Transcript Chapter 5 - Appendix

Chapter 5 Appendix
Indifference Curves
Problem 1
• Suppose a consumer’s income is M=$1,200 per month, all of
which he spends on some combination of rent and restaurant
meals. If restaurant meals cost $12 each and if the monthly
rent for an apartment is $3 per square foot, draw this
consumer’s budget constraint, with his monthly quantities of
restaurant meals per month on the vertical axis and
apartment size on the horizontal axis. Is the bundle (300
square feet/month, 50 meals/month) affordable?
Solution to Problem 1
• If she spends all of her income on meal, , the
vertical intercept of the consumer’s budget
constraint is 100 meals/month
•If she spends all of her income on rent, the
horizontal intercept of his budget constraint is
400square feet/month
meals/month
100
A
50
•Bundle A:
•50 meals/month, costs $600/month
•300 square feet/month, costs $900/month
•Thus, total income requires is $1,500/month
square feet/month
300
400
Bundle A lies beyond the budget constraint, and is hence
unaffordable
Problem 2
• Show what happens to the budget constraint in problem 1 if
the price of restaurant meals falls to $8. Is the bundle (300,
50) affordable?
Solution to Problem 2
meals/month
•Price of meals falls to $8
150
• If she spends all of her income on meal, the
vertical intercept of his budget constraint is
150 meals/month
•If she spends all of her income on rent, the
horizontal intercept of his budget constraint is
400square feel/month
100
A
•Bundle A:
•50 meals/month, costs $400/month
•300 square feet/month, costs $900/month
•Thus, total income requires is $1,300/month
50
square feet/month
300
400
Bundle A lies beyond the budget constraint, and is hence
unaffordable
Problem 3
• What happens to the budget constraint in problem 2 if the
monthly rent for apartments falls to $2 per square foot? Is
the bundle (300, 50) affordable?
Solution to Problem 3
meals/month
150
•Price of monthly rent falls to $2
B
• If she spends all of her income on meal, the
vertical intercept of his budget constraint is
150 meals/month
•If she spends all of her income on rent, the
horizontal intercept of his budget constraint is
600square feel/month
A
•Bundle A:
•50 meals/month, costs $400/month
•300 square feet/month, costs $600/month
•Thus, total income requires is $1,000/month
50
C
square feet/month
300
400
600
Bundle A lies within the budget constraint, and is hence
affordable
Problem 4
• When inflation happens, prices and incomes generally rise at
about the same rate each year. What happens to the budget
constraint from problem 1 if the consumer’s income rises by
10 percent and the prices of restaurant meals and apartment
rents also rise by 10 percent? Has the consumer been
harmed by inflation?
Solution to Problem 4
•
•
•
meals/month
100
•
•
•
square feet/month
400
•
Her new income is $1320/month
The price of restaurant meals is $13.20,
If she spends all of her income on meal, the
vertical intercept of the consumer’s budget
constraint is 100 meals/month, exactly the
same as before
The price of monthly rent is $3.3/square
foot,
If she spends all of her income on rent, the
horizontal intercept of his budget constraint
is 400 square feet/month, exactly the same
as before.
Since the consumer’s budget constraint has
not changed, he is able to buy exactly the
same combinations of goods he was able to
buy before.
So he has not been harmed by this inflation.
Problem 5
• A consumer spends all his income on two goods, X and Y. Of the
labeled points on his indifference map, indicate which ones are
affordable and which ones are unaffordable. Indicate how the
consumer ranks these bundles, ranging from most preferred to least
preferred. Identify the best affordable bundle.
IC
Y
IC
IC
4
3
1 IC2
C
E
G
H
J
F
A
D
X
Solution to Problem 5(1)
• Affordable bundles:
- any bundle that lies on or within the budget constraint
- Bundles A, C, D, E, F, G are affordable
• Unaffordable bundles:
- any bundle that lies beyond the budget constraint
- Bundles H and J are unaffordable
Solution to Problem 5(2)
• Bundles that lie on the highest indifference curve are the
most preferred bundles
• Bundles that lie on the same indifference curve are equally
preferred
• The best affordable bundle should lie on an indifference curve
that intersects the budget constraint only once
Solution to Problem 5(3)
IC
Y
IC
• To rank these bundles:
- H is preferred to J, which is
equivalent to G, which is
preferred to E, which is
equivalent to F, which is
preferred to D, which is
equivalent to A and C.
