Individals are of two di §erent abilities: high ( H ) and low ( L ). An individu
ID: 1187795 • Letter: I
Question
Individals are of two di §erent abilities: high (H) and low (L). An individual knows his or her own
ability but an employer does not. Employers believe that both types of individuals are equally likely
in the population, and therefore has an initial (prior) belief that an individual is high ability with
probability 1. Before an individual looks for a job, he or she has an opportunity to go to college. 2
Assume that attending college does not change an individualiÌs ability; this problem shows that even in
this circumstance, college can perform a useful social function. The e §ort cost of attending college is
di §erent for individuals of di §erent abilities. In order to attend college, high ability individuals must
expend e §ort 1, and low ability individuals must expend e §ort 1, where a < 3 (this means that a 3a
low ability individual has a higher cost of attending college). Not attending college costs 0. After
observing an individualiÌs education (that is, whether he or she attended college) an employer makes
the individual a job o §er. The wage that the individual receives is equal to the employeriÌs belief that
the individual is high ability, given the level of schooling that the individual has chosen to acquire. For
example, if the employer believes that a college graduate is high ability with probability 2 he will o §er 3
a college graduate a wage of 2 . If he believes that an individal with no college education is high ability 3
with probability 1 , he will o §er an individual without college a wage of 1 : An individualiÌs payo § is 44
equal to his wage, minus the cost of education..
First consider a separating equilibrium. In a separating equilibrium, high ability individuals attend college, but low ability individuals do not.
(a) If the employer observes that an individual did not attend college, what is his belief about the individualiÌs ability? What wage will he o §er individuals who do not attend college?
(b) If the employer observes that an individual did attend college, what is his belief about the indi- vidualiÌs ability? What wage will he o §er individuals who attend college?
(c) Given the wages paid to college graduates and those who do not attend, will the high-ability individual chooose to attend college? (Hint: compare the payo § of attending college for the high ability graduate to the payo § of not attending college)
(d) Given the wages paid to college graduates and those who do not attend, for which values of a will the low-ability individual chooose to attend college? (Hint: compare the payo § of attending college for the low ability graduate to the payo § of not attending college)
(e) In a separating equilibrium, a low ability individual does not attend college. For which values of a is this expectation consistent with the low ability individualiÌs strategy?
Now, consider a pooling equilibrium in which all individuals attend college; that is, both high and low ability individuals attend college. If some individual were to choose not to attend college, the employer would believe that he or she must be low ability, and would o §er a wage of 0.
(f) If the employer observes that an individual attended college, what is his belief about the individ- ualiÌs ability? What wage will he o §er to college graduates? (Hint: The employer expects that all individuals attend college. This means that attending college conveys no information about the individualiÌs true ability).
(g) Given the wages paid to college graduates (and the wage that would be paid to non-grads) would the high-ability individual choose to attend college? For which values of a would the low ability individual choose to attend college?
(h) In a pooling equilibrium, both high and low ability individuals attend college. For which values of a is this expectation consistent with the individualsiÌstrategies?
Finally, consider a sem-separating equilibrium in which high-ability individuals attend college (for sure), but low ability students attend college with probability 0 < s < 1:
(i) If the employer sees that an individual attends college what is his belief that the individual is high-ability? What is the wage to college graduates? (Hint: Remember, all high ability individuals attend, but low ability individuals attend with probability s. Divide the probability of an individual being high ability and attending college by the overall probability of an individual attending college).
(j) If the employer sees that an individual did not attend college, what are his beliefs about the individualiÌs ability? (Hint: all high ability individuals attend college)
(k) The low-ability individual is willing to randomize between attending college and not attending college. Use this to Önd the probability that the low-ability individual attends in equilibrium.
Bonus: Comment on the purpose of college illustrated in this example. How is this purpose a §ected as college becomes easier for the low-ability type (i.e. as a increases)?
Explanation / Answer
REASONS FOR ATTENDING COLLEGE...................... 3. Knowledge Leads to Happiness College students have a higher level of happiness and self worth when they graduate than non graduates. Not saying that you can't be happy or more successful than non college graduates, but on average it holds true. 4. Networking No matter where you go to college you will most likely meet a diverse group of people that will act as future connections, which can help you get a job down the road. 5. Job Opportunities How many times have you searched the classifieds and seen that you needed a college degree just to apply? With a college degree no matter the major you will have many more job opportunities than your peers who did not go to college. 6. Study Habits Help Future Work During college you will most likely have intense study periods, which actually helps with discipline for jobs. 7. Broad Base of Knowledge Are you one of those people who feel awkward in social situations because you don't know what to talk about? College is a great way to expand your knowledge base and have fun doing it. 8. Partying Although many parents would cringe if they knew that partying made my top 10 list of why to go to college, but many students do in fact party. Partying is not always a bad thing; I went to a party and got an offer to join my fraternity that I am currently in, which has given me many job contacts. 9. Writing College essay writing is intense, and a lot different than almost any other kind of writing. You will develop strong writing skills that will help you get your thought out clearly on paper. College is not necessary to becoming a good writer; I know a few writers who are amazing that have not attended college; however they have a natural talent. 10. Greek Life Many people may disagree with Greek Life being on the reasons to go to college; however joining a sorority or fraternity are great ways to meet new people and strengthen your networking skills.