TRENT UNIVERSITY DEPARTMENT OF ECONOMICS ECON 3250H ASSIGNMENT #2 Dr. M. Arvin XXXXXXXXXX DATE GIVEN: Wednesday, October 13, 2021. DUE DATE: Beginning of class on Wednesday, November 17, XXXXXXXXXXAs...

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TRENT UNIVERSITY DEPARTMENT OF ECONOMICS ECON 3250H ASSIGNMENT #2 Dr. M. Arvin 2021-2022 DATE GIVEN: Wednesday, October 13, 2021. DUE DATE: Beginning of class on Wednesday, November 17, 2021. As your course outline states: “late penalty is 20% for each day or part thereof for which the assignment is late.” You have five weeks to complete this assignment. Please complete your assignment in ink or type it. Questions 1 and 2 are each worth 50 marks. 1. Consider a household’s utility function 4/32 4/1 1 )1()1(8 −−= qqu where )2,1( =iqi is quantity consumed of good i . Suppose unit price of good 1 and good 2 are $5 and $4 , respectively. The budgeted income of the household is $129. i) By setting up a constrained optimization problem and using a Lagrangian function find the optimal quantity consumed of goods 1 and 2. ii) Verify that your second-order condition is satisfied. (Note: answers lacking final simplification and appropriate substitution will be penalized.) iii) Without performing another optimization, comment on the change in the level of the consumer’s maximized utility if she has a budgeted income of $130 instead. 2. Suppose you are studying in an American university. Suppose it is late in the semester and you have two exams left. You must decide how to allocate your working time during the study period. After eating, sleeping, exercising, and maintaining some human contact, you have 12 hours each day in which to study for your exams. You have figured out that your grade in Mathematical Methods and Chemical Methods take the form of M)3/4( and C2)3/4( , respectively. M is the number of hours per day spent studying for Mathematical Methods and C is the number of hours per day spent studying for Chemical Methods. i) By setting up a constrained optimization problem and using a Lagrangian determine the optimal number of hours per day spent studying for each course if you wish to maximize your grade point average. If you follow this strategy, what will your grade point average be? (Notes: Suppose GPA is an average standing determined out of six. You may assume your second-order condition is satisfied. That is, you do not have to show it.) ii) Without performing another optimization problem, comment the impact on your grade point average if you study time increases by one hour each day. iii) Now suppose your marks production function changes to M for Mathematical methods and to C2 for Chemical methods.  is a parameter measuring how much you concentrate during your study time. By totally differentiating your F.O.Cs. and performing comparative statics, comment on the impact of a rise in  on your optimal M and C . (Note: you may assume your second-order condition is satisfied. That is, you do not have to prove that it is satisfied.)