21

1
Exercise n 7

• Chapter
• 21 The theory of consumer choice

2

• Construction of the budget constraint
• Hypotheses
• only two goods
• the consumer spends all the income to buy the
  two goods

Information Income 500 Price of good 1
10 Price of good 2 5
The budget constraint curve represents all the
combinations of the two goods that can be bought
by spending all the income.
3
If the consumer spends all his income to buy good
2, he can get 100 units. Point A 100 units of
good 2 and zero of good 1
By spending the income in equal parts to buy both
goods, the consumer can get 50 units of good 2
and 25 units of good 1. Point C 25 units of
good 1 and 50 units of good 2
If the consumer spends all his income to buy good
1, he can get 50 units. Point B 0 units of
good 2 and 50 units of good 1
4
Slope of the budget constraint it corresponds to
the price of good 1 relative to the price of good
2
slope of the budget constraint ? x2 /
?x1 (vertical variation divided by the horizontal
variation)

• For example passing from point C to point B ?
  x2 (0-50) -50 and ?x1 (50-25) 25
• x2 / ?x1 (50/25) -2 slope of the budget line
• (For the consumer one additional unit of good 1
  costs two units of good 2)

Putting aside the negative sign of the slope
(which is considered in absolute values), it
corresponds to the relative price of the two
goods Relative price Pgood1 / Pgood2 10/5
2
5
Comparative statics of the budget constraint
The budget constraint moves due to two main
reasons Changes in the income Changes in the
price of the two goods
6
Preferences they are represented
through Indifference curves (the points along the
indifference curve are the combinations of the
two goods that give the same level of utility to
the consumer)
Properties of indifference curves

1. Higher indifference curves are characterised by a
   higher utility (satisfaction level)
2. Indifference curves have a negative slope
3. Indifference curves do not intersect each other
4. Indifference curves are convex to the origin

7
Marginal Rate of Substitution MRS
Rate to which the consumer agrees to change one
good with another
It represents the slope of the indifference curve
and depends on the quantity of goods already
available to the consumer
8
Optimal choice of the consumer
Reach the higher indifference curve, associated
with the highest utility, respecting the budget
constraint.
In the optimal point the MRS (the relative
valuation of the two goods by the consumer)
equals the relative price (the relative valuation
of the two goods by the market)
9
Price of good 1 1 Price of good 2 2
Income 14
Practical case n.1
Given the indifference curves, draw the budget
constraint and show the optimal choice of the
consumer.
10
The income icreases from 14 to 16 and prices do
not vary. How does consumption change? What type
of goods are goods 1 and 2?
The consumption of good 1 decreases with the
increase in the income. Good 1 is an inferior
good
The consumption of good 2 increases with the
increase in the income. Good 2 is a normal good
11
Practical case n. 2
A consumer has an income of 75 to be spent in
books and videotapes.
7,5 Price of videotapes
7,5 Price of books
The preference of consumers for books and
videotapes are described by the following
indifference curves
Draw a budget constraint and show the choice of
the consumer
12
If all the income is spent in videotapes the
maximum consumption possible is 10 units, and the
same is for books the budget constraint
represents all the possible combinations and is
as follows
Quantities consumed 5 books and 5
videotapes
13
The price of books decreases to 5. How does
consumption change?
The maximum quantity of books that can be bought
passes from 10 to 15, but that of videotapes does
not change. The new available combinations after
the change in the price are shown in the dotted
line.
Quantity consumed 9 books and 4 videotapes
N.B. consumption has changed and the utility of
the consumer has increased (higher indifference
curve).
14
Show the income effect and the substitution
effect due to the change of book prices.
Income effect the change of consumption due to
the passage to a higher or lower indifference
curve.
Substitution effect the change of consumption
due to the passage to a different point of the
same indifference curve, as the MRS changes.
Reduction of the price of books (income effect-
increase in income)
Income effect Substitution effect Aggregate effect
Book consumpt consumpt
Video consumpt consumpt
?
15
The substitution effects is exclusively due to
the change in the MRS. It can be shown by drawing
a line parallel to the new budget constraint and
by showing on the initial indifference curve the
new optimal (tangent) point, for which the MRS
equals the new price ratio.
The change in the MRS determines an increase of
the consuption of the cheapest good and a
decrease of the other.
The income effect causes an increase in the
consumption of both goods, but it is not
sufficient to compensate the reduction for the
good which has become relatively more expensive.
16
Practical case n. 3
Suppose that a consumer reduces his consumption
of good X as the price of good Y increases. How
can such behaviour be explained (income
effect/substitution effect)?
Increase in the price of good Y (income
effect-reduction of income)
Income effect Substitution effect Aggregate effect
good x Consumpt Consumpt
good y Consumpt Consumpt
N.B. given data
17
The increase in the price of one of the two goods
is associated with an income effect similar to a
reduction of the available income. If the two
goods are normal goods, consumption will decrease
for both of them.
The increase of the price of one of the two goods
makes the latter relatively more expensive. Due
to the substitution effect consumption will
increase for the good whose price has not changed
and will reduce for the good whose price has
risen.
For good y (price increase) consumption will
certainly decrease, since the two effects act on
the same direction.
For good x the two effects have an opposite sign.
By knowing the sign of the aggregate effect
(reduction of consumption, as assumed by this
exercise), we are able to say that the variation
due to the income effect is higher in magnitude
(in absolute value) than the variation due to the
substitution effect (in absolute value).
18
N.B. the change from A to B is only apparent and
helps to separate the two effects.
19
Problem n. 1 pag. 395

