Suppose that a firm wants to hire a new worker.Suppose that high ability candida

Question

Suppose that a firm wants to hire a new worker.Suppose that high ability candidates’ productivity is worth about $80,000 per year while low ability candidates’ productivity is worth about $40,000 per year. Also suppose that 60 percent of the population is high ability while 40 percent of the population is low ability. Finally, assume that the nature of production is such that firms cannot observe workers’ true abilities.

a. Suppose that no education or other training exists and that firms have to hire workers “blind.” What wage will they offer?

b. Now suppose th at the firm hires a training firm to “train” their candidates. The training firm focuses on basic skills that is costless (except foregone earnings)to learn for high ability candidates. Workers get no pay during the ir training period. They project that attending the training for each year costs low ability workers$60,000 in effort.The firm covers the other tuition costs of the training.Suppose that the world lasts 10 years total which includes training and work (and then workersretire). If the worker chooses not to get training, the worker gets 40,000.Set up an inequality which helps us know if the high ability type will want to attend training for some number “q” of years.

c.Set up an inequality showing when the low-ability types will not choose to attend thetraining for q years.

d.The firm can decide how many years of training to assign.If the firm chose offer training, how would they decide the right number of hours? Explain how we would solve for the optimal number of years of training.

e.Suppose that another firm arrives and begins to offer $80,000 to workers who attend training for q years. Should the original firm continue to subsidize the training? Why or why not or can you tell?

Explanation / Answer

Solution: According to the question, low ability worker's (proportion=0.4) productivity is worth $40,000 per year while, high ability worker's (proportion=0.6) productivity is worth $80,000 per year.

a) If the firm hires workers blind, it will pay same wage to both type of workers.

The pooled wage = 0.4*40000 + 0.6* 80000

= 16000 + 48000 = $64,000

Thus, firm offers $64,000 to all workers.

Now, if training takes place, cost incurred is $60,000 and $0 per year (of training) to low and high quality workers, respectively. While both are paid (both types earn) nothing (or $0) during training period.

Also, if workers don't take training, their earnings (for 10 years) = 40000*10 = $400,000

Then, comparing the earnings with and without training to obtain the required inequalities as follows:

b) For high ability workers, training is beneficial if:

earnings with training for q years > earnings without training

i.e., (0-0)*q + 64000*(10 - q) > 40000*10

c) For low ability workers, training isn't beneficial if:

earnings with training for q years < earnings without training

i.e., (0-60000)*q + 64000*(10 - q) < 40000*10

d) If the firm chooses to offer training, it will decide the number of years to offer training as per the inequalities obtained above:

solving inequality in b), we get, 640000 - 64000q > 400000

(640000 - 400000)/ 64000 > q

3.75 > q

solving inequality in c), we get, -60000q + 640000 - 64000q < 400000

-124000q < - 240000

q > 1.935

Thus, the optimum number of training years should lie in (1.935,3.75)

Assuming, the number of years is an integer (for simplicity), no. of years should be 2 or 3.

Further, for both type of workers, smaller no. of training years will be better and also, any small no. greater than 1.935 will demotivate low quality workers from taking training, optimum no. of years = min{2,3} = 2years.

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