Q1) TRUE or FALSE:
a) If consumer 1 has the demand function x1 = 1000 – 2p and consumer 2 has the demand function
x2 = 500 – p, then the aggregate demand function for and economy with just these two
consumers would be x = 1500 – 3p
True: In order to find the aggregate demand function, we need to sum individual demands
(quantities) for any price, that is, x(p) = x1(p) + x2(p) = 1000 – 2p + 500 – p = 1500 – 3p
b) If the supply curve is horizontal, then an upward shift in the demand function will lead to a
higher price and quantity in equilibrium.
False: If supply is horizontal, then for any quantity demanded firms will put the same price. Thus, a
positive shift in demand will result in higher quantity, but the price will stay the same.
c) The supply curve slopes up and to the right. If the demand curve shifts upward and the supply
curve does not shift, then the equilibrium price and quantity must necessarily increase.
True: If supply is strictly increasing in the price then the new demand curve will intersect supply
curve in a point with higher price and quantity
Q2) If Kamile is willing to pay $35000 in cash for a convertible BMW, her consumer surplus from
getting one free is:
a)
b)
c)
d)
$0
-$35000
$35000
Insufficient data
Consumer surplus is the difference between what consumer is willing to pay for a commodity and its
market price (in this situation, what consumer really paid for the commodity). Since Kamile got the
car for free, the price she paid for it is 0. Then, her consumer surplus is $35000 - $0 = $35000
Answer: c)
Q3) The demand function for fresh strawberries is q = 200 – 5p and the supply function is q = 60 +
2p. What is the equilibrium price?
a)
b)
c)
d)
e)
10
20
40
50
None of the above
In equilibrium, supply and demand quantities are equal: qS = qD,
solving 200 – 5p = 60 + 2p yields p = 20
Answer: b)
Q4) The (inverse) demand function for eggs is given by p = 200 – 4q where q is the number of cases
of eggs. The (inverse) supply function is p = 2 + 2q. In the past, eggs were not taxed, but now a tax of
$18 per case has been introduced. What is the effect of the tax on the quantity of eggs supplied?
a)
b)
c)
d)
e)
Quantity drops by 2 cases
Quantity drops by 3 cases
Quantity drops by 6 cases
Quantity drops by 4 cases
None of the above
Solve for the equilibrium before the tax was introduced:
200 – 4q = 2 + 2q implies q = 33; p = 68
After the tax was introduced, demand did not change (tax doesn’t influence individual preferences),
but supply function shifted to p = 2 + 2q + tax, because cost per unit increased by tax quantity, thus
p = MC also increased by tax quantity. Thus, the new equilibrium will be 200 – 4q = 2 + 2q + 18, and
equilibrium quantity is 30.
Then, quantity dropped by 33 – 30 = 3 cases.
Answer: b)
Q5) The (inverse) demand function for cases of whiskey is p = 300 – 5q and the (inverse) supply
function is p = 6 + 2q. Originally there was no tax on whiskey. But now government began to tax
suppliers of whiskey $14 for every case they sold. How much did the price paid by consumers rise
when the new equilibrium was reached?
a)
b)
c)
d)
e)
$15
$12
$10
$6
None of the above
As in previous example, old equilibrium is 300 – 5q = 6 + 2q, q = 42, p = 90
New equilibrium is 300 – 5q = 6 + 2q + 14, q = 40, p = 100.
Then price rises by 100 – 90 = 10 dollars
Answer: c)
Q6) The (inverse) demand function for cigars is p = 240 – 2q where q is the number of boxes of
cigars. The (inverse) supply function is p = 2 + 2q. Cigars are taxed at $4 per box. Who pays the larger
share of the tax?
Before the tax: equilibrium is defined by 240 – 2q = 2 + 2q, q1 = 59,5; p1= 121 (point A);
After the tax: equilibrium is defined by 240 – 2q = 2 + 2q + 4, q2 = 58,5; p2 = 123 (point B).
Tax shifts the supply curve, decreasing both consumer surplus (area between demand curve and
price) and producer surplus (area between price and supply curve).