• Matilde spends her income to buy cappuccinos and
  croissants. An unexpected frost in Brazil has the
  effect of increasing the price of coffee, and
  therefore that of cappuccino.
• Show in a graph the effects of the frost on
  Matildes budget constraint.
• Show the impact of the frost in Brazil on the
  optimal mix chosen by Matilde, supposing that for
  croissants the substitution effect is higher than
  the income effect.
• Show the impact of the frost on the optimal mix
  of goods chosen by Matilde in the case in which,
  for croissants, the income effect is higher than
  the substitution effect.

20
a) The frost has the effect of decreasing the
maximum amount of cappuccinos that can be bought,
given her income. It has no effects on the amount
of croissants that can be bought. Given the same
income, after an increase in the price of
cappuccino, the new budget constraint is the
dashed red line.
21
b) The increase in the price of cappuccino has an
income effect similar to a reduction of the
available income. Therefore, if both goods are
normal goods, consumption will reduce for both of
them.
The increase in the price of cappuccino makes it
relatively more expensive. Due to the
substitution effect the consumption of croissants
will increase and the consumption of cappuccino
will decrease.
Income effect Substitution Effect Aggregate Effect
Cappuccino consump consump
Croissant consump consump
As for cappuccinos, both effects are of the same
sign, and both lead to a reduction of the
consumed quantity. As for croissants, the income
effect brings a reduction of consumption, while
the substitution effect goes in the opposite
direction, since such goods have become
relatively cheaper. It the substitution effect
prevails, the aggregate effect will be an
increase in the consumption of croissants for
Matilde.
22
Substitution effect is greater than the income
effect in absolute value.
The initial optimal choice is point 1. After the
price increase of cappuccino, with the new budget
constraint, the optimal mix chosen by Matilde is
point 2.
The passage from 1 to 3 is due exclusively to the
substitution effect.
The passage from 3 to 2 is due to the income
effect.
N.B. point 3 is only for exposition purposes and
does not represent a real choice by Matilde. It
helps to separate the substitution effect from
the income effect.
23
c) If for croissants the income effect prevails
over the substitution effect, the aggregate
effect is a reduction of the croissants consumed
by Matilde. The optimal combination of
cappuccinos and croissants is represented by
point 2, which is associated with a smaller
quantity of both goods, as compared to point 1.
Point 3 does not represent a real choice by
Matilde but shows the change in consumption due
to the substitution effect only.
24
Problem n. 2 pag. 395

• Compare the following pairs of goods
• Coca Cola and Pepsi Cola
• Ski and ski bindings
• a) In which case the indifference curve is
  relatively flat and in which case it can appear
  as very steep?
• b) In which of the two cases the consumer has a
  stronger reaction to a price variation?

25
a) In the case of Coca Cola and Pepsi Cola one
would expect indifference curves which are
relatively flat. In fact the two goods are very
similar and satisfy the same needs. They are
close to be perfect substitutes, in which case
the indifference curve would be a straight
line. In the case of sky and sky bindings one
would expect indifference curves which are
relatively steep. In fact, the two goods must be
used together, which brings to a situation
similar to the one with perfect complements
goods, where indifference curves are with angles
b) In the Coca Cola-Pepsi Cola case consumers are
more reactive to a price variation, since they
can easily substitute the two goods faced to a
price increase/decrease of one of them. In the
other case (ski and ski bindings) the price
increase of one of the two goods brings a
reduction of the consumption of both goods but it
hardly implies a substitution of one good with
the other.
26
Problem n. 3 pag. 395

• Mario consumes only cheese and crackers.
• Can both cheese and crackers be inferior goods
  for Mario? Why?
• Suppose that, for Mario, cheese is a normal good
  and cracker an inferior good. If the price of
  cheese decreases, what happens to the consumption
  of crackers? What happens to the consumption of
  cheese? Why?

27

1. Cheese and crackers cannot be inferior goods in
   this case. As long as Mario increases his
   consumption after and increase in his income, one
   of both goods will be consumed in higher
   quantities, as it happens for normal goods.
2. After a reduction of the price of cheese, due to
   the substitution effect Mario will consume a
   higher quantity of cheese. The income effect will
   determine a further increase of the quantity of
   cheese consumed (normal good) and will cause a
   decrease of the quantity of crackers consumed
   (inferior good). Thus both effects act in the
   same direction and lead Mario to buy a higher
   amount of cheese and a lower amount of crackers.

