economics 14
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Question 1
Multiple choice. John Parker Nosey works for the Canada Revenue Agency. He is in charge of auditing income of selfemployed 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 firstclass carriage and travel the rest of the way in a secondclass carriage. The price is 10 cents a mile for a secondclass carriage and 20 cents a mile for firstclass carriage. Agatha much prefers firstclass to secondclass 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 secondclass tickets that Agatha can just afford to purchase with her $200. Use blue ink to show the locus of combinations of first and secondclass tickets that are sufficient to carry her entire distance from Istanbul to Paris. Locate the combination of first and secondclass miles that agatha will choose on your graph and label it A.
(b) Let m1 be the number of miles she travels by firstclass coach and m2 be the number of miles she travels by secondclass coach. Write down two equations that you can solve to find the number of miles she chooses to travel by firstclass coach and the number of miles she chooses to travel by secondclass coach.
(c) What is the number of miles she travels by secondclass coach?
( d) Just before she was ready to buy her tickets, the price of secondprice tickets fell to $0.05 while the price of firstclass tickets remained at $0.20. On the graph that you drew in section (a), use pencil to show the combinations of first and secondclass tickets that she can afford with her $200 at these prices. On your graph, locate the combination of firstclass and secondclass tickets that she would now choose. (Remember, she is going to travel as much firstclass 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 secondclass now? (Hint: For an exact solution you will have to solve two linear equations with two unknowns.)
(f) Is secondclass 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.
Multiple choice. John Parker Nosey works for the Canada Revenue Agency. He is in charge of auditing income of selfemployed 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 firstclass carriage and travel the rest of the way in a secondclass carriage. The price is 10 cents a mile for a secondclass carriage and 20 cents a mile for firstclass carriage. Agatha much prefers firstclass to secondclass 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 secondclass tickets that Agatha can just afford to purchase with her $200. Use blue ink to show the locus of combinations of first and secondclass tickets that are sufficient to carry her entire distance from Istanbul to Paris. Locate the combination of first and secondclass miles that agatha will choose on your graph and label it A.
(b) Let m1 be the number of miles she travels by firstclass coach and m2 be the number of miles she travels by secondclass coach. Write down two equations that you can solve to find the number of miles she chooses to travel by firstclass coach and the number of miles she chooses to travel by secondclass coach.
(c) What is the number of miles she travels by secondclass coach?
( d) Just before she was ready to buy her tickets, the price of secondprice tickets fell to $0.05 while the price of firstclass tickets remained at $0.20. On the graph that you drew in section (a), use pencil to show the combinations of first and secondclass tickets that she can afford with her $200 at these prices. On your graph, locate the combination of firstclass and secondclass tickets that she would now choose. (Remember, she is going to travel as much firstclass 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 secondclass now? (Hint: For an exact solution you will have to solve two linear equations with two unknowns.)
(f) Is secondclass 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.

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economics 14