5A_Consumer theory
Exercises (B. Czarny, 2017, Podstawy ekonomii.
Wprowadzenie do ekonomii. Mikroekonomia, 4th ed., Oficyna
Wydawnicza SGH, Warszawa, pp. 193-208)
A. "Yes or no?" type tasks.
Are these opinions true or false? Give reasons for your answer.
1. The points on the budget constraint line correspond to the minimum quantity of one
good that the consumer can purchase for a given quantity of the other good.
2. An increase in consumer income (ceteris paribus) will result in a rotation of the
budget constraint line around one of the points in its intersection with the axis of the
coordinate system.
3. A change in the price of one of the goods (ceteris paribus) will lead to a parallel
shift in the budget constraint line.
4. From the assumption that the consumer behaves in an internally consistent (logical)
manner, it follows that there are no 'white spaces' on the consumer taste map.
5. It follows from the assumption that the consumer prefers more, not less, that
indifference curves are convex towards the origin of the coordinate system.
6. The optimal basket of goods corresponds to such a point on the budget constraint
line at which this line intersects the indifference curve.
7. Good X costs 2, good Y costs 4; the marginal rate of substitution of good Y with
good X is 1. In this situation, by changing the composition of his basket of goods, a
rational consumer should make the marginal rate of substitution of good Y with good
X and the relation of the price of good Y to the price of good X equal.
8. When one of the goods is inferior and the other is normal, as income increases, the
path of income growth moves closer and closer to the axis which the amount of the
inferior good is marked.
9. In the case of a Giffen good, the income effect more than offsets the substitution
effect and, as a result, an increase in price is not accompanied by a decrease in demand
for such a good.
B. Open tasks
1. In order to shop, one needs both money and vouchers (a rule applies: 4 vouchers for
a unit of good X and 2 vouchers for a unit of good Y). Paul, who saves nothing, has 16
vouchers and also has an income of 20 units of money. Good X costs 2 and good Y
costs 4. How many units of X and Y will Paul buy?
2. Hypothetians' favourite alcohol is halucinol, a type of liqueur. The Hypothetians'
satisfaction with having baskets of goods consisting only of a certain sum of ifs and
100 ml bottles of halucinol, which had to be drunk quickly, was tested on a
representative sample. All the respondents unanimously claimed that baskets A to E
from the table below were equally useful. a) Draw the indifference curve of the tested
group (assume that the curve is continuous, and connect the points with straight lines).
b) What do you say about the attitude of Hypothetians towards halucinol? Do they
prefer more to less? c) Would the indifference curve be the same if the Hypothetians
did not have to drink the liquor immediately?
Number of bottles of
Amount of money
Basket
halucinol
(in ifs)
A
0
8,0
B
3
6,0
C
4
5,5
D
6
6,5
E
9
7,5
3. In the figure below, good X has become strongly more expensive.
(a) Identify the substitution effect concerning good X. Will it be stronger with a flat
(I1) or with a strongly curved (I2) indifference curve? b) For which good do you think
the indifference curve will be very flat? Justify your answer. (c) Which goods in
particular are bad substitutes? What shape of indifference curves do you expect for
these goods?
4. Is it possible that the figure below shows three indifference curves: U1, U2 and U3,
presenting a piece of the rational consumer's taste map? Justify your answer by giving
as many arguments as possible: a) concerning only the indifference curve U1, b)
concerning only the indifference curve U2, c) concerning only the indifference curve
U3. d) Indicate one more argument.
5. Maria is rational and does not save anything. She likes ribbons, X, and raw meat, Y.
The figure shows her budget constraint line and a section of the indifference map. Point
out: a) The best of the baskets of goods that Maria can afford. b) The points where
Maria buys only ribbons. c) Three baskets of goods that require Maria to spend all her
money. d) The basket that Maria cannot afford, although it is as useful as basket C.
6. Goods X and Y cost the same; line ABC is the consumer's budget constraint line; the
marginal rate of substitution of good Y with good X is 2 at point A and 0.5 at point C.
(a) How many units of good Y do we exchange for a unit of good X according to the
market value of goods and how many according to the subjective value of goods at
points A, B and C? (b) What should a utility-maximising consumer do with basket A?
(Be sure to use the answer to question (a)). (c) What should a utility-maximising
consumer who has basket C do? (Necessarily use the answer to question (a)). (d) What
do the answers to questions (b) and (c) have in common with the answer to question
(a)?
