Consider the following simple signaling model of education. A worker is either high productivity or low...

Consider the following simple signaling model of education. A worker is either high productivity or low productivity. The worker can be high productivity with probability 1/3 and low productivity with probability 2/3. The worker knows her productivity. The firm that she approaches for employment does not.

The firm must decide whether to offer the worker a High Skill Job or a Low Skill Job. The High Skill Job pays the worker 8 units (regardless of productivity), and the Low Skill Job pays the worker 5 units (regardless of productivity).The firm earns a payoff of 3 from hiring the worker into the Low Skill Job, regardless of the worker's productivity. If the firm hires the worker into a High Skill Job, the firm earns a payoff of 8 if the worker is high productivity, and zero if she is low productivity.

(a) In equilibrium, what job will the firm offer the worker? Explain your answer and show all work.

Next, suppose that before approaching the firm for a job, the worker decides whether or not to obtain a university education. Education costs a high productivity worker 2 units of utility, but costs a low productivity worker 5 units of utility. Upon observing whether the worker has acquired education (but without observing directly the productivity of the worker) the firm must decide whether to offer the worker a High Skill Job or a Low Skill Job.

(b) Is there an equilibrium in which high productivity workers get education but low productivity workers do not? Show all work and explain your answer.

(c) What type of market failure is illustrated in this question? Explain. Offer one other way that the firm and worker may be able to work around this market failure, and explain.

Expert Solution

a) Since the firm will have a payoff of 3 if the firm hires the worker in a low skill job, the expected payoff from offering a low skill job is 3

If the firm hires the worker in a high skill job, the probability that the worker is high productivity is 1/3 and so the probability that the firm has a payoff = 8 is 1/3

And the probability that the worker is low productivity is 2/3 and so the probability that the firm has a payoff of 0 is 2/3

The expected payoff from offering a high skill job is 8*(1/3) + 0*(2/3) = 8/3 = 2.67

Since the expected payoff for the firm is higher with offering a low skill job, in equilibrium the firm will offer the worker a low pay job.

b) For the worker, the payoff from high skill job is 8 units and doing a low skill job is 5 units regardless of productivity.

For a high productivity worker, education will cost 2 units and for a low productivity worker, education will cost 5 units. Since education will lead to being offered the high skill job, the payoff for high productivity workers if they get educated and get a high skill job will be (8-2) = 6 which is higher than the payoff from no education and getting a low skill job (5)

The payoff for low productivity workers if they get educateed and get a high skill job will be (8-5) = 3 which islower than the payoff from no education and getting a low skill job (5)

So there is an equiilbrium where high productivity workers get educated as their payoff will increase after being educated and having a high skill job, and the low productivity workers will not get educated as their payoff will decrease with education and a high skill job compared to the low skill job without education.

c) The type of market failure in this situation is productive and allocative inefficiency. As the resources are not being allocated efficiently for maximum welfare/surplus. The firm or the worker can work around the market failure if they didn't require education to demonstrate their productivity. Since education decreases the utility of workers, if the firm was able to independently determine the productivity of workers through better HR and feedback systems, or if the workers were able to independently demonstrate their productivity, there will be no market failure and both the firms and the workers will get a maximum payoff they can in this situation.

Hope it helps. Do ask for any clarifications if required.

Rahul Sunny answered 6 months ago

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