Suppose that there are 2 types of workers in the economy, low and high ability o

Question

Suppose that there are 2 types of workers in the economy, low and high ability ones. The fraction of low ability workers in the population is q. Low ability types have productivity $200,000 and high ability types have productivity $300,000. Individuals can attend school for a number of years s. The utility cost of each additional year of school is $20,000 for the high ability type and $25,000 for the low ability type. You should interpret the cost as the monetary equivalent of the effort a student has to exert or her/his distaste for school work. Notice also that the cost is per year of school.

(a) Compute the wage that a firm would offer in a pooling equilibrium in which the firm believes that a worker is a low ability type with probability q and high ability type with probability 1-q, independently of the individual’s education level s. Notice that the wage offered by the firm is a function of q. Compute the optimal years of schooling selected by each type of agent. Hint: Firms will offer a wage equal to the expected productivity of the worker.

(b) In a separating equilibrium firms presume that if a worker attends school for at least s years then he/she is a high ability type and if the worker attends school for less than s years he/she is a low ability type. Given these expectations, workers select how many years of schooling to attend. Find the wage offered by a firm to a worker as a function of her/his years of schooling. Also find the range of values for s such that a high ability type chooses to attend school for s years while a low ability type chooses not to attend school at all.

(c) Suppose that s = 4.5. For what values of q are all agents better off in the pooling equilibrium than in the separating one?

Explanation / Answer

(a). The probability of the firm selecting a low ability type worker is ‘q’ and the probability of selecting a high ability worker from the labor pool is ‘1-q’.

The productivities of the low ability workers and the high ability workers are $200,000 and $300,000 respectively.

So, the expected productivity that the firm could enjoy is,

EP = $200,000 * q + $300,000 * (1-q)

We know that the firm would be giving the wage according to the expected productivity; so the wage that the workers will get is $(300,000 – 100,000 q).

Now, for the low ability workers, the cost of attaining the school is,

CL = $25,000 * sL

Where sL is the level of schooling attended by the low ability workers.

On the other hand, if sH be the level of schooling attended by the high ability workers, then the cost of attaining that level of schooling would be,

CH = $20,000 * sH

An optimal year of schooling for the workers would be that whose cost would get fully covered by the wages they get.

In case of the low ability workers, if we assume that the expected wage they would get in the near future is known and so, they would choose that level of schooling which would cover their current level of schooling. That is, by equaling the expected wage with the cost of schooling for the low ability workers, we’ll get,

$300,000 - $100,000 q = $25,000 * sL

That is, the optimum level of schooling will depend upon the probability that the firm would be assigning of them being low ability.

On the other hand, for the high ability workers, by equaling the expected wage with the cost of schooling they incurred we would get,

$300,000 - $100,000 q = $20,000 * sH

So, the optimum years of schooling for the high ability type would depend upon the probability that the firm would be assigning on them as well.

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