28
Problem n. 4 pag. 395

• Antonio buys exclusively milk and cookies.
• In 2001 Antonio earned 100, the price of milk
  was 2 per litre and a pack of cookies costed 4.
  Draw Antonios budget constraint.
• Suppose now that in 2002 all prices increase by
  10 and that Antonios wage increase in the same
  proportion. Draw the new budget constraint. How
  could vary the optimal combination of milk and
  cookies in 2002, as compared to 2001?

29
a) In 2001 if Antonio spends all his income to
buy milk, he can buy no more than 50 litres. If
he buys exlcusively cookies, he can get 25 packs
at maximum. The budget effect, given the income
and the prices of the two goods, is shown in the
graph.
b) After the 10 increase in the prices and in
the income, the budget constraint does not
change. In fact with an income of 110 he can buy
50 litres of milk (at the cost of 2,2 per litre)
and 25 packs of cookies (at the cost of 4,4
each). The proportional increase of all prices
and of the income does not modify the budget line
as well as Antonios optimal choice
30
Problem n. 8 pag. 396

• Suppose you accept a job with a yearly wage of
  30.000 and that you assign a share of this
  income for savings, for which you get an interest
  rate of 5 per year. By using a graph including a
  budget constraint and indifference curves, show
  how the consumption changes in each of the
  following situations, provided that the income is
  not taxed.
• The income raises up to 40.000.
• The interest rate rises up to 8.

31
a) If one spends all the income (30.000 per
year) for present consumption, the maximum
aumount of expenditure is 30.000. Given an
interest rate of 5, by saving all the income one
could spend 31.500 in the future (the budget
constraint is the red line). If the income
increases up to 40.000 the budget constraint
becomes the dashed red line (40.000 available
for present consumption and 42.000 for future
consumption).
With the preferences summarized by the green
indifference curves in the graph, both present
and future consumption are normal goods. The
increase in the income will allow a greater
consumption in both periods.
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b) Straight red line initial budget line with an
income of 30.000 and an interest rate of 5. If
the latter increases up to 8, the horizontal
intercept does not change, while the vertical
intercept increaes (maximum consumption in the
future is now 32.400). Dashed red line new
budget constraint.
Given the preferences (green lines), present and
future consumption are both normal goods. The
increase in the interest rate makes the present
consumption relatively more expensive in terms of
future consumption. Due to the substitution
effect the latter will increase while the former
will be reduced. The income effect is positive
and lead to an increase of both present and
future consumption. The final aggregate effect is
surely positive for future consumption, and
depends on which effect prevails for present
consumption. In the case shown in the graph the
income effect prevails.
33
Problem n. 10 pag. 396

• Suppose that the State gives a yearly financial
  aid of 5 millions to each municipality. In the
  past each town was free to decide how to use such
  a contribution, but now the Government forces the
  town to use it for improving education. Show the
  effect of such intervention on the expenditure
  for education of the town by using a graph
  including budget constraints and indifference
  curves. The two goods are education and
  consumption of other goods.
• Draw the budget line of the town in the initial
  situation, supposing that its only incoming cash
  is a yearly tax on real estate property of the
  amount of 10 million . On the same graph draw
  the budget line after the Government
  intervention.
• Does your town afford a higher education
  expenditure in the initial situation or after the
  Government intervention? Why?.
• Compare now two towns, Youngville and Oldville,
  characterized by the same incomes and the same
  Goverment financial aids. Youngville has a higher
  share of the population going to school, while
  Oldville has a higher share of already educated
  inhabitants. In which of the two towns has the
  Government proposal more chances to cause an
  increase of education spending? Why?

34
Red line budget constraint of the town with 10
mil of income and 5 mil of free (i.e. not
dedicated) financial aid. The maximum amount for
expenditure (in education and in other
expenditures) is 15 mil .
Blue line budget constraint of the town with 10
mil of income and 5 mil of financial aids
that must be spent only for improving education.
The town can spend 10 mil for other goods at
maximum and 15 mil for education at maximum.
Other expenditures
35
b) If the preferences foresee an expenditure for
education higher than 5 mil (green indifference
curves in the graph) the Government desire to
intervene on the destination of the aid does not
produce any distortion and the optimal choice is
unchanged.
If the town preferences are such that the
expenditure for education would have been lower
than 5 mil (orange indifference curves) the
Government intervention causes a reduction of
expenditure in other goods (10 million euros) and
an increase in the expenditure for education
(above 5 million). The lower orange indifference
curve implies a lower utility for the town.
36
c) Youngville, in which the population is
relatively young, probably is already spending an
high amount for education. On the contrary,
Oldville, will spend less on education. Therefore,
the Government act has a higher probability to
cause an increase in expenditures for education
in Oldville.