Econ 3710.02, Advanced Microeconomics, Fall 2002, MIDTERM
This midterm is worth 30% of your final mark. Answer all questions. Show how you got your answers. You have 50 minutes.
1. Jane has the utility function, U = αXY, where α is a positive constant. She has an income of I and faces the market prices Px and Py. She has the option of joining a club where she will pay 25% of her income as membership fee but can buy good X at 70% of the market price and good Y at 80% of the market price. Will she join the club? (If you need to use demand functions for this question, you can use them without deriving them. Please note that I am not asking you to calculate WTP or WTA). 10 marks
2. In a world with only two goods, if the marginal utility of each good is positive, then the indifference curves will be convex to the origin. True or false? 10 marks
3. Mario has the utility function U = 100Y – 0.5Y2 + X. Let I be his income, Px be the market price of X and Py be the market price of Y.
(i) Derive his demand function for Y. 5 marks
(ii) If Px = 4, Py = 40, and I = 5000, how much X does he buy? 5 marks
(iii) Is X a normal good or an inferior good? Explain your answer without deriving or making reference to the mathematical expression for the demand function for X. 5 marks
(iv) Let Px = 4, Py = 40, and I = 5000 as in (ii). Mario is given the opportunity to join a society whose members can buy Y at a price of $30 and X at a price of $5. What is the maximum amount that he would be prepared to pay in membership fees to join this society? 10 marks
(v) Suppose the membership fee is $222. Will he join? Explain your answer without calculating his utility when he pays a membership fee of $222. 5 marks
Good Luck!!!!! Good Luck !!!!! Good Luck!!!!! Good Luck!!!!! Good Luck!!!!!!
J. Atsu Amegashie
Department of Economics
University of Guelph
October 21, 2002