Transcript ECON 102 Tutorial: Week 4

ECON 102 Tutorial: Week 4
Ayesha Ali
www.lancaster.ac.uk/postgrad/alia10/econ102.html
[email protected]
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Question 1: Ch 4 Question 8
Using indifference curves, show how a price rise for
one good affects consumption of that good by:
a) Lowering the consumer’s real income, and
b) Altering relative prices of the two goods.
Using Indifference Curves
to show Income and Substitution Effects
In a two-good model of consumption, when a price change occurs, we will have two
effects on our consumption: a substitution effect and an income effect:
How do we graph this?
First, we draw our original budget constraint, original indifference curve, and the
new budget constraint which comes from the change in price of one good.
Next, we can find the substitution effect, the movement along the indifference
curve, to a point whose MRS is equal to the slope of the new budget constraint.
Finally, we can find the income effect – which will move us to a new indifference
curve on the new budget constraint. Where we move due to the income effect
depends on whether our good whose price changed is a normal, inferior or giffen
good.
For a detailed explanation of how to use indifference curves to show income and
substitution effects in response to a price change this video is very thorough.
Another Example:
We have two goods, pizza and Pepsi. Pizza is on the x-axis and Pepsi is on the y-axis.
Show what happens when the price of Pepsi decreases if Pepsi is a normal good.
Question 1: Ch 4 Question 8
Here is Prof. Rietzke’s solution; basically it gives the same explanation as we did in class:
A price rise in one good means that less of it can be bought given a fixed budget. Hence, the
budget constraint swivels around the intercept point of the other good.
In reference to Figure 4.17 in the textbook, we can demonstrate that if good B has become
more expensive the budget constraint becomes steeper, hence the intercept for good B
moves closer to the origin (no change to the price of good A).
Two things happen: 1) there is an income effect, which means
that the consumer is moved to a lower indifference curve
(the consumer’s purchasing power is reduced, and hence can
no longer attain the original indifference curve); and 2) The
substitution effect kicks in as the relative prices of goods A
and B have changed.
Good A now is a better bargain and there is a substitution towards the now cheaper good. In
Figure 4.17, start at point 1, the original bundle before the price change. Now good B
becomes more expensive and the budget constraint becomes steeper. If we could
compensate the consumer for the loss in income, then this consumer could remain on the
old indifference curve, and would only have to consider the change in relative prices (i.e. we
strip out the income effect with this trick and concentrate on the substitution effect only).
Graphically this is shown by a parallel shift of the new budget constraint until it just touches
the old indifference curve (shown by the orange budget constraint in Figure 4.17).
Consumption would be at point 3. The move from point 1 to 3 shows the substitution effect
only. Hence, the move from point 3 to point 2, the new bundle after the price change,
shows the income effect only.
Question 1: Ch 4 Problem 6(a)
Anna Lucia lives in Cremona and commutes by train each day to her job in
Milan (20 round trips per month).
When the price of a round trip goes up from €10 to €20, she responds by
consuming exactly the same number of trips as before, while spending €200
per month less on restaurant meals.
Does the fact that her quantity of train travel is completely unresponsive to
the price increase imply that Anna Lucia is not a rational consumer?
The concept of consumer rationality states that a consumer will allocate his
or her budget between goods so that the ratio of marginal utility to price is
the same across all goods (that’s the rational spending rule from last week).
So, even at twice the original price, the marginal utility per euro of the 20th
train trip may be higher than the corresponding ratio for any other good
that Anna Lucia might consume, in which case she would be perfectly
rational not to alter the number of trips she takes. After all, missing a trip
would be to miss a whole day’s work.
Question 1: Ch 4 Problem 6(b)
Explain why an increase in train travel might affect the amount she
spends on restaurant meals.
The higher price of train tickets makes Anna Lucia poorer. The income
effect of the price increase is what leads to the reduction in the
number of restaurant meals she eats.
Question 2(a)
Karen divides her budget between two goods: good one and good two.
Using indifference curve analysis, graphically illustrate the effect on consumption of
both goods if the price of good one decreases; goods one and two are substitutes.
