam, alphas have to spend 1/2 hour studying and betas have to spend 1 hour. A worker will be paid $3000 if she gets at least X answers right and $2,500 otherwise. For either type, an hour’s studying is as bad as giving up $20 income. Determine the minimum score needed to separate alphas from betas.

Explanation / Answer

Answer: Minimum Score needed to seperate Alphas and Betas is 26 answers.

explaination: if a beta does X number of questions he will get $3000, otherwise irrespective of number of questions done, he will get $2500.

He will get an additional payoff of $500 by studying and doing minimum required question. We know that he is giving up $20 of income (per hour) to answer 1 question (time required to study for 1 question is 1 hour).

the maximum number of questions he will attempt = 500/20 = 25

on the 26th question, he will be earning $500 extra, but giving out 26x20 = $520

there for by puttting up a teat of 26 questions, only aplha will do 26 qyestions.

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