_172.20.40.61_Materials_fedward21-0002_Answers_to_Previous_Exam_I

_172.20.40.61_Materials_fedward21-0002_Answers_to_Previous_Exam_I

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Solutions to Selected Questions from Exam 1 Form A Finley Edwards This document contains answers to all Multiple Choice and True False Questions, as well as complete solutions to all four problems. Multiple Choice and True False Answers 1. B 2. D 3. A 4. C 5. C 6. D 7. D 8. B 9. D 10. A 11. D 12. E 13. C 14. A 15. C 16. D 17. B 18. B 19. FALSE 20. TRUE Question 21 Part (a) - 5 points In each case the budget equation takes the form p x x + p y y = m - F where F is the fee associated with that plan. Plan A: x + 2 y = 80 Plan B: x + y = 60 Part (b) - 10 points I only asked for the optimal amount of y , but we’ll need x for part (c) so I’ll solve for both. The simplest way to solve this part is to recognize that this is a Cobb-Douglas utility function with c = 0 . 5 and recall that the demand function for a Cobb-Douglas utility function is given by y ( m,p x ,p y ) = c m p y . This gives the 1
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desired quantities. Plan A: y = 0 . 5 80 2 = 20 and x = 0 . 5 80 1 = 40 Plan B: y = 0 . 5 60 1 = 30 and x = 0 . 5 60 1 = 30 If you did not recognize that this was Cobb-Douglas utility, you would need to solve for the optimal choice. Using the MRS = - p x p y condition, we have: MRS = - MU x MU y = - y x = - p x p y Solving for x gives x = y p y p x . Plugging this result into our budget equation gives the optimal amount of y . Plan A: Plugging x = 2 y into the budget constraint we have 2 y + 2 y = 80 which gives y = 20. This implies that x = 2 * 20 = 40. Plan B: Plugging x = y into the budget constraint we have y + y = 60 which gives y = 30. This implies that x = y = 30. Part (c) - 5 points To choose between the two plans, we need to compare the utility under the two plans. Plan A: U (40 , 20) = 40 * 20 = 800 Plan B: U (30 , 30) = 30 * 30 = 900 Since Plan B gives a higher utility, he would choose plan B. I graded this part of the question based on the amount of
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_172.20.40.61_Materials_fedward21-0002_Answers_to_Previous_Exam_I

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