7. The income of a certain consumer who does not save is 120, the price of good X is
8 and the price of good Y equals 12. a) Draw the budget constraint line of this
consumer. b) The consumer's tastes are such that, for good X, the substitution effect of
an increase in the price of good X has the opposite direction of the income effect and
is weaker than it. Draw this situation. What do you say about good X? c) Draw the
income growth path of this consumer.
8. Janek spends all his income, which is 60 PLN, on bread, X, and jam, Y. Bread costs
15 PLN per loaf and jam costs 12 PLN per jar. a) Draw Janek's budget constraint line.
b) Draw Janek's preferences and the point that corresponds to his chosen basket of
goods. c) Jam has cheapened to 10 PLN. How will Janek's demand change in this
situation (indicate the new optimal basket)? (d) Indicate the substitution effect and the
income effect of the reduction in the price of jam, which was mentioned in (c), on the
demand for jam.
9. Here are drawings, discovered in the ruins of the ancient capital of Hypothetia.
Presumably they show the indifference curves of the ancient Hypothetians, about
whom we know only that they did not behave according to the consumer theory
assumptions made in this chapter. a) Did the ancient Hypothetians prefer more to less
(compare baskets A and B, C and D, and F and G, respectively, in figures (a), (b) and
(c))? (b) Did they evaluate goods according to the principle of a decreasing marginal
rate of substitution? (c) Give examples of goods that could be X and Y in the case of
Figures (a), (b) and (c), respectively.
a) b) c)
10.The marginal rate of substitution of good Y with good X for a basket of goods A (X
= 20, Y = 15) consumed by Peter is 3. The price of X is 4 gb and the price of Y is 8 gb.
Peter has 200 gb, is rational and does not save. a) Show this situation in the figure;
mark the budget constraint line, basket A and the corresponding indifference curve. b)
Give the prices of the two goods at which basket A turns out to be optimal. c) The price
of Y has increased to 10. Indicate the possible quantities of good Y consumed (assume
Y is a Giffen good).
11. Zosia, who does not save money, eats only sour soup (Y) and dumplings (X). She
has 12 złoty and a voucher to buy 8 dumplings for 1 złoty each. (On the black market
the dumplings are twice as expensive). Sour soup is available for free sale at 2 PLN
per plate. a) Draw a line of Zosia's budget constraint. b) Zosia's "taste map" consists
of an indifference line with the formula y = -3x + U(x, y), where x and y are the number
of units of good X and good Y in the basket, and U(x, y) is the utility index of the basket
in which there are x units of good X and y units of good Y. Complete the drawing with
an excerpt from her 'map' of tastes." c) Mark the basket of goods that Sophie decides
on; how many sour soup and dumplings are in it?
12. Hypothetians eat fish, X, and wine, Y. The government controls the price of fish.
The poor get vouchers, for which they can get 4 fish for free (vouchers cannot not be
sold, given away or exchanged for wine). In addition, Hypothetians get vouchers,
entitling them to buy 8 fish at 2 ifs one (on the black market fish are twice as
expensive). Wine is available for free sale at 4 ifs per bottle. a) Draw the budget
constraint line of the poor Hypothetian who has 20 ifs. b) The Hypothetian does not
save. His taste is described by the utility function U(x, y) = x + 4y. Draw a 'map' of his
tastes. How much fish and wine will he buy?
13. Rational Frank, who does not save money, got a prepaid mobile phone card worth
30 PLN. On his network, a SMS costs 1 złoty and a minute of calling costs 50 gr. a)
Draw Frank's budget constraint line (BCL). b) Frank's indifference curves are
described by the equation: U(MIN, SMS) = SMS + 3MIN, where U(MIN, SMS) is the
total utility, MIN is the number of minutes of calls and SMS is the number of SMS.
Draw Frank’s indifference curve (U) passing through the point at which he can buy
the most SMS; give the optimal combination of minutes of calls and number of SMS
for him. c) A minute of calls has become twice as expensive and an SMS has become
ten times as expensive. What combination of both goods is optimal this time?
14. Johnny is rational, does not save, and his income is 120 ifs. Having chosen the
optimal basket of goods (8 units of good X and 6 units of good Y), which corresponds
to point A in the figure below, Johnny values a unit of good Y twice as much as a unit
of good X. (a) Give the prices of goods X and Y. (b) The simple price elasticity of
demand for good X is positive and the income elasticity of demand for this good is
negative. The price of good X has increased. In the figure, using the labels provided,
indicate the substitution and income effects of the increase in the price of good X.