Before the tax: CS =
𝑞1
0
𝐷 − 𝑝1 𝑑𝑞 =
𝑞1
0
240 − 2𝑞 − 𝑝1 𝑑𝑞 = (240𝑞 − 𝑞 2 − 121𝑞)
59,5
0
= 119 ∙
59,5 − 59,5 ∙ 59,5 = 59,5 ∙ 59,5 = 3540,25
PS =
𝑞1
0
𝑝1 − 𝑆 𝑑𝑞 =
𝑞1
0
121 − 2 − 2𝑞 𝑑𝑞 = (119𝑞 − 𝑞 2 )
59,5
0
= 119 ∙ 59,5 − 59,5 ∙ 59,5 =
3540,25
After the tax: CS =
𝑞2
0
𝐷 − 𝑝2 𝑑𝑞 =
𝑞2
0
240 − 2𝑞 − 123 𝑑𝑞 = (240𝑞 − 𝑞 2 − 123𝑞)
58,5
0
= 117 ∙
58,5 − 58,5 ∙ 58,5 = 58,5 ∙ 58,5 = 3422,25
PS =
𝑞2
0
𝑝2 − 𝑆 𝑑𝑞 =
𝑞2
0
123 − 6 − 2𝑞 𝑑𝑞 = (117𝑞 − 𝑞 2 )
58,5
0
= 117 ∙ 58,5 − 58,5 ∙ 58,5 =
3422,25
As we see, decrease in consumer surplus and producer surplus is the same, that is, both consumers
and producers pay the same share of the tax.
Note: consumer and producer surpluses are equal, because absolute values of slopes of demand
and supply functions are same. In this case, CS and PS are represented by equivalent triangles with
areas qi2.
Q7) In a certain country, the demand function for bread is q = 480 – 6p and the supply function is q =
120 + 3p where p is the price in tilas and q is the loaves of bread. The government made it illegal to
sell bread for a price above 30 tilas per bread. To avoid shortages, he agreed to pay bakers enough
of a subsidy for each loaf of bread so as to make supply equal demand. How much would the
subsidy per loaf have to be?
If there wouldn’t be the government intervention, the price would satisfy 480 – 6p = 120 + 3p, p =
40, which is greater than the maximum legal price. In order to maintain prices at level 30, the
quantity of bread should satisfy demand function: q = 480 – 6p = 480 – 180 = 300. Then, after the
subsidy is performed, the supply function is p = q/3 – 40 – s, and s = q/3 – 40 – p = 100 – 70 = 30.
Q8) The demand function for butter is q = 600 – 5p and the supply function is q = 120 + 3p, where q
is the number of units sold per year and p is the price per unit, expressed in dollars. The government
decides to support the price of butter at a price floor of $86 per unit by buying butter and destroying
it. How many units of butter must the government destroy per year?
At price $86, quantity demanded is qD = 600 – 5p = 600 – 430 = 170; the quantity supplied is qS =
120 + 3p = 120 + 258 = 378. The difference is the amount that the government should buy and
destroy: 378 – 170 = 208.
Q9) The demand function for rental apartments is q = 960 – 7p and the supply function is q = 160 +
3p. The government makes it illegal to charge a rent higher than 35. How much excess demand will
there be?
At price 35, quantity demanded is 960 – 7p = 960 – 245 = 715; quantity supplied is 160 + 3p = 160 +
105 = 265. Then, excess demand is 715 – 265 = 450.
Q10) The demand function for potatoes is q = 200 – p and the supply function is q = 50 + 0.5p. The
government sets the price of potatoes at 150 and agrees to purchase and destroy any excess supply
of potatoes at that price. How much money does it cost the government to buy this corn?
At price 150, quantity supplied is qS = 50 + 0.5p = 125 and the quantity demanded is pD = 200 – p =
50. In order to maintain equilibrium, the government has to buy the excess supply equal to 125 – 50
= 75 at price p = 150, and it will cost 75 ∙ 150 = 11250.
Q11) Suppose that all firms in a given industry have the same supply curve given by Si(p) = 2p when
p is greater than or equal to $2 and Si(p) = 0 when p is less than $2. Suppose that market demand is
given by D(p) = 14 – p. If firms continue to enter the industry as long as they can do so profitably,
what will be the long-run equilibrium price and the long-run equilibrium number of firms?
