Education as a signal:

Yet another type of signal occurs in the labor-market. Employers may be unable to distinguish good, or high-ability, from bad (low-ability) workers, at the employment stage. They therefore get the same wage, reflecting their average productivity. However, the good workers (who know they are good) may invest in costly education. Education may improve their productivity, but its main function could also be to signal that the worker is of high quality. This would follow if it’s difficult and costly to get a degree. It must also be more costly for the less able person, in order for it to be effective as a signal.

Assume that employers know that the proportion of high ability workers in the population is θ (the proportion of low ability workers is 1−θ).Without any way to distinguish high from low ability workers, and if the labor-market is perfectly competitive, all workers receive the same wage, which reflects their average productivity:

" ‾w = θw_h + (1 − θ)w_l,

there w_h (w_l) is the wage that high (low)ability workers would have received with perfect information. Risk-neutral firms expect to just break even, but they effectively under (over)pay high(low) ability workers. This type of equilibrium is called a pooling equilibrium.

We now assume that high ability workers can get an upper education degree at a personal cost of c, low ability workers cannot (or the cost would be too high for them). Note that this is not the cost of school fees, but the personal cost of passing exams etc, which is much lower for high, than for low, ability individuals. In order for education to pay for high ability workers it must be the case that:

w_h − c > w_l,
or,
w_h − w_l > c,

i.e., the wage-premium associated with a university degree must exceed the cost of the education. In a pooling equilibrium:

w_h−‾w < c,
or, solving this for θ :

This inequality tells us that if θ is large (and/or c high), the high ability person will not get an education. In that case the average wage approaches wh anyway, so the wage-premium from getting an education, w_h−‾w, is not high enough. Figure below shows the possible equilibrium in this model. Above the line c = w_h−w_l, education is too costly so there is only a pooling equilibrium. Below the line θ = 1 – [c /(w_h−w_l)], there is a separating equilibrium because, given the cost of education, there are relatively few high ability persons, but as c falls, this proportion increases and the likelihood for a separating equilibrium falls. In the region between these two lines there could be either a pooling or a separating equilibrium.

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