Question 1
Multiple choice. John Parker Nosey works for the Canada Revenue Agency. He is in charge of auditing income of self-employed people. In any year, people divide their total income between consumption and saving. John cannot determine people's consumptions, but he is able to determine how much people have saved over the course of a year. From years of experience, he has learned that people act as if they are maximizing a utility function of the form U (c, s) = 10, 000 ln (c) + s, where c is the number of dollars' worth of consumption in a year and s is the number of dollars saved.
(a) If someone saves at least $1,000, then that person's income is at least $11,000.
(b) If someone saves nothing, then that person must earn less than $1,000.
(c) If someone saves exactly $1,000, then that person's income must be greater than $1,000 and less than $10,000.
(d) If someone saves exactly $10,000, then that person must earn exactly $21,000.
(e) If someone saves more than $1,000, then that person's income must be more than $20,000.
Question 2
Agatha must travel on the Orient Express from Istanbul to Paris. The distance is 1,500 miles. A traveler can choose to make any fraction of the journey in a first-class carriage and travel the rest of the way in a second-class carriage. The price is 10 cents a mile for a second-class carriage and 20 cents a mile for first-class carriage. Agatha much prefers first-class to second-class travel, but because of a misadventure in an Istanbul bazaar, she has only $200 left with which to buy her tickets. Luckily, she still has her toothbrush and a suitcase full of cucumber sandwiches to eat on the way. Agatha plans to spend her entire $200 on her tickets for her trip. She will travel first class as much as she can afford to, but she must get all the way to Paris, and $200 is not enough money to get her all the way to Paris in first class.
?(a) Use red ink to show the locus of combinations of first- and second-class tickets that Agatha can just afford to purchase with her $200. Use blue ink to show the locus of combinations of first- and second-class tickets that are sufficient to carry her entire distance from Istanbul to Paris. Locate the combination of first- and second-class miles that agatha will choose on your graph and label it A.
(b) Let m1 be the number of miles she travels by first-class coach and m2 be the number of miles she travels by second-class coach. Write down two equations that you can solve to find the number of miles she chooses to travel by first-class coach and the number of miles she chooses to travel by second-class coach.
(c) What is the number of miles she travels by second-class coach?
( d) Just before she was ready to buy her tickets, the price of second-price tickets fell to $0.05 while the price of first-class tickets remained at $0.20. On the graph that you drew in section (a), use pencil to show the combinations of first- and second-class tickets that she can afford with her $200 at these prices. On your graph, locate the combination of first-class and second-class tickets that she would now choose. (Remember, she is going to travel as much first-class as she can afford to and still make the 1,500 mile trip on $200.) Label this point B.
(e) How many miles does she travel by second-class now? (Hint: For an exact solution you will have to solve two linear equations with two unknowns.)
(f) Is second-class travel a normal good for Agatha? Is it a Giffen good for her?
Question 3
Juan likes to drink his coffee with milk. Specifically, he has preferences such that milk is a gross complement for coffee. Now consider the reverse direction: can you determine whether coffee is a gross complement for milk, a gross substitute for milk, or neither? Prove your answer mathematically.
Question 4
True/False?1 If the Engel curve slopes up, then the demand curve slopes down.
Question 5
Multiple choice. The following can be said about the income and substitution effects of a price increase on the demand for a good whose price rose:
(a) The former is always positive and the latter is always negative. (b) Both can be either positive or negative.
(c) While the latter is always negative, the former can be either positive or negative.
(d) While the former is always negative, the latter can be either positive or negative.
(e) The former can at times be negative, but it will never overwhelm the latter.
Question 6
Multiple choice. Herbie consumes two goods and his utility function is U (x1, x2) = x1^3 x2^4. The price of good 2 does not change and his income does not change, but the price of good 1 decreases.
(a) The substitution effect of the price change reduces the demand for good 2 and increases the demand for good 1.
(b) The substitution effect reduces the demand for good 2, and since the income effect is zero, the demand for good 2 falls.
(c) The substitution effect on the demand for good 2 is zero, since the price of good 2 did not change.
(d) The income effect is zero, since his income remained constant.
(e) More than one of the above statements is true.