時(shí)間:2024-06-26  來(lái)源:  作者: 我要糾錯

ECON2101: Microeconomics 2
Assignment 2
Term 2, 2024
1. DEADLINE: 6pm Friday, the 28th of June.
2. The assignment comprises 2 pages excluding this cover page.
3. There are 3 questions. Answer all questions. Start each question on a new page.
4. There are a maximum of 20 points to obtain in this assignment.
5. This assignment is worth 10 course marks.
6. Answers must be supported by clear working and concise explanations. Full marks will not
be awarded if reasoning is unclear, or if working is illegible.
7. A small leeway is allowed for word/page limits, but blatant disregard for the limit or attempts
to game the system (e.g., very small writing) will result in a zero awarded for that part.
8. Submit your assignment as a PDF.
9. Late assignments will attract a penalty of 5% for each day it is late or part thereof, up to
a maximum of five calendar days. Technological failure is not a valid excuse for special
10. Any evidence of academic misconduct will be reported to the Academic Integrity
Committee and may result in a mark of zero being awarded for this assessment
item or the course.
Question: 1 2 3 Total
Points: 5 6 9 20
Question 1 (5 points)
Prim has three hours a day to gather one of two plants: honeysuckle (h), and pond lilies (l).
Each honeysuckle takes 5 minutes to collect, and each pond lily takes 10 minutes to harvest.
Further, suppose that Prim has a fixed amount of energy to use each day. She currently exhausts
this entire daily energy by picking seventeen honeysuckles and two pond lilies. She could also
have chosen to exhaust this daily energy by picking exactly five honeysuckles and twenty-six
pond lilies.
Assume that both goods are perfectly divisible.
(a) (1 point) Write down Prim  s time constraint as an algebraic inequality. (Working is not
(b) (2 points) Show that Prim  s energy constraint is given by 2h+ l    36.
(c) (2 points) Plot Prim  s energy constraint using a red dotted line and her time constraint
using a blue dotted line. Clearly label each constraint, any axis intercepts, and any points
of intersection between the two constraints. Shade in Prim  s budget set, using solid black
Question 2 (6 points)
Continue to consider Prim from the previous question. Suppose that Prim finds honeysuckles
and pond lilies to be perfect complements. She needs four pond lilies and one honeysuckle to
make one plant-based dessert, and more desserts are always better. Therefore, one valid utility
representation of Prim  s preferences is u(h, l) = min{4h, l}.
(a) (1 point) On the same picture as before, plot indifference curves for the utility levels
u = 8, 16, 24.
(b) (1 point) Explain in 40 words or fewer why Prim  s utility-maximising consumption
bundle must fully use up her available time or energy or both.
(c) (1 point) Given that we know Prim  s utility-maximising bundle must use up all her time
and/or energy, write down Prim  s utility-maximising bundle. (No working is required for
this part.)
(d) (3 points) Justify your answer to the previous part with working not exceeding half
an A4 page. (Hint: this argument should be similar to the one used to find the optimal
bundle when an individual expresses preferences over goods that are perfect complements.)
ECON2101 Assignment 2 1
Question 3 (9 points)
Tommy is a tank locomotive who must consume coal (x) and oil (y) in order to function. His
preferences over these inputs are quasilinear, and can be represented by the utility function
u(x, y) = x+2
y. Each ounce of coal costs ten pounds and each quart of oil costs two pounds.
Tommy has 100 pounds to spend. Assume that both coal and oil are perfectly divisible goods.
(a) (2 points) Find Tommy  s utility-maximising bundle of coal and oil.
(b) (1 point) Suppose that a miners   strike causes the price of coal to increase to 30 pounds
per ounce. What is Tommy  s new utility-maximising bundle?
(c) (3 points) Find Tommy  s demand for coal and demand for oil as functions of the price of
coal, the price of oil, and his income. In other words, find x?(px, py,m) and y?(px, py,m).
(Hint: don  t forget the case of the corner solution.)
(d) (3 points) Suppose that the government commits to funding a riot squad to suppress the
strike and return the price of coal to ten pounds per ounce. However, such an initiative
would only be possible if each citizen pays a tax that reduces their existing income. As
a utility maximiser, what is the maximum tax which Tommy is willing to pay? (In other
words, find the maximum tax that Tommy can pay so that he is at least well off as he was
under the miners   strike.) You may assume that Tommy  s utility-maximising bundle after
the tax is an interior solution. Round your final answer to three decimal places.
ECON2101 Assignment 2 2

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