You own a company that produces chairs, and you are thinking about hiring one more employee. Each chair produced gives you revenue of \(\$ 10\). There are two potential employees, Fred Ast and Sylvia Low. Fred is a fast worker who produces ten chairs per day, creating revenue for you of \(\$ 100\). Fred knows that he is fast and so will work for you only if you pay him more than \(\$ 80\) per day. Sylvia is a slow worker who produces only five chairs per day, creating revenue for you of \(\$ 50 .\) Sylvia knows that she is slow and so will work for you if you pay her more than \$ 40 per day. Although Sylvia knows she is slow and Fred knows he is fast, you do not know who is fast and who is slow. So this is a situation of adverse selection. a. Since you do not know which type of worker you will get, you think about what the expected value of your revenue will be if you hire one of the two. What is that expected value? b. Suppose you offered to pay a daily wage equal to the expected revenue you calculated in part a. Whom would you be able to hire: Fred, or Sylvia, or both, or neither? c. If you know whether a worker is fast or slow, which one would you prefer to hire and why? Can you devise a compensation scheme to guarantee that you employ only the type of worker you prefer?

Step by step solution

01

Calculate expected value of revenue

To calculate the expected value of revenue, we first need to find the probability of hiring the fast worker (Fred) and the slow worker (Sylvia). Since there are only two candidates, we can assume the probability of hiring either is equal at 0.5. Now, calculate the expected value of revenue: Expected Revenue = (Probability of hiring Fred x Revenue from Fred) + (Probability of hiring Sylvia x Revenue from Sylvia) Expected Revenue = \((0.5 * 10 * \$10) + (0.5 * 5 * \$10) = \$75\)

02

Determine whom we can hire based on expected revenue

If we offer to pay a daily wage equal to the expected revenue (\$75), would we be able to hire Fred, Sylvia, both, or neither? Fred will work for us if we pay him more than \(80 per day. Since our offered wage is \)75, this is not enough to hire Fred. However, Sylvia will work for us if we pay her more than \(40 per day. Our offered wage is \)75, which is higher than her condition. Therefore, we can hire Sylvia.

03

Decide which worker to hire and propose a compensation scheme

If we know whether a worker is fast or slow, we would prefer to hire the worker who can produce maximum chairs per day at the lowest possible daily wage rate. In this scenario, Fred is the preferred worker as he produces 10 chairs per day (compared to Sylvia's 5 chairs per day), and the difference in their minimum required daily wage (\$80 - \$40 = \$40) is less than the revenue difference between them (\$100 - \$50 = \$50). To create a compensation scheme that guarantees hiring only Fred, we can offer a wage higher than Fred's minimum daily wage requirement (\$80) and lower than the revenue generated by Fred (\$100). For example, we can offer Fred a wage of \$85 per day. This wage will be attractive for Fred as it is higher than the minimum wage he demands, and it will not be attractive for Sylvia, as her total revenue generation per day is lower than the potential daily wage (\$50 < \$85).

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