(for each part of this question, put good two on the y-axis and good one on the x-axis)
Question 2(a)
Karen divides her budget between two goods: good one and good two.
Using indifference curve analysis, graphically illustrate the effect on consumption of
both goods if the price of good one decreases; goods one and two are substitutes.
(for each part of this question, put good two on the y-axis and good one on the x-axis)
Before the price decrease, the optimal bundle
is at the point A.
When the price of good one decreases, the
budget line shifts out from B1 in red to B2 in
green.
After the price decrease, the optimal bundle is
at the point B.
Because goods 1 and 2 are substitutes, when
the price of good 1 decreases, the consumer
consumes less good 2. So, at the new optimal
bundle, the consumer consumes more good 1
and less good 2.
Question 2(b)
Karen divides her budget between two goods: good one and good two.
Using indifference curve analysis, graphically illustrate the effect on consumption of
both goods if the price of good one increases; goods one and two are complements.
(for each part of this question, put good two on the y-axis and good one on the x-axis)
Question 2(b)
Karen divides her budget between two goods: good one and good two.
Using indifference curve analysis, graphically illustrate the effect on consumption of
both goods if the price of good one increases; goods one and two are complements.
(for each part of this question, put good two on the y-axis and good one on the x-axis)
Before the price decrease, the optimal bundle
is at the point A.
When the price of good one increases, the
budget line shifts inwards from B1 in red to B2
in green.
After the price increase, the optimal bundle is
at the point B.
Because goods 1 and 2 are complements,
when the price of good 1 increases, the
consumer consumes less good 2. So, at the
new optimal bundle, the consumer consumes
less good 1 and less good 2.
Question 2(c)
Karen divides her budget between two goods: good one and good two.
Using indifference curve analysis, graphically illustrate the effect on consumption of
both goods if Karen’s income increases; goods one and two are normal.
(for each part of this question, put good two on the y-axis and good one on the x-axis)
Question 2(c)
Karen divides her budget between two goods: good one and good two.
Using indifference curve analysis, graphically illustrate the effect on consumption of
both goods if Karen’s income increases; goods one and two are normal.
(for each part of this question, put good two on the y-axis and good one on the x-axis)
When Karen’s income increases, her budget
line shifts outwards from B1 in red to B2 in
green.
Her optimal bundle moves from point A to
point B.
Since both goods are normal, her consumption
of both goods increases following the increase
in her income
Question 2(d)
Karen divides her budget between two goods: good one and good two.
Using indifference curve analysis, graphically illustrate the effect on consumption of
both goods if Karen’s income decreases; good one is normal and good two is
inferior. (for each part of this question, put good two on the y-axis and good one on the x-axis)
Question 2(d)
Karen divides her budget between two goods: good one and good two.
Using indifference curve analysis, graphically illustrate the effect on consumption of
both goods if Karen’s income decreases; good one is normal and good two is
inferior. (for each part of this question, put good two on the y-axis and good one on the x-axis)
When Karen’s income decreases, her budget
line shifts inwards from B1 in red to B2 in green.
Her optimal bundle moves from point A to
point B.
Because good 1 is normal, Karen decreases her
consumption of good 1. And because good 2 is
inferior, a decrease in her income leads her to
consume more of good 2.
Question 3: Ch. 5 Problem 1(a)
Zoe is trying to decide how to divide her time between her job as a wedding
photographer, which pays €27 per hour for as many hours as she chooses to
work, and as a fossil collector, in which her pay depends both on the price of
fossils and the number of them she finds. Earnings aside, Zoe is indifferent
between the two tasks, and the number of fossils she can find depends on
the number of hours a day she searches, as shown in the table below.
Hours per day
Total fossils per day
(1)
(2)
1
5
2
9
3
12
4
14
5
15
Derive a table with price in euro increments from €0
to €30 in column (1) and the quantity of fossils Zoe is
willing to supply per day at that price in column (2).
Question 3: Ch. 5 Problem 1(a)
Derive a table with price in euro increments from €0 to €30
in column (1) and the quantity of fossils Zoe is willing to
supply per day at that price in column (2).
