esercitazione n°6 jose franchinoistituzioni di economia 2002/2003 corso c 1 chapter: 21 – the...

Jose Franchino Istituzioni di economia 2002/2003 corso C

1

Esercitazione n°6

Chapter:

21 – The theory of consumer choice

Exercise n° 7


2

Esercitazione n°6

Information:

Income = 500€

Price of good 1 = 10€

Price of good 2 = 5€

Construction of the budget constraint

Hypotheses: only two goods; the consumer spends all the income to buy the two goods;

The budget constraint curve represents all the combinations of the two goods that can be bought by spending all the income.


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Esercitazione n°6If the consumer spends all his income to buy good 2, hecan get 100 units. Point A: 100 units of good 2 and zero of good 1

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

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

Quantitygood 2

Quantitygood 1

0

A100

B

50

C50

25


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Esercitazione n°6Quantitygood 2

Quantitygood 1

0

A100

B

50

C50

25

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)

x2 =-50

x1 = 25

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

x2 / x1 = Pgood1 / Pgood2


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Esercitazione n°6

Comparative statics of the budget constraintThe budget constraint moves due to two main reasons:

Changes in the income

Changes in the price of the two goods

good2

Good1

Increase in the income

Decrease in the income

good2

good1

I ncrease in the price of good 2

Decrease of the price of good 1


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Esercitazione n°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


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Esercitazione n°6

Good 2

Good 1

Marginal Rate of Substitution: MRSRate to which the consumer agrees to change one good with another

3

1

MRS = 3

13

MRS = 1/3

Indifference curve

It represents the slope of the indifference curve and depends on the quantity of goods already available to the consumer


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Esercitazione n°6G

ood 2

Good 1

Optimal choice of the consumer:Reach the higher indifference curve, associated with the highest utility, respecting the budget constraint.

MRS = P1 / P2

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)

Optimal point: the budget constraint is just tangent to the highest indifference curve compatible with the budget


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Esercitazione n°6

I1

I2

I3

Good 2

Good 1

7

14

Practical case n.1

Price of good 1 = 1 €; Price of good 2 = 2€ ;Income = 14€

Given the indifference curves, draw the budget constraint and show the optimal choice of the consumer.Choice of the consumer: where the

budget constraint is just tangent to the highest indifference curve compatible with the budget line


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Esercitazione n°6

I1

I2

I3

Good 2

Good 1

7

14

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” goodThe consumption of good 2 increases with the increase in the income. Good 2 is a “normal” good

8

16


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Esercitazione n°6Practical case n. 2A 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

Books

Videotapes

I1

I2

I3


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Esercitazione n°6

I1

I2

I3

10

10

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:

Book

Videotapes

Quantities consumed: 5 books and 5 videotapes

Optimal choice, tangency point between the budget constraint and the highest indifference curve.

At the tangency point MRS = PV/PB = 1

5

5


13

Esercitazione n°6

15

10

10

The price of books decreases to 5€. How does consumption change?

Book

Videotapes

I1

I2

I3

Quantity consumed: 9 books and 4 videotapes

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.

Optimal choice, tangency between the budget constraint and the highest indifference curve compatible with the budget.

At the tangency point MRS = PV / PB = 1,59

4

N.B. consumption has changed and the utility of the consumer has increased (higher indifference curve).


14

Esercitazione n°6Show 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.

Income effect Substitution effect Aggregate effect

Book consumpt consumpt

Video consumpt consumpt ?

Reduction of the price of books (income effect- increase in income)


15

Esercitazione n°6

9

4

15

10

10

I1

I2

I3

Book

Videotapes5

5

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.


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Esercitazione n°6Practical 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


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Esercitazione n°6

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

Esercitazione n°6

I1

I2

good y

good x

AB

From A to B there is only the substitution effect. The quantity of good y decreases and that of good x increases

C

From B to C the income effect reduces the quantities of both good x and y.

N.B. the change from A to B is only apparent and helps to separate the two effects.


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Esercitazione n°6Problem 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.

a) Show in a graph the effects of the frost on Matilde’s budget constraint.

b) 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.

c) 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

Esercitazione n°6

Cappucc

Croissa) 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.


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Esercitazione n°6b) 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

Esercitazione n°6

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.

I1

I2I3

Cappucc

Croiss

21

3

C1C2 C3

B1

B2

B3


23

Esercitazione n°6

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.I1 I2

I3

Cappucc

Croiss

21

3

C1C2 C3

B1

B2

B3Income effectSubstitution effect


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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

Esercitazione n°6

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.


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Mario consumes only cheese and crackers.

a) Can both cheese and crackers be inferior goods for Mario? Why?

b) 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

Esercitazione n°6

a) 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.

b) 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.


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Antonio buys exclusively milk and cookies.

a) In 2001 Antonio earned 100€, the price of milk was 2€ per litre and a pack of cookies costed 4€. Draw Antonio’s budget constraint.

b) Suppose now that in 2002 all prices increase by 10% and that Antonio’s 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

Esercitazione n°6

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 Antonio’s optimal choice

50

25

Milk

Cookies


30


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.

a) The income raises up to 40.000€.

b) The interest rate rises up to 8%.


31

Esercitazione n°6

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.

Future consum

presentconsump

30

40

31,5

42


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Esercitazione n°6

Future

consum

presentconsum

30

40

31,5

32,4

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.


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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.

a) 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.

b) Does your town afford a higher education expenditure in the initial situation or after the Government intervention? Why?.

c) 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?


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Esercitazione n°6

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 €.

Other expenditures

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.

15

15

Education

10


35

Esercitazione n°6b) 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.

15

15

Education

10

5

Other expenditures


36

Esercitazione n°6

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.

esercitazione n°6 jose franchinoistituzioni di economia 2002/2003 corso c 1 chapter: 21 – the...

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units of good

price of good

quantity good

corso c

additional unit of good

consumer slide

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quantity of goods