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ECE103
Dr. Secrieru
ECE103
Assignment #2
Handed-out March 31, 2022
Due: April 14, 2022 @23:55 EST
1. [20 marks] Miss Bates spends her money on
ead and low-quality meat, and her
indifference curves obey the four properties of indifference curves for ordinary goods.
Suppose that, for Miss Bates,
ead is a normal good. Bread costs $1.5 per loaf, and a
ation of meat costs $3.5. Miss Bates has $18 a week to spend on
ead and meat.
a. [6 marks] Draw Miss Bates’ budget line and indifference curve that illustrates her
optimal consumption bundle. [It is fine if either intercept is not an integer.] Place
meat on the horizontal axis and
ead on the vertical axis. Suppose her optimal
consumption bundle is 3 rations of meat and 5 loaves of
ead. Illustrate that
undle and draw the indifference curve, ?0, on which it lies.
. [6 marks] The price of meat increases to $4.5; the price of
ead remains the
same. Miss Bates now buys 2 rations of meat and 6 loaves of
ead. Illustrate her
new budget line and new consumption bundle on your diagram. Also draw the
indifference curve, ?1, on which this bundle lies.
c. [8 marks] Emma Woodhouse decides to compensate Miss Bates for the increase
in the price of meat by giving her an allowance of $1.5 per week, which would
give Miss Bates the same utility as she was getting before the price increase.
Assume that at the new prices and with Emma’s allowance, Miss Bates consumes
1 ration of meat and 10 loaves of
ead (this bundle is on indifference curve ?0).
Indicate this situation on your diagram and show the income and substitution
effects from this increase in the price of meat. Is meat a normal or inferior good?
Justify your answer.
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2. [30 marks] Cassandra allocates her income to frozen Dinners and Thai Take-out meals.
The accompanying table shows her utility from the quantity of frozen Dinners or the
quantity of Take-out meals.
Quantity of Dinners
??
Utility from
Dinners
???
Quantity of Take-
out Meals
??
Utility from Take-
out Meals
???
0 0 0 0
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
Cassandra has ? = $150 per month to spend on Dinners and Take-out meals. The price of a
frozen Dinner is ??
0 = $9 and the price of a Take-out meal is ??
0 = $15.
a. [3 marks] Plot Cassandra’s budget line with Dinners on the horizontal axis and Take-out
meals of the vertical axis. What do the horizontal and vertical intercepts represent?
(Don’t wo
y if either of these intercepts is not an integer.)
. [4 marks] Calculate Cassandra’s marginal utility of Dinners (???) and marginal utility
of Take-out meals (???).
c. [4 marks] Calculate Cassandra’s marginal utility per dollar spent on Dinners,
???
??
0 , and
her marginal utility per dollar spent on Take-out meals,
???
??
0 , at the given prices, i.e.
??
0 = $9 and ??
0 = $15.
d. [2 marks] Determine all bundles for which the marginal utility per dollar spent on each of
the two goods is equalized.
e. [3 marks] What is Cassandra’s optimal consumption bundle? Represent this bundle on
your graph obtained in part (a) and denote it by ?0. Draw Cassandra’s indifference curve
at the optimal consumption bundle and denote it by ?0.
f. [7 marks] Now assume that the price of frozen Dinners decreases and is now ??
1 = $5.
Assume that the price of Take-out meals and Cassandra’s income have not changed. Re-
do parts (a) to (e) for prices. ??
1 = $5 and ??
0 = $15. Plot the new budget line, the new
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optimal consumption bundle, ?1, and the new indifference curve, ?1, on the same graph
obtained in part (a).
g. [3 marks] Indicate the substitution effect (SE) and income effect (IE) of a decrease in the
price of Dinners from ??
0 = $9 to ??
1 = $5 on your graph, assuming that frozen Dinners
are an inferior good.
h. [4 marks] Assuming that frozen Dinners are an inferior good, how much money income
would Cassandra’s parents (Hecuba and Priam) have to take away from her so that, at the
new prices, ??
1 = $5 and ??
0 = $15, bundle ???? consisting of 12 Dinners and 4 Take-out
meals gives Cassandra the same utility as bundle ?0?
3. [20 marks] A te
orist group has indifference curves (which obey the four properties of
indifference curves for ordinary goods) over te
orist activities (T) and non-te
orist
activities (N). The te
orist group faces a resource constraint
?? ∙ ? + ?? ∙ ? = ?,
where ?? and ?? are the unit costs of generic te
orist (T) and non-te
orist actions (N),
and I is the groups income or resources for the cu
ent period.
a. [2 marks] If the te
orists devote all of their resources to te
orist attacks, how many
attacks can they accomplish?
. [2 marks] If the te
orists devote all of their resources to non-te
orist activities, how
many non-te
orist activities can they accomplish?
c. [3 marks] Draw the te
orist group’s resource constraint with te
orist activities (T) on
the horizontal axis. [The intercepts are a
itrary since you do not have numbers for
the costs of the two activities and the group’s resources.]
d. [3 marks] The te
orist group is choosing the optimal bundle of te
orist (T) and non-
te
orist (N) activities to maximize utility subject to the resource constraint. Indicate
the optimal bundle and the co
esponding indifference curve on your previous
diagram. [Pick an a
itrary bundle as, again, you do not have numbers for the costs
of the two activities and the group’s resources.]
e. [5 marks] The government is engaging in proactive measures to reduce the te
orist
group’s resources, I. Illustrate this situation on your previous diagram, indicating the
new optimal combination of te
orist and non-te
orist activities. Be explicit about
the assumptions you make regarding the two types of activities (i.e. normal or inferior
goods). [Either assumption is fine as long as you justify it and draw a diagram that is
consistent with your assumption.]
f. [5 marks] Now consider an alternative defensive policy which increases the cost of
te
orist activities for the group. Illustrate this situation on a separate diagram,
indicating the new optimal combination of te
orist and non-te
orist activities chosen
y the te
orist group. Indicate the substitution and income effects on your diagram.
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4. [30 marks] Milo Minde
inder runs M&M Enterprises which produces crates of
tangerines. Milo hires soldiers in Italy at $10 per day and rents one plane at $50 per day.
Milo buys crates of tangerines in Morocco and pays local workers $1 per crate. M&M
Enterprises’ total product schedule is given by the following table:
L
(soldiers)
Q
(crates of tangerines)
1 10
2 30
3 45
4 52
5 57
6 59
7 60
where labour, L, is measured in numbers of soldiers hired and output, Q, in numbers of
crates of tangerines.
a. [4 marks] Plot M&M’s total product curve (Graph 1).
. [7 marks] Determine the marginal product of labour (???) of each unit of labour;
determine the average product of labour (??) at each level of labour; plot the
marginal product and the average product curves on the same graph (Graph 2). What
is the shape of the marginal product of labour curve? How do you interpret this?
c. [6 marks] Determine M&M’s total fixed cost (???), total variable cost (???), and
total cost (??) of production at each level of output. Plot the total fixed cost, variable
cost, and total cost curves on the same graph (Graph 3).
d. [8 marks] Determine M&M’s average fixed cost (???), average variable cost (???),
and average total cost (???) at each level of output. Plot the average fixed cost,
average variable cost, and average total cost on the same graph (Graph 4). What is
the shape of the average fixed cost? What about that of the average variable cost and
average total cost? What explains the shape of these curves?
e. [5 marks] Determine M&M’s marginal cost (??) at each level of output. Plot the
marginal cost curve on Graph 4 obtained in part (d). What is the relationship between
the average total cost and the marginal cost curves?