1. If the price of a fossil is less than €6, Zoe should devote all her
time to photography because when the price is, say, €5 per fossil, an
hour spent looking for fossils will give her 5(€5) = €25, or €2 less
than she’d earn doing photography. If the price of fossils is 6, Zoe
should spend one hour searching, will supply 5 fossils, and will get
€30 revenue, which is €3 more than she’d earn from photography.
However, an additional hour would yield only 4 additional fossils or
€24 additional revenue, so she should not spend any further time
looking for fossils. If the price of fossils rises to €7, however, the
additional hour gathering fossils would yield an additional €28, so
gathering fossils during that hour would then be the best choice,
and Zoe would therefore supply 9 fossils per day. Using this
reasoning, we can derive a price-quantity supplied relationship for
fossils as follows:
Price of fossils (€)
0-5
6
7, 8
9-13
14-26
27+
Hours per day
Total fossils per day
(1)
(2)
1
5
2
9
3
12
4
14
5
15
Number of fossils supplied per day
0
5
9
12
14
15
Question 3: Ch. 5 Problem 1(b)
Using the table you found in part (a), plot these points in a
graph with price on the vertical axis and quantity per day
on the horizontal. What is this curve called?
If we plot these points, we get Zoe’s daily supply curve for
fossils:
Price of
fossils (€)
0-5
6
7, 8
9-13
14-26
27+
Number of fossils
supplied per day
0
5
9
12
14
15
Question
4(a)
The table below gives the relationship between the number of workers in a firm, and the
total output that can be produced per day. Workers are paid $20 per day.
Fill in the rest of the table, expressing each of the costs in the cost per day for the firm.
(Note: AFC is average fixed cost, AVC is average variable cost, ATC is average total cost, and MC is marginal cost)
Average fixed cost:
Average variable cost:
Average total cost:
AFC = FC/Q
AVC = VC/Q
ATC = TC/Q
Marginal cost per unit of output: MC =
Workers
Q
0
0
1
25
2
63
3
94
4
119
5
140
6
158
Fixed
Costs
∆𝑇𝐶
∆𝑄
Variable
Costs
Total
Cost
AFC
AVC
ATC
MC
10
-
-
-
-
Question 4(a)
The table below gives the relationship between the number of workers in a firm,
and the total output that can be produced per day. Workers are paid $20 per day.
Fill in the rest of the table, expressing each of the costs in the cost per day for the
firm.
Average fixed cost:
AFC = FC/Q
Average variable cost: AVC = VC/Q
Average total cost:
ATC = TC/Q
Marginal cost per unit of output:
Workers
Q
Fixed
Costs
0
0
10
1
25
2
MC =
∆𝑇𝐶
∆𝑄
Variable
Costs
Total
Cost
AFC
AVC
ATC
MC
0
10
-
-
-
-
10
20
30
0.400
0.800
1.200
0.800
63
10
40
50
0.159
0.635
0.794
0.526
3
94
10
60
70
0.106
0.638
0.745
0.645
4
119
10
80
90
0.084
0.672
0.756
0.800
5
140
10
100
110
0.071
0.714
0.786
0.952
6
158
10
120
130
0.063
0.759
0.823
1.111
Question 4(b)
Graph the firm’s ATC, AVC, and MC curves.
1.400
$
1.200
1.000
0.800
AVC
ATC MC -
0.600
0.400
0.200
0.000
1
2
3
4
5
6
No. of workers
-
Question 4(c)
Does this production technology exhibit diminishing marginal products? Explain.
From our table, we know the second worker produces an additional
38 units, which is more than the first worker produces. After the
second worker, each additional worker produces less additional
output than the previous worker.
Therefore, for W > 2 (where W is the number of workers) the
production technology does exhibit decreasing marginal products.
For W ≤ 2, the production technology exhibits increasing marginal
products.
Next Week
 Multiple Choice Exam in Week 6 on Friday
 20 questions from Prof. Rietzke (economics questions)
 Covering material up until the Tutorial 6 worksheet
 10 questions from Prof. Peel (maths questions)
 Exactly like his maths practice questions at the end of lecture notes.
 Check your timetable for exam time and location.
 Study & Review lecture slides, tutorial questions, and maths
questions.