1. Education can be thought of as a decision to pay costs now in order to earn higher wages over a lifetime. Consequently, it makes sense to think about the benefits (and costs) of education in present value (PV) terms. Consider a situation in which education can be used as a potential signal to employers. A high school graduate can make a choice today to commit to and acquire any number of years of educa- tion. Firms believe that any worker with a bachelors degree (16 years of education) has higher productivity. Consequently, over a college graduate's lifetime, firms would be willing to pay them wages with PV of $3,000,000. Firms believe that any worker without at least a bachelors degree has lower productivity, and are only willing to pay them wages with a PV over their lifetime of $1,500,000 (1.5 million). For simplicity, assume that education does not influence productivity at all, and is only of value as a potential signal. See figure 1 for a visualization of this situation. Now consider two workers, A and B, with high school diplomas (12 years of school). B faces a higher cost to education than A, as repre- sented by the blue dotted lines. Earning a bachelors degree will cost worker A $1,000,000 in PV, but will cost B $1,750,000 in PV. (a) What is person A's net benefit from attaining 16 years of educa- tion? What about if person A goes straight to work with only their current level of education? (b) What is the optimal level of education for person A? (C) What is person B's net benefit from attaining 16 years of educa- tion? What about if person B goes straight to work with only their current level of education? (d) What is the optimal level of education for person B? (e) Now imagine that the whole labor market is made up of indi- viduals exactly like A and B. What type of equilibrium does the current wage structure lead to? Is education an effective signal to employers? Figure 1 Present Value of Lifetime Income (Millions) Cost for B $3 $2 Cost for A $15 $1 12 13 14 15 16 17 18 19 Years of Education 1. Education can be thought of as a decision to pay costs now in order to earn higher wages over a lifetime. Consequently, it makes sense to think about the benefits (and costs) of education in present value (PV) terms. Consider a situation in which education can be used as a potential signal to employers. A high school graduate can make a choice today to commit to and acquire any number of years of educa- tion. Firms believe that any worker with a bachelors degree (16 years of education) has higher productivity. Consequently, over a college graduate's lifetime, firms would be willing to pay them wages with PV of $3,000,000. Firms believe that any worker without at least a bachelors degree has lower productivity, and are only willing to pay them wages with a PV over their lifetime of $1,500,000 (1.5 million). For simplicity, assume that education does not influence productivity at all, and is only of value as a potential signal. See figure 1 for a visualization of this situation. Now consider two workers, A and B, with high school diplomas (12 years of school). B faces a higher cost to education than A, as repre- sented by the blue dotted lines. Earning a bachelors degree will cost worker A $1,000,000 in PV, but will cost B $1,750,000 in PV. (a) What is person A's net benefit from attaining 16 years of educa- tion? What about if person A goes straight to work with only their current level of education? (b) What is the optimal level of education for person A? (C) What is person B's net benefit from attaining 16 years of educa- tion? What about if person B goes straight to work with only their current level of education? (d) What is the optimal level of education for person B? (e) Now imagine that the whole labor market is made up of indi- viduals exactly like A and B. What type of equilibrium does the current wage structure lead to? Is education an effective signal to employers? Figure 1 Present Value of Lifetime Income (Millions) Cost for B $3 $2 Cost for A $15 $1 12 13 14 15 16 17 18 19 Years of Education