4
3
IC IC
1 2
C
E
G
H
J
• The Best affordable bundle is G
F
A
D
X
Problem 6
• A consumer spends all his income on two goods, X and Y. His
income and the prices of X and Y are such that his budget constraint
is the line AF. Of the labeled points on his indifference map, indicate
which is the best affordable bundle. (Hint: This problem does not
have a tangency solution.)
Y
F
G
IC
E
IC
6
5
D
IC
IC
1
4
IC
C
IC2
A
3
X
Problem 6(1)
• The best affordable bundle should lies on the budget
constraint and attains the highest possible indifference curve
• Bundle G is unaffordable as it lies outside the budget
constraint
• Bundle A, C, D, E, F are all affordable as it lies on the budget
constraint
• The best affordable bundle is F
- at this bundle, he attains the highest possible indifference
curve (IC5) along his budget constraint
• Bundle F is called a “corner solution.”
Problem 6(2)
• For a corner solution,
- all income will spend on only one good and zero
consumption on the other good
- utility is maximized at a point where the highest possible
indifference curve intersects the budget constraint at zero
consumption for Good X and with all income used for Good Y
Additional Question 1
• Jane has $100 to spend. There are only 2 goods for her to
choose: compact discs (CDs) and hamburgers. Price of CD =
$10. Price of hamburger = $2.
• a) Graph Jane’s budget line for compact discs and
hamburgers, x-axis for hamburgers and y-axis for compact
disc, and use an indifference curve to show on the graph the
point that represents a given optimal quantities of compact
discs and hamburgers Jane chooses to consume. (Given
equilibrium: 5 units of compact discs with 25 units of
hamburgers)
(a)Draw Jane’s Budget Line and find the optimal quantities of
CDs and hamburgers to be consumed.
• What is a Budget Line?
• A Budget Line is the ‘Budget Constraint’ of the economic
agent. It represents all the different combinations of the 2
goods that Jane can consume when spending all her $100.
• How do we draw a Budget Line?
• In a simple setting like in this question (no change in price of
either goods throughout, no restrictions or special pricing
arrangements), the Budget Line is usually a downward sloping
straight line.
• The X and Y-intercepts represents the amount of CDs or
Hamburgers Jane can buy if she spends all her money on only
one good.
• If Jane is spending all $100 on CDs, and price of a CD is $10,
she can at most buy 10 CDs.
• Hence, the Y-intercept of Jane’s Budget Line is 10.
• Similarly, if she spends all the money only on hamburgers
(Price = $2), she can buy 50 hamburgers.
• So the x-intercept of the Budget Line is 50.
Compact
Discs
10
50
Hamburgers
• The question also asks us to identify the optimal consumption
point by using indifference curves. Given the equilibrium, 5
units compact disc, 25 units of hamburgers.
• The optimal consumption point, which is given in this
question, is the point at which the Indifference curve is
tangential to the Budget Line.
(b) Show what happens to the Budget Line if the Price of CDs
drops from $10 to $5. Sketch the new optimal consumption
point for Jane.
•
•
•
•
•
If the Price of CDs drops, the Y-intercept of the Budget Line
rises.
Because if Jane is spending all her $100 just on CDs, she can
get 20.
However, the X-intercept of the Budget Line remains
unchanged.
Because even if she spends all her money on hamburgers,
as the price of hamburgers has not changed, she ends up
getting 50.
the Budget Line ‘rotates’ out on the Y-axis.
Compact Discs
20
10
50
Hamburgers
• Again, we need to find the optimal consumption point.
• The Price of compact discs falls; thus, the Budget Line has
changed, Jane may be better off choosing another optimal
point to maximise her utility.
• The new point is, again, the tangency point of the Budget Line
and the (new) Indifference Curve.
• TWO effects will be induced in the consumption choice of
compact discs.
