A question about utility maximization.
Nancy Lerner is trying to decide how to allocate her time instudying for her Economics course.There are two examinationsin this course. Her overall score for the course will be theminimum of her scores on the two examinations.She has decided todevote a total of 1,200 minutes to studying for these twoexams, and she wants to get as high an overall score aspossible. She knows that on the first examination if she doesnâtstudy at all, she will get a score of zero on it. For every 10minutes that she spends studying for the first examination,she will increase her score by one point.If she doesnâtstudy at all for the second examination she will get a zero onit. For every 20 minutes she spends studying for the secondexamination, she will increase her score by one point.
What is Nancy's utility maximizing scores for exam 1 and exam 2?What is her maximum utility? Find how much time she must spend oneach exam to maximize her overal score?
I am able to determine that Nancy's budget line here would be 10X +20Y = 1200, where X = exam 1 score, Y = exam 2 score, however, I amhaving trouble determining the utility maximization since I can'tfigure out how to determine her utility function, U(X, Y), fromthere I can use the Lagrangian method to determine how to maximizeher utility. It could be that I am going about this the wrong waythough. Any help would be appreciated.
Thank you.
A question about utility maximization.
Nancy Lerner is trying to decide how to allocate her time instudying for her Economics course.There are two examinationsin this course. Her overall score for the course will be theminimum of her scores on the two examinations.She has decided todevote a total of 1,200 minutes to studying for these twoexams, and she wants to get as high an overall score aspossible. She knows that on the first examination if she doesnâtstudy at all, she will get a score of zero on it. For every 10minutes that she spends studying for the first examination,she will increase her score by one point.If she doesnâtstudy at all for the second examination she will get a zero onit. For every 20 minutes she spends studying for the secondexamination, she will increase her score by one point.
What is Nancy's utility maximizing scores for exam 1 and exam 2?What is her maximum utility? Find how much time she must spend oneach exam to maximize her overal score?
I am able to determine that Nancy's budget line here would be 10X +20Y = 1200, where X = exam 1 score, Y = exam 2 score, however, I amhaving trouble determining the utility maximization since I can'tfigure out how to determine her utility function, U(X, Y), fromthere I can use the Lagrangian method to determine how to maximizeher utility. It could be that I am going about this the wrong waythough. Any help would be appreciated.
Thank you.
