Question

As a college student, I can divide my career prospects into two categories: a high-status job that pays $160,000 per year or low-status job that pays $40,000 per year. My probability of landing the high-status job is equal to the amount of studying I do, S, where S can vary from 0 (no studying) to 1 (constant studying). Studying is costly, such that my utility function can be expressed as: U(Y,S) = Y0.5 – 400*S2 , where Y is income. If I’m maximizing expected utility, how much should I study? **Only consider income in the first year, not as a stream of payments over time.**

Answer 1

Given utility function, UCYS) = you - 4005² Now we know that Y= 160oooxs + 40,000x (1-5) Where s is the probability of getting a high income job. Putting this value in lin ea U = (120000 x S + 90000) Os - hoos? Now, to mammise uhlity, du 05(120,000) (120000 S+40000) ds Equating it with zero, soos

O = 6000o C120090S+ hood - soos S = 60000 C120, 000 $ +40000) 800 S = 75 (40000)- C 35+1) S: 75 (35+00:9 200 S (35+10.5 - 3/8 (Approx) Solving it, . S- 0.28 to check the second Now order condition, d²U a d l Goooo (35 + 1) - soos zou i. e, solving 60,000 (120000 5+ 40000) as to ger 60000 (35+*0.5 200 d [ 300 (35+1)-os_ soos ds = 300Ⓡ (+05) <3(35+)-1-5-800 - 450(35+15 1-S-800 d20 ds? Now since, so Hence, Utility at S= 0.28 is meant the maximum utility attainable should study and to reach S=0-28. Hence the student