• A change in the price of a good changes
- Relative price of the good (substitution effect) and
- Overall purchasing power of the consumer (income effect)
• Substitution effect:
- is observed with changes in relative price of goods
When PCD falls, other things being constant ( PHamburger,
income), people consume more compact disc and less
hamburger.
• Applying the Rational Spending Rule:
• At the optimal combination of goods, the Rational Spending Rules,
MUCD / PCD = MUH / PH
• When PCD falls, the MU per dollar of CD rises relative to Hamburger. That
is,
MUCD / PCD > MUH / PH
• To satisfy the Rational Spending Rule, we will increase our consumption of
CD and decrease our consumption of Hamburger.
• Therefore, the reduction of PCD will not only change (increase) the amount
of CD we could afford but also change (decrease) the amount of
Hamburger we could afford in combination with any given amount of CD.
• The reallocation of our optimal combination due to a change in “relative”
prices as described in here, is called the substitution effect.
• Income effect:
- Decrease in price of a good just like giving consumer a gift,
which is rather like an increase in income
- is observed through changes in purchasing power
• When PCD drops, purchasing power of the individual increases
• Both hamburger and compact discs are assumed to be normal
goods in this case
• That is, he should buy more CD and hamburger in the new
equilibrium (income effect).
•
Applying Rational Spending Rule:
•
If we simply switch our consumption from Hamburger to CD until the MU
per dollar are the same, we will have some income not spent resulted
from the lower price of CD. Thus, we are now richer than before.
•
We have to allocate this “extra” purchasing power to both good. Thus,
we may increase our consumption of both goods.
•
The allocation of our “additional” purchasing power to the two goods, as
described in here, is called the income effect.
Compact Discs
•As PCD falls, the new optimal consumption point moves
from pt. A to pt. B
20
10
B
A
5
25
50
Hamburgers
(c) Suppose there is an increase in Jane’s wealth. Jane now has
$150 rather than $100. Show the change in diagrams for
the cases of CDs being normal and CDs being inferior.
•
•
Jane has an increase in wealth. At the same time, prices of
CDs and health have not changed.
Therefore, the Budget Line should shift outwards in a
parallel manner.
Compact Discs
15
10
50
75
Hamburgers
• Here, we should consider only the ‘income effect’.
• If CDs are normal goods, income effect on CDs should be
positive (the more wealthy/ purchasing power one gets, the
more CDs needed)
• Note: hamburger is assumed to be normal good in this case as
well.
Positive Income Effect on CDs
Compact Discs
•CDs and Hamburger are normal goods
• Consumption of CDs increases
•Consumption of Hamburger increases
15
10
B
A
50
75
Hamburgers
• If CDs are inferior goods, income effect on CDs should be
negative. (i.e. higher income, less CDs consumed)
• The new consumption point will contain less CDs than the
original point.
• Note: hamburger is assumed to be normal good in this case as
well.
Negative Income Effect on
CDs
Compact Discs
•CDs are inferior goods and Hamburger is a normal
good
• Consumption of CD decreases
•Consumption of Hamburger increases
15
10
A
B
50
75
Hamburgers
Additional 2
Substitution effect and Income effect
True or false (income and substitution effects):
In a market with only two goods, say A and B, if the price of good A
lowers and other things being equal (income and the price of good
B), the consumer will always buy more good A and less good B.
(Assume Good A and B are normal goods)
Substitution Effect:
i.e. When price of a good X increases, substitutes for that good, good Y,
become relatively more attractive. Consumers switch to good Y and buy
less on good X.
Income Effect:
Refers to the fact that when price of a good changes, it makes the
consumers either poorer or richer in real terms.
True or false (income and substitution effects):
In a market with only two goods, say A and B, if the price of good A
lowers and other things being equal (income and the price of good
B), the consumer will always buy more good A and less good B.
(Assume Good A and B are normal goods)
Not necessary.
-It is true according to Substitute Effect.
- It is not true according to Income Effect. You will consume more
of both goods if real income increases.
- It is true unless Good A is a normal good and Good B is an inferior
good.
End of Chapter 5 Appendix