Microeconomics, IB and IBP
ORDINARY EXAM SOLUTIONS, December 2010
Open book, 4 hours
There are six questions in the exam. Answer all questions in the exam. Your answers
should be clear and concise, and your hand writing should be legible.
1. Explain in your own words why a credible signal must be costly to fake and give an example of a credible
signal.
Solution:
A credible signal must be costly to fake otherwise the signal would not contain information. If there
is a cost associated with giving a signal then an individual or firm would only give the signal if the
benefit outweighs the cost. If it were costless everybody would give the signal and then the signal
would contain no information.
There are many possible examples, here is one: A degree from CBS is a signal of ability and motivation. It is costly to fake because it takes time and effort to obtain a degree from CBS.
2. What is the price elasticity of demand for one firm selling its output in a perfectly competitive market?
Explain your answer. Explain whether the price elasticity of demand for a monopolist is lower or higher
than the elasticity of demand for one firm in a perfectly competitive market.
Solution:
The price elasticity of demand for a single firm in a perfectly competitive market is negative infinity,
because demand for a single firm is a flat line equal to the market price. Products sold by different
firms in perfectly competitive markets are standardized such that consumers can perfectly substitute
across firms. If one firm raised its price above market price by even 1 øre the firm would lose all
customers. If it lowered its price, the firm would gain all customers (but the firm would never charge
a lower price than the market price).
A monopolist’s demand curve is the market demand curve. The law of demand suggests that when
prices increase market demand falls. In other words, a monopolist’s demand curve is downward
sloping. Demand is therefore less elastic for a monopolist in comparison to the demand curve facing
a single firm.
3. The supply and demand curves for a market are shown in the figures below. Find the equilibrium price
and quantity in this market.
P
P
26
30
20
10
4
Supply
Q
2
Q
Demand
Solution:
The supply function is: P = 10 + 5Q and the demand function is P = 26 − 3Q. Equilibrium price
and quantity is found by solving this system of equations: Q = 2 and P = 20
Page 2
4. In a perfectly competitive market, a firm produces output using the technology:
√
Q=
KL
This means that the firm’s short run variable cost curve is V C = 2Q2 when its capital stock is fixed at 4
units and wages are w = 8. The marginal rate of technical substitution is K
L . Assume the price of capital
is r = 2 and the output price is p = 16. Assume prices do not change, so p = 16, w = 8 and r = 2 in the
short and long run.
(a) In the short run, how much does the firm produce? What are the firm’s profits?
(b) If in the long run the firm wants to produce the same amount it did in part (a), how much labour
and capital will it use? What are the firm’s profits?
(c) Does the firm earn more profits in part (a) or in part (b)? Give an intuitive explanation for your
answer.
Solution:
(a) The firm chooses its output by setting marginal cost equal to the price. In the short run,
marginal cost is the derivative of the variable cost curve: M C = 4Q
MC
=
P
4Q =
16
Q =
4
Profit is total revenue minus total costs:
Π
= TR − V C − FC
Π
=
16 ∗ 4 − 2 ∗ 42 − 2 ∗ 4
Π
=
24
The firm produces 4 units and earns a profit of 24.
(b) To find K and L we need two equations. The question states that the firm wants to produce
the same amount as in part (a). We can substitute this into the production function for one
equation, and use the long run optimality condition for the other equation.
√
4
K
L
=
=
KL
w
K
8
⇒
=
r
L
2
Solving this system of two equations and two unknowns gives us: K = 8 and L = 2
Profit is Π = 16 ∗ 4 − 8 ∗ 2 − 2 ∗ 8 = 32.
(c) Profits are higher in the long run in part (b) because capital is no longer fixed. Firms can choose
the cost minimizing mixture of capital and labour.
Page 3
5. Suppose the entire market for eggs on Møn is made up of 100 people. Half of the people have the demand
function P = 10 − 5Q while the other half have the demand function P = 10 − 10Q. Prices are Kroner
per carton of eggs and the quantity demanded is cartons of eggs per week. The market supply function
1
Q. By how much does total consumer surplus in the market change if the government imposes
is P = 10
a per unit tax on buyers of 2 Kroner.
Solution:
Aggregate market demand is found by horizontally summing the demand curves.
P1
5
P2
P2 = 10 − 10Q2 ⇒ Q2 = 1 −
10
P
P
+ 50 2 −
Q = 50 1 −
10
5
Q = 150 − 15P
Q
P = 10 −
15
P1
=
10 − 5Q1 ⇒ Q1 = 2 −
1
Before the tax, the equilibrium price and quantity are found by equating supply P = 10
Q to market
Q
demand P = 10 − 15 . The before tax equilibrium is P = 6 and Q = 60. Consumer surplus is
therefore: CS = .5 ∗ 60 ∗ (10 − 6) = 120
After the tax, the demand curve shifts inward by the value of the tax, therefore the after tax demand
Q
is P = 8 − 15
The new equilibrium price and quantity are, P = 4.8 and Q = 48. This means that
consumer surplus is: CS = .5 ∗ 48 ∗ (8 − 4.8) = 76.8
The loss in consumer surplus that results from the imposition of the tax is therefore, 120−76.8 = 43.2.
Page 4
6. There are two firms operating in a market. The market demand is P = 28 − Q where Q = Q1 + Q2 .
Both firms have the same total cost function: T C = 10Q.
(a) If the firms act as Cournot duopolists, what price does each firm charge, how much do they each
sell and what are their profits?
(b) If the firms act as Bertrand duopolists, what price does each firm charge, how much do they each
sell and what are their profits?
Solution:
(a) The marginal revenue for firm one is: M R1 = 28 − 2Q1 − Q2 . To find the reaction function for firm
1, set marginal revenue equal to marginal cost: M C = 10
MC
10
Q1
Q2
= MR
28 − 2Q1 − Q2
Q2
= 9−
2
Q1
by symmetry
= 9−
2
=
The equilibrium is where Q1 = Q2 . We can find the firms’ output by imposing the equilibrium
condition on a reaction function:
Q1
=
9−
Q1
=
6
Q2
=
6
Q1
2
by symmetry
Market price will be, P = 28 − 6 − 6 = 16, which means profits are: Π1 = Π2 = 6 ∗ 16 − 10 ∗ 6 = 36
(b) Bertrand duopolists are price setters. At the equilibrium P1 = P2 = M C. Marginal cost is 10,
so P1 = P2 = 10 The quantity sold in the market is found by inserting the price in the market
demand: 10 = 28 − Q ⇒ Q = 18. The duopolists split the market, so that Q1 = Q2 = 9. Profits
are: Π1 = Π2 = 10 ∗ 9 − 10 ∗ 9 = 0
Page 5
Microeconomics, IB and IBP
RE-EXAM, January 2011
Open book, 4 hours
There are six questions in the exam. Answer all questions in the exam. Your answers
should be clear and concise, and your hand writing should be legible.
1. Explain in your own words why two indifference curves which represent the preferences of a single rational
person can not intersect.
Solution:
If two indifference curves intersect they can not represent the preferences of a rational person because
transitivity and monotonicity would be violated.
To explain why this is the case, consider a person who consumes only food and shelter and with two
indifference curves shown in the figure above.
Because consumption bundles D and F lie on the same indifference curve, the person is indifferent
between D and F. Because consumption bundles D and E lie on the same indifference curve, the
person is indifferent between D and E. Transitivity implies the person is indifