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ECON7030 MICROECONOMIC ANALYSIS
创建日期：2024-05-22 16:37:09
所属分类：经济Economics
标签： ECON7030
MICROECONOMIC ANALYSIS

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ECON7030 MICROECONOMIC ANALYSIS

TUTORIAL EXERCISE 5
Question 1
Madam Lim consumes only two goods: Kopi (good x) and Kuih (good y).1 Her utility
over the two goods is given by
U(x, y) = ln x + 2 ln y.
Madam Lim is a retiree and has no income. However, her dutiful daughter-in-law,
Priscilla, gives her an allowance every week to spend on the two goods. The price of
Kuih remains at $1 each through out this exercise.
(a) In Week 1, Kopi costs $1 each. Madam Lim has an allowance of $36. Find her
utility maximising consumption bundle in Week 1. Calculate also the utility she
achieves at her optimal consumption bundle. (For now, leave utility in ln(·)).
(b) In a diagram with Kopi on the x-axis and Kuih on the y-axis, draw Madam Lim’s
Week 1 budget line. Label the optimal bundle you have found in part (a) and
sketch the indifference curve passing through it.
(c) In Week 2, the price of Kopi increases to $2. Suppose Priscilla is still giving
Madam Lim $36, how many Kopi and Kuih will Madam Lim consume? Draw the
budget line associated with this price and income on your diagram in part (b),
and label the consumption bundle you have found.
(d) How much does Priscilla have to give to Madam Lim in Week 2 so that Madam Lim
can afford her Week 1 bundle?
(e) Calculate Madam Lim’s utility maximising bundle in Week 2 had she been given
the income you found in part (d). Calculate also the utility she achieves at this
optimal consumption bundle. Is it higher, lower or the same as the utility you
found in part (a)?
(f) How much does Priscilla have to give to Madam Lim in Week 2 so that Madam Lim
can attain her Week 1 utility? Is this amount higher than, lower than or equal to
the income you have found in part (d)? As you are calculating this amount, find
also the consumption bundle Madam Lim will choose in Week 2 if she is given this
income.
(g) On the same diagram you have drawn earlier, draw the budget line associated with
the part (f) budget. Label the consumption bundle you have found in part (f).
(h) What is the change in amount of Kopi from part (a) to part (c) (i.e., the change
associated with a change in price but not money income)? What is the change in
1In case you are wondering: “Kopi” means “coffee” and “Kuih” means “cake”.
1
amount of Kopi from part (a) to part(f) (i.e., the change associated with a change
in price but with a compensation in income to make up the same utility)? Which
of the two changes is larger?
(i) In Week 3, the price of Kopi decreases to $0.5. Suppose Priscilla is still giving
Madam Lim $36 (her Week 1 income), how many Kopi and Kuih will Madam Lim
consume? On a separate diagram (please don’t draw this on the old diagram — it
will be incomprehensible), re-draw the graph of part (b), then draw in the budget
line associated with the Week 3 price and the Week 1 income. Label the utility
maximising bundle you have solved for this part.
(j) How much does Priscilla have to give to Madam Lim in Week 3 so that Madam Lim
can afford her Week 1 bundle?
(k) Calculate Madam Lim’s utility maximising bundle in Week 3 had she been given
the income you found in part (j). Calculate also the utility she achieves at this
optimal consumption bundle. Is it higher, lower or the same as the utility you
found in part (a)?
(l) How much does Priscilla have to give to Madam Lim in Week 3 so that Madam Lim
can attain her Week 1 utility? Is this amount higher than, lower than or equal to
the income you have found in part (j)? As you are calculating this amount, find
also the consumption bundle Madam Lim will choose in Week 3 if she is given this
income.
(m) On the same diagram you have drawn for part (i), draw the budget line associated
with the part (l) budget. Label the consumption bundle you have found in part (l).
(n) What is the change in amount of Kopi from part (a) to part (i) (i.e., the change
associated with a change in price but not money income)? What is the change in
amount of Kopi from part (a) to part(l) (i.e., the change associated with a change
in price but with a compensation in income to make up the same utility)? Which
of the two changes is larger?
(o) Do your comparisons of the utility levels in parts (e) and (k) (i.e., whether
Madam Lim is attaining a utility level higher than that in Week 1 when she
is given an income to make her Week 1 bundle affordable) depend on whether it
is a Kopi price increase or Kopi price decrease? Give an intuitive explanation.
(p) Madam Lim’s sister, Angela, has the following utility function
U(x, y) = min{x, y}.
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