MARKET DEMAND
TRUE OR FALSE STATEMENTS
1. The aggregate demand function is the vertical sum of the individual demand
curves.
2. The slope of the market demand curve of two consumers who have the same
individual demand equals the slope of their individual demand curves.
PROBLEMS / EXERCISES
1, A rent-a-car company has three consumers: Kate, Sophie and Peter. Their individual
demands are the following:
Kate: q1=40-p
Sophie: q2=60-p
Peter: q3=30-0,5p
a) Illustrate the individual demand curves!
b) Determine the market demand curve!
2, The individual demands of a product are the following:
d1: p=10-0,1q
d2: p=12-0,2q
d3: p=20-0,2q
d4: p=15-0,125q
a) Determine the market demand curve!
b) The equation of the supply curve in the examined sector is S: Q=12P-15.
Determine the consumers’ surplus!
3, The consumers in the market of apple can be divided into three groups, their
individual demand equations are give per person. Into the first group belong 20 people,
their individual demand is: q=10-0,2p. The second group consists of 15 consumers, the
individual demand is: q=20-0,4p. There are 5 people in the third group, whose
individual demand equation is q=18-0,5p per person.
a) Determine the market demand equation!
b) How will the market demand change if another (4th) group of 10 consumers
appears in the market with an inverse demand curve, p=60-5q per person?
c) Calculate the equilibrium price and quantity in both cases if the market’s
supply is S: Q=140+2,5P?
4,The individual demand functions of three consumers in the banana market are:
q1=100-2p; q2=180-5p; q3=200-4p.
a) Determine the market demand curve!
b) How will the demand curve change if there is a 4th consumer in the market
whose inverse individual demand is: p=60-0,5p.
c) Illustrate the demand curves!
5,Consumers of a product are divided into 2 groups. There are 50-50 people in both
groups. People in the same group have the same equations of demand which are the
following:
d1: q=10-0,5p
d2: q=5-0,3p.
The supply in the examined sector is: S:Q=10P+200.
a) Calculate the consumers’ surplus!
b) The demand increases by 10%, while the prices didn’t change. Determine the
new supply curve and the change of the consumers’ surplus if the supply
adapts to the increased demand!
6, We know the individual demand curves of the 3 consumers of the jet-ski shop called
Speedy Ltd.
q1=90-p
q2=120-3p
q3=60-2p
a) Illustrate the market!
b) Determine the market demand curve!
c) How much is the market demand if the Ltd has the following supply curve:
S=-20+2p. Also determine the consumers’ surplus!
SOLUTIONS
1. If 40<P<60, D=90-1,5P. If P<40, D=130-2,5P.
2. a) If ≤10 D=380-28p; if 10<p≤12, D=280-18p; ha 12<p≤15, D=220-13p; if
15<p≤20, D=100-5p; if p>20, D=0.
b) Consumers’ surplus=372,72.
3. a) If 36<P≤50, D=500-10P. If P≤36, D=590-12,5P
b) The market demand in case of 4 groups: If 50<P≤60, D=120-2P. If 36<P≤50,
D=620-12P. If P≤36, D=710-14,5P
c) Equilibrium: P=33,3, Q=223,8.
4. a) If p≥50, D=0, if 36≤p<50 D=300-6p, if p<36 D=480-11p
b) If 50<P≤60, D=120-2P. If 36<P≤50, D=420-8P. If P≤36, D=600-13P.
5. a) If 16,6<P≤20, D=500-25P. If P≤16,6, D=750-40P. Equilibrium: P=11, Q=310.
Consumers’ surplus: 1238,68
b) Q’=341, S’=10p+231
6. b) If P≤30, D=270-6p; if 30<P≤40, D=210-4p, if 40<P≤90, D=90-p; if p>90, D=0
c) Q*=56,6, Consumers’ Surplus=1338,8
OPTIMAL CHOICE OF THE CONSUMERS
TRUE OR FALSE STATEMENTS
3. The consumer spends his income optimally, if the MRS equals the rate of the
marginal utility.
4. The MRS shows the slope of the budget line.
5. At the optimum point of consumption the slope of the budget line equals the ratio
of prices.
6. If the price of a product is increases, while the income of the consumer does not
change, the optimum of consumption will stay unvaried.
7. In case of a linear indifference curve, the point of optimal consumption can’t be
determined.
8. The hypothesis of the diminishing marginal utilities means, when the consumption
is decreased we sacrifice less and less utility.
