ECON 11 Final Exam
Name:
Student ID:
TA:
Exam Rules
1. The exam starts at 8:00 and ends at 11:00.
2. There are 10 short answer questions worth 15 points each and 3 long questions (2 worth
40 points and 1 worth 50 points). The last 20 points will come from completing course
evaluations (10 points) and the post-final survey (10 points) for a total of 300 points.
3. Calculators are allowed, including graphing calculators.
4. You may use one double-sided 8.5x11 sheet of paper with notes as a cheat sheet.
5. Please put all materials other than your calculator, cheat sheet, and a pen or pencil in
your bag. If you have a phone or other item out for any reason you will be given a 0
on the exam.
6. You must SHOW ALL WORK. No credit will be given for an answer with no work.
You may leave an answer unsimplified, but be clear about the steps you took to get
there so the graders can easily see if it’s correct
1
,Short Questions (15 Points Each)
1. Two consumers have utility functions given by U A = x1/3y2/3 and U B = x1/3 + y2/3.
If each consumer has an income of 10 and the price of each good is 1, do the two
consumers choose the same consumption bundle to maximize their utility? Would
they always choose the same bundle for any income and prices?
ANSWER: The MRS of two consumers can be computed as (10 points):
y y1/3
MRSA = MRSB =
2x 2x2/3
At the income I = 10 and px/py = 1, we have (xA, yA) = (100 , 200 ), which is clearly not
3 3
the utility maximizing bundle for B as yB = 8x2B as not satisfied. So consumer would
not choose the same bundle at the current prices and income and they will not always
choose the same bundle for other prices and income.
2. A consumer has an MRS of x for y equal to 1/3 for any quantity of x and y. They
currently have 10 units of x and 10 units of y. Would they prefer to have 8 units of x
and 11 units of y? Explain why or why not.
ANSWER: Consumer with MRS = 1/3 means that they would trade 1/3 units of y
for one unit of x, or 1 y for 3 x. (5 points) To ask the consumer to switch from the
bundle (10,10) to (8,11) is to ask the consumer to gain 1 y by giving up 2 x. (5 points)
So consumer should prefer the deal of (8,11). (5 points)
2
, 3. Write utility functions for the following two scenarios (no explanation necessary - just
the function is enough)
(a) A consumer’s utility is unchanged after trading 2 hamburgers (H) for 1 slice of
pizza (P)
(b) A consumer gets utility from complete peanut butter and jelly sandwiches. Each
sandwich requires 2 ounces of jelly (J) and 3 ounces of peanut butter (P).
ANSWER:
(a) U (H, P ) = H + 2P
(b) U (J, P ) = min (3J, 2P )
4. A consumer has a utility function given by U = xy + 10x. Explain why it could be
optimal for this consumer to consume y = 0 but never optimal to consume x = 0.
(Hint: A complete answer does not need to fully solve for the Marshallian demand,
but can if it helps)
ANSWER: The consumer’s MRS = y+10 x
(5 points). If x = 0, then consumer’s utility
is 0. Therefore, they would always want to have a positive demand for x. Alternatively,
we can look at MRS and see that it wouldn’t make sense to send x to 0. The MRS
goes to infinity as we send x to 0, which means that the marginal unit of x is infinitely
more valuable than y. (5 points). Demand for y can be zero when the price ratio is
really small and the consumer is needs to reduce MRS as much as possible and still
end up with a corner solution on x (5 points).
3
Name:
Student ID:
TA:
Exam Rules
1. The exam starts at 8:00 and ends at 11:00.
2. There are 10 short answer questions worth 15 points each and 3 long questions (2 worth
40 points and 1 worth 50 points). The last 20 points will come from completing course
evaluations (10 points) and the post-final survey (10 points) for a total of 300 points.
3. Calculators are allowed, including graphing calculators.
4. You may use one double-sided 8.5x11 sheet of paper with notes as a cheat sheet.
5. Please put all materials other than your calculator, cheat sheet, and a pen or pencil in
your bag. If you have a phone or other item out for any reason you will be given a 0
on the exam.
6. You must SHOW ALL WORK. No credit will be given for an answer with no work.
You may leave an answer unsimplified, but be clear about the steps you took to get
there so the graders can easily see if it’s correct
1
,Short Questions (15 Points Each)
1. Two consumers have utility functions given by U A = x1/3y2/3 and U B = x1/3 + y2/3.
If each consumer has an income of 10 and the price of each good is 1, do the two
consumers choose the same consumption bundle to maximize their utility? Would
they always choose the same bundle for any income and prices?
ANSWER: The MRS of two consumers can be computed as (10 points):
y y1/3
MRSA = MRSB =
2x 2x2/3
At the income I = 10 and px/py = 1, we have (xA, yA) = (100 , 200 ), which is clearly not
3 3
the utility maximizing bundle for B as yB = 8x2B as not satisfied. So consumer would
not choose the same bundle at the current prices and income and they will not always
choose the same bundle for other prices and income.
2. A consumer has an MRS of x for y equal to 1/3 for any quantity of x and y. They
currently have 10 units of x and 10 units of y. Would they prefer to have 8 units of x
and 11 units of y? Explain why or why not.
ANSWER: Consumer with MRS = 1/3 means that they would trade 1/3 units of y
for one unit of x, or 1 y for 3 x. (5 points) To ask the consumer to switch from the
bundle (10,10) to (8,11) is to ask the consumer to gain 1 y by giving up 2 x. (5 points)
So consumer should prefer the deal of (8,11). (5 points)
2
, 3. Write utility functions for the following two scenarios (no explanation necessary - just
the function is enough)
(a) A consumer’s utility is unchanged after trading 2 hamburgers (H) for 1 slice of
pizza (P)
(b) A consumer gets utility from complete peanut butter and jelly sandwiches. Each
sandwich requires 2 ounces of jelly (J) and 3 ounces of peanut butter (P).
ANSWER:
(a) U (H, P ) = H + 2P
(b) U (J, P ) = min (3J, 2P )
4. A consumer has a utility function given by U = xy + 10x. Explain why it could be
optimal for this consumer to consume y = 0 but never optimal to consume x = 0.
(Hint: A complete answer does not need to fully solve for the Marshallian demand,
but can if it helps)
ANSWER: The consumer’s MRS = y+10 x
(5 points). If x = 0, then consumer’s utility
is 0. Therefore, they would always want to have a positive demand for x. Alternatively,
we can look at MRS and see that it wouldn’t make sense to send x to 0. The MRS
goes to infinity as we send x to 0, which means that the marginal unit of x is infinitely
more valuable than y. (5 points). Demand for y can be zero when the price ratio is
really small and the consumer is needs to reduce MRS as much as possible and still
end up with a corner solution on x (5 points).
3