15. Here is the paradox! Bread and water are cheap in spite of their high utility, and
people pay a lot of money for ornaments made of gold, even though their utility value
seems low. Try to explain this consumer behaviour by appealing to assumptions about
their rationality.
16. We have just learnt to measure human satisfaction, and it turns out that Janek's
marginal utility from the last złoty spent on jam is as high as 50, and from the last złoty
spent on bread is only 30. a) Has Janek maximised his utility? (Hint: How would
Janek's utility change if he gave up 1 złoty's worth of jam and used the money he saved
to buy himself a portion of bread?) b) What condition should be met for Janek's utility
to be maximised? c) Generalise the principle from point (b) so that it applies to the
achievement of arbitrary goals. For example, how do you divide hours of free time
between different uses (e.g. cinema, book, trip?)?
17. Initially, the consumer's equilibrium point was point E. The price of good X
increases (ceteris paribus). Point S in the figure is the consumer's new equilibrium
point when there is no income effect. Indicate the final equilibrium point of the
consumer after taking into account the income effect when the good in question is: a)
a normal good; b) an inferior good (but not a Giffen good); c) a luxury good; d) a
Giffen good. Explain the answers.
A. Test
Mark the true and false answer options with pluses and minuses.
1. The budget constraint line is a set of baskets that:
(a) have the same utility,
(b) at given prices and consumer’s income contain the maximum available quantity of
one good for a given quantity of the other good,
(c) cost the same,
(d) are not available to the consumer at given prices and income.
2. It is true that:
(a) below the budget constraint line there are baskets of goods that the consumer can
afford,
(b) on the budget constraint line there are baskets of goods where the consumer spends
all his income.
(c) above the budget constraint line there are baskets of goods that the consumer cannot
afford,
(d) the slope of the budget constraint line depends on the size of the consumer's
income.
3. A parallel shift of the budget constraint line will be the effect of:
(a) a decrease in consumer income (prices remain constant),
(b) changes in consumer preferences,
(c) an increase in the consumer’s income (prices remain constant),
(d) changes in the marginal rate of substitution between the two goods.
4. The indifference curve consists only of:
(a) baskets of goods that have different utility level for the consumer,
b) baskets of goods that have the same utility level for the consumer,
(c) baskets of goods chosen by a rational consumer at different income levels and fixed
prices,
d) baskets of goods that have a fixed value (cost of purchase).
5. It follows from the assumption that the consumer prefers more, not less, that:
(a) indifference curves have a positive slope,
(b) indifference curves never intersect,
(c) indifference curves farther from the origin of the co-ordinate system correspond to
higher utility rates,
(d) indifference curves are convex.
6. The indifference curve is a straight line in the case of:
(a) pairs of perfectly substitutable goods,
(b) a decreasing marginal rate of substitution,
(c) pairs of perfectly complementary goods,
(d) a consumer, who values a good the more the less he has of it.
7. A rational consumer does not save and has a suboptimal basket of goods. In this
situation:
(a) this basket corresponds to the point where the indifference curve crosses the budget
constraint line,
(b) the marginal rate of substitution of good Y with good X is equal to the ratio of the
prices of good X and good Y,
(c) the market exchange ratio of good X for good Y is equal to the subjective exchange
ratio of good Y for good X,
(d) the marginal rate of substitution of this basket is constant.
8. The price of good X is 6 and the price of good Y is equal to 3. The marginal rate of
substitution of good X with good Y is equal to –2. A rational consumer should in this
situation:
(a) do nothing,
(b) give up a certain amount of good X and purchase a certain amount of good Y with
the money saved,
(c) give up a certain amount of good Y and purchase a certain amount of good X with
the money saved,
(d) buy only good X.
9. The income growth path is:
(a) the set of consumer equilibrium points, corresponding to different prices of the
goods he/she buys (ceteris paribus),
b) the set of consumer equilibrium points, corresponding to different levels of the
consumer's income (ceteris paribus),
c) the set of consumer equilibrium points, arising from changes in consumer
preferences (ceteris paribus),
d) a line whose shape depends on the income elasticity of consumer demand for the
two goods in question.