PROBLEMS / EXERCISES
1, A family spends the monthly income, 3400 Ft, on two goods: X and Y. The price of
Y is 1,5 times higher than price of X. Determine the optimal consumption of the two
goods according to the information given in the chart. The family members are on a
diet, so they can take a maximum of 1700 calories. One unit of X gives 200 calories,
while one unit of Y contains 300 calories.
a) Determine the optimal consumption of the two goods.
b) Determine the prices of the goods.
Q
(consumed
quantity)
1
2
3
4
5
6
TUx
TUy
30
58
81
101
111
117
50
105
135
165
193
208
2, A family of 4 members spends 4000 Ft on the weekend meals (Saturday and
Sunday), which is meat soup (X) and roast meat (Y). Preparing the 2 meals
approximately costs the same. The following chart shows the utility of the meals for
the family.
a) Calculate the optimal combination of the two meals, the quantity of the meals
that should be prepared and their possible prices.
Q
TUx
TUy
1
2
3
4
5
(soup)
(roast meat)
72
152
272
448
528
276
372
452
530
597
3, A family spends the monthy income, 60.000Ft on two goods. The maximum amount
they can buy of X is 20, of Y is 10. They consume the 2 goods in a fixed ratio, which
is 2:1.
d) Determine the points of the PCC curve and of the demand curve of product
X, if the price of X increases first by 1/3 and later by an additional 10%.
4, A consumer spends his income on two goods (A, B). If he spends the whole amount
of money on “A”, he could buy 198 units, if he spends only on “B” , he can buy 66
units. Price of “A” is 40 Ft. The utility function of the consumer is U(A,B)= 2A2B.
d) Determine the price of product “B”.
e) Determine how many units the consumer will buy of product “A” and of “B”
if he is maximizing his utility.
f) How does the optimal consumption change if the income of the consumer
increases by 20%?
5, The Smith family usually eats bread rolls and ham for breakfast. One unit of ham is
10dkg. They used to buy 2 bread rolls per 10dkg of ham. The price of bread rolls used
to be 25Ft, and at that price the family bought 6 of them for breakfast. Later the price
of the bread rolls increased by 20%, so the demand of the Smith family dropped to 5
bread rolls.
a) Determine the income of the family that they are spending on the two
mentioned goods, their budget line, if the price ratio of the two goods was 0,2
in the beginning.
b) Determine the points of the PCC curve!
6, A consumer spends his income on two goods: X and Y. For hime X always gives
the same utility as Y.
a) Determine the demanded quantity of the goods, if the price of Y is 20, 25 and
50 Ft, His income is 1000 Ft and price of X is 25 Ft.
b) How does the consumption change if the goods are perfect complements and
their utility can be determined as 1:1.
7, A consumer eats “A” and “B” in a fixed rate. In the beginning he spends 1/3 of his
income on “B”, the unit price of which was 150€. The optimal consumption of “A” is
5 units. He can buy maximum 30 units of “B” if he spends all his income on this
product.
a) Determine the consumption of this consumer if the price of “A” increases by
25%, but the rate of consumption of the two goods does not change.
b) Determine the points of the PCC curve!
8, The utility function of a consumer concerning two goods “A” and “B”, is
U=A(2AB+A), the price ratio of the goods is 0,5. PA0=100 Ft/unit, the maximum
quantity that can be bought of B is 10 units.
a) Determine the original optimal consumption and also in case of an income
increased by 20%.
b) Determine the points of the ICC curve!
9, A family consumes product “A” and “B” in a fixed ratio (3:1). PA0=200 Ft/ unit.
They can by maximum 20 units of “A” and maximum 10 units of “B”. First the price
of “A” increased by 10 %, later price of “B” decreased by 10%.
a) Determine the optimal consumption of the 2 products.
10, Peter spends his money on hamburger (H) and ice cream (C). The price of one
hamburger is 50$ and of an ice cream is 25$. The utility function of Peter is U= H*C.
a) Determine the optimal consumption.
b) Determine the change in optimal consumption if the state imposes a tax of
20% on the price of hamburger.
SOLUTIONS
1. Px=400; Py=600
2. 2 soups and 3 roast meat, the price is P=200 or 5 soups and 3 roast meat, P=125
3. x0=5
x1=8,57
x2=8,1
y0=10
y1=4,28
y2=4,05
4. PB=120
A0=132
A1=158,4
B0=22
B1=26,4
5. I=525
PCC (6;3) and (5;3)
6. If X and Y has the same utility: at Py=20, he consumes only product Y (50 units)
Py=25, any point of the budget line is optimal
(consumption is 40 units)
Py=50, he consumes only product X (40 units)
