The cost, c, of a college education that serves only as a signal of a high-quality worker is $20,000. The wage of a known high-quality worker, wh, is $75,000. The wage for a known low-quality worker, w1, is $50,000
For what value of the share of the work force that is of high quality, t, is a pooling equilibrium possible?
The high-quality workers will not go to college if wh - (t ? wh + (1 - t)w1 ) < c. This can be rearranged so that t > 1 - c/(wh - w1 ). By substituting in the numbers, t > 1/5 will result. Thus with a share of the work force that is high quality that is greater than 1/5, a pooling equilibrium can result.
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