Question

(10 points) Mary has 24 hours before her microeconomies midterm. She has a econon after the micro midterm and has no time to study in between. Her utility function is given by erm. She has a econon etrics midterm directly u (e, m) 6104 omics midterm. where e is the score on the econometrics midterm and m is the score on the microecon Although she cares more about econometrics, she is better at microeconomics; for each hour spent st udying microeconomics she will increas e her score by 3 points, but her econometrics score will only increase by 2 ints for every hour spent studying econometrics. Studying zero hours results in a score of zero on both subjects. (a) (2 points) What constraints does Mary face in her test score maximization problem? (b) (2 points) How many hours should Mary optimally spend studying econometrics? How many hours studying microeconomics? (hours are divisible) (2 points) What microeconomics and econometrics test scores will she acheve (ie. e*)? what are m* and (e) (d) (2 points) What utility level will she achieve? (e) (2 points) Suppose Mary can get an microeconomics tutor. If she goes to the tutor, she will increase her microeconomics test score by 5 points for every hour spent studying instead of 3 points, but will lose 4 hours of study time by going to the tutor. She canmot study while at the tutor, and going to the tutor does not directly improve her test score. Should Mary go to the tutor?

Answer 1

u(e, m) = e^.6 m^.4, B.C. 24 = e/2 + m/3 constrains rightarrow total time = 24 = e/2 + m/3 Now at equation: L = e^.6 m^.4 + lambda[24 - e/2 - m/3] FOC: Partialdifferential L/Partialdifferential e = > .6(m/e)^.4 - lambda/2 = 0, Partialdifferential L/Partialdifferential m = .4(e/m)^.6 - lambda/3 = 0 so .6(m/e)^.4 times 2 = .4 times 3(e/m)^.6 so 1.2/1.2 = e/m, thus e = m Thus from B.C rightarrow 24 = e/2 + e/3 = > (24 times 6) = 3e + 2e 144 = 5e, e* = 28.8 hours of study to get e* = 28.8, = > 28.8/2 = 14.4 hours Now m* = 28.8 so study hours = 28.8/3 = 9.6 hours so m* = 28.8 = e* 4(28.8, 28.8) = 28.8