If the fixed rate is 1:1
Py=20, x=y=22,2
Py=25, x=y=20
Py=50, x=y=13,3
7. the fixed rate of consumption is B=2A, A=4,29 and B=8,57
the original consumption is B=10 and A=5
8. A0=14
A1=16,6
B0=3
B1=3,66
9. A0=12
A1=11,32
A2=11,76
B0=4
B1=3,77
B2=3,92
10. H0=6
H1=5
C0=12
C1=12
ELASTICITY
TRUE OR FALSE STATEMENTS
9. The shorter the reaction time is, the higher the price elasticity of the product is.
10. If y is a complement to product x and price of product x is increasing, the crossprice elasticity is negative.
11. The income elasticity of luxury goods is constant
12. If the real income of a consumer increases he can decrease consumption of every
goods.
13. The less substitute goods a product has, the more elastic the demand of this product
is.
6. If a 2% increase in the price of a product causes less than 2% increase in the
demand for it, the demand of this product is non-elastic.
PROBLEMS / EXERCISES
1, In the market of fruits there are 2 types of oranges: Cuban and Spanish orange. The inverse
demand curve of the Cuban orange is: p=500-2Q. In January 200 Spanish orange was sold,
while the price of the Cuban orange was 250 Ft. In February the price of Cuban orange
decreased by 20%, so the sold quantity of the Spanish orangedecreased to 4/5 of January’s
quantity.
a) Determine the price elasticity of the Cuban orange and the cross-price elasticity of the 2
types of oranges.
b) What kind of goods are they?
2, The inverse demand curve of the Silver fir is P=15.000-2Q. In the first part of the season
2000 Nordmann firs were sold, the price of Silver fir was 2500 Ft. If the price of Nordmann
fir decreases by 20%, the demand of the Silver fir decreased to 4/5.
a) Determine the cross-price elasticity of the products.
b) Illustrate the market!
3, In a shopping centre there are 2 cell phone shops, Nokia and Samsung. The demand curve
of Nokia is D=241000-30p, the supply curve is S=50p-399000. The price of Samsung
increased from 9000 Ft to 10800 Ft, that caused a 10% increase in the demand of Nokia.
e) Calculate the change in the sold quantity of Samsung if previously it was 860 units.
We also know that its price elasticity is -1,25!
f) Caracterize the elasticity of the 2 products and their relation.
4, We know the following about product X and Y. In the 1st month from X 120 units were
sold and the inverse demand curve was p=560-3Q, the demand in the 2nd month decreased by
15%. Price of Y in the 1st month was 180 Ft, while its demand curve was p=450-27Q. The
cross-price elasticity of Y is 0,75.
Determine price of X and Y, and their revenue in the 2 months.
5, Price of petrol increased by 10%, what equals to a 12 Ft increase. As a result of the
changing price, the demand of petrol decreased to 2000 litres.
a) Calculate the original demand of petrol, if the price elasticity is -0,4.
b) Caracterize the elasticity of the 2 products and their relation.
6, There are two companies in the market selling pálinka, Flóra Ltd. and Nóra Ltd. The price
elasticity of the pálinka of Flóra Ltd.’s is -0,2. If it increases the current price of 1240 Ft, the
demand for their product would decreasse by 63 bottles, while its revenue would increase by
16,5%, what equals to 296.100 Ft.
Determine the sold quantity, the change in price and the elasticity of revenue.
7, We know the following information about goods X and Y:
The inverse demand curve of X is: p=1520-8Q, the inverse supply curve is
p= 320+4Q. The original quantity sold from X is the equilibrium quantity, what decreased by
15%, by the end of the period. Price of Y was originally 180 Ft, its inverse demand curve is
p=450-2Q and its cross-price elasticity is 0,75.
a) Determine the price of X and Y, the revenue and the revenue elasticity of X.
b) Illustrate the market!
SOLUTIONS
1.
 C ,P  1 ,  S , PC  1 .
2.
 S ,P  1
C
N
3. QS1=645.
 N , P  0,5 , so it is a substitute product.
S
4. Px0=200, Px1=237,5. Py does not change. Qy0=10; Qy1=11,4.
Revenue of product X: 1st month: 24 000 Ft, 2nd month 24 225 Ft
Revenue of product Y: 1st month 1 800Ft, 2nd month 2 052 Ft.
5. Q0=2083,33. TR=0,56.
6. Q0=1447 units. Q1=1384 units. P1=1510 Ft. =0,76.
7. Px0=720, Px1=840, Py does not change.
Qy0=135, Qy1=151,875. Revenue elasticity of X is: =0,049.
8. PP0=40; PP1=65, QR1=2625. S’=300P-12 500.
 P,P  0,6
P