For p < 2, whatever the number of firms n would there be, the total supply is n ∙ Si(p) = 0, and this
cannot be an equilibrium, because D(p) = 14 – p > 12, and there is excess demand. For price p ≥ 2,
equilibrium is characterized by equation n ∙ Si(p) = D(p), or n ∙ (2p) = 14 – p
14
and 𝑝 = 2𝑛+1 ≥ 2. The equation 2n+1 ≤ 7 is the constraint for the number of firms: the firms will
continue to enter the industry until 2n + 1 = 7 (after this point, the price drops under 2 and supply
becomes 0). Thus, n = 3 and p = 2.
Q12) A company can rent one of two copying machines. The first costs $34 a month to rent and
costs an adiitional 2 cents per copy to use. The second costs $107 a month to rent and and
additional 1 cent per copy to use. How many copies would the company need to make per month in
order for it to be worthwhile to rent the second machine?
Cost function of the first machine is c1(q) = 34 + 0.02q; of second machine is c2(q) = 107 + 0.01q. In
order for the second machine to be more profitable, it is necessary to c2(q) be less than c1(q):
107 + 0.01x ≤ 34 + 0.02x, or x ≥ 7300.
Q13) Tosun has quasilinear preferences and loves to eat “simit”. His inverse demand function for
simits is p(x) = 29 – 2x, where x is the number of simits he consumes per week. What will be the
change in his consumer surplus if the price of simit rises from 1 TL to 3 TL?
Tosun’s consumer surplus is the area between his demand function and the price. At the old price,
the quantity he consumed was q = (29 – p)/2 = 14 and his surplus was (29 – 1)(14 – 0)/2 = 196 (area
A + B + C); at new price, quantity is q = (29 – p)/2 = 13 and surplus is (29 – 3)(13 – 0)/2 = 169 (area
A). Change in his surplus is 169 – 196 = -27.
Q14) Suppose the demand for a good is D(p) = 100 – p, where p is the price in TL. The supply
function is S(p) = p. What will be the effect on consumers’ surplus if government imposes a price
ceiling of 40 per unit of the good?
Without the price ceiling, the equilibrium would be 100 – p = p, p = 50, q = 50. With the
government intervention, the quantity supplied will be q(p) = p = 40. Then, the consumer surplus
without intervention is (50 ∙ 50)/2 = 1250 (area A + D), and the consumer surplus with price ceiling is
(40 ∙ 40)/2 + 20 ∙ 40 = 1600 (area A + B). In total, consumer surplus increased by 1600 – 1250 = 350.
Q15) Suppose that King Canuta, demands that each of his subjects give him 1 coconut for every
coconut that they consume. The king then sells all of the coconuts that he collects in the market at
the going market price. The supply of coconuts is given by S(pS) = 100pS, where pS is the price
received by suppliers. The demand for coconuts by the king’s subjects is given by D(pd) = 4500 –
100pd, where pd is the price paid by the consumers. In equilibrium, how much will be the price
received by the suppliers?
The price will be determined by equation
D(p)
+
D(p)
=
quantity that quantity that people have
people want
to give to the king (equal
to consume
to quantity consumed)
S(p)
+
quantity sold
by fellow
suppliers
D(p)
quantity sold by the king (which is
equal to quantity he received, that
is, quantity consumed)
9000 – 200p = 100p + 4500 – 100p, or p = 22,5; q = 2250.
Q16) TRUE or FALSE. Explain.
a) If the demand curve is linear, then the elasticity of demand is the same at all prices.
False: elasticity of demand is calculated as
𝑑𝑄 /𝑄
𝑑𝑃 /𝑃
𝑑𝑄
𝑃
𝑃
= 𝑑𝑃 ∙ 𝑄 = −𝑎 ∙ 𝑎−𝑏𝑃 if demand is linear, and
depends on P, which means it is not same at all prices.
b) If the demand function is q = 3m/p, where m is income and p is price, then the absolute value of
the price elasticity of demand decreases as price increases.
𝑑𝑄/𝑄
𝑑𝑄
𝑃
𝑝
False: elasticity is𝑑𝑃/𝑃 = 𝑑𝑃 ∙ 𝑄 = −3𝑚 ∙ 𝑝−2 ∙ 3𝑚 𝑝 −1 = −1 is constant for all prices.
c) If the demand curve for beans is price inelastic at all prices higher than the current price, we
would expect that when bad weather reduces the size of the bean crop, total revenue of bean
producers will fall.
False: total revenue is just P ∙ Q, an increasing function in both P and Q. When size of bean crop (Q)
drops, its price (P) rises (by the law of demand). Thus, there are two effects on total revenue: fall in
Q decreases, and rise in P increases total revenue. When the demand curve is inelastic, the price
effect is higher and total revenue rises:
𝑑𝑅𝑒𝑣𝑒𝑛𝑢𝑒
𝑑𝑃
=
𝑑(𝑄∙𝑃)
𝑑𝑃
𝑑𝑄
= 𝑑𝑃 ∙ 𝑃 + 𝑄 = 𝑄
𝑑𝑄
𝑑𝑃
𝑃
𝑑𝑄
𝑃
∙ 𝑄 + 1 > 0 because −1 < 𝑑𝑃 ∙ 𝑄 < 0 (demand is
inelastic). Thus, as P increases, Revenue also rises.
d) The demand function for potatoes has the equation q = 1000 – 10p. If the price of potatoes goes
from 10 to 20, the absolute value of the elasticity of demand increases.
True: for the given function, elasticity of demand is
𝑑𝑄 /𝑄
𝑑𝑃 /𝑃
𝑑𝑄
𝑃
𝑝
= 𝑑𝑃 ∙ 𝑄 = −10 1000 −10𝑝 .
Atp1 = 10, Ed = -1/9. Atp2 = 20, Ed = -1/4, which is greater in absolute value than -1/9.
e) If the price elasticity of demand for a good is -1, then doubling the price of that good will leave
total expenditures on that good unchanged.
True: Expenditure on some good is quantity of that good multiplied by the price: Exp = P ∙ Q. Then,
𝑑𝐸𝑥𝑝
𝑑𝑃
=
𝑑(𝑄∙𝑃)
𝑑𝑃
=
𝑑𝑄
𝑑𝑃
∙𝑃+𝑄 =𝑄
𝑑𝑄
𝑑𝑃
𝑃
𝑄
∙ + 1 = 0 because
𝑑𝑄
𝑑𝑃
∙
𝑃
𝑄
= −1. Thus, expenditure on this
good doesn’t depend on the price, and if the price doubles, expenditure will remain the same.
Q17) The transit authority is thinking about raising the fare on its buses. Suppose demand is
currently inelastic. This will lead to:
a)
b)
c)
d)
a reduction in total revenues
an increase in total revenues
no change in total revenues
not enough information is given to answer this question
The question is the same as Q16, c). The fare on the bus is the same as price of the service. As we
have showed, when price is inelastic, increase in price leads to increase in the total revenue (despite
the negative effect of decrease in quantity sold on the total revenue).
Q18) Macit’s demand for spaghetti is given by X = 100 – 2p, where X is the servings of spaghetti and
p is the price per serving. Macit’s demand elasticity when p = $2 is:
a)
b)
c)
d)
20
-20
2/3
none of the above
𝐸𝑑 =
𝑑𝑄 /𝑄
𝑑𝑃 /𝑃
𝑑𝑄
𝑃
𝑝
1
= 𝑑𝑃 ∙ 𝑄 = −2 ∙ 100−2𝑝 = − 24 .
Q19) In a perfectly competitive market, the economic incidence of a tax depends on:
a)
b)
c)
d)
whether the tax is levied on producers or consumers
the demand elasticity
the supply elasticity
both b) and c)
Answer: d)
Incidence of a tax doesn’t depend on a): suppose that before the tax the inverse demand function is
P = Pd(Q), and inverse supply is P = PS(Q). If a tax is levied on suppliers, then they add the tax
quantity to the price they charge, and supply becomes P = Ps(Q) + tax. If the tax is levied on
consumers, then they have to pay price and tax when they buy a good, that is, price they pay
increases by tax quantity and the new demand becomes P + tax = Pd(Q). In both cases, the new
equilibrium is determined by equation PS(Q) + tax = Pd(Q), and equilibrium price and quantity are the
same in both cases.
The elasticity of demand and supply are percentage changes of quantity, caused by percentage
change of price. These values determine the share of tax burden payed by consumers and producers
as shown on figure below.
Inelastic supply, elastic demand:
the burden is on producers
Similar elasticities: burden shared