Suppose there are two types of people: high-ability and low-ability. The schooling required to obtain a particular diploma costs a high-ability person $8,000 per year, and it costs a low-ability person $10,001 per year. Firms wish to use this diploma as a signal of an individual’s ability. The firms intend to pay workers such that the present value of lifetime earnings for a worker without the diploma is $250,000, and the present value of lifetime earnings for a worker with the diploma is $450,000.

1. What range of years of education must be required to obtain this diploma in order for the diploma to be an effective signal of worker ability?
2. In equilibrium, in a competitive labor market with workers making rational decisions, how many years of education will be required to obtain this diploma? Briefly explain.
3. Consider this model relative to the model of learned human capital. Briefly discussion the implications of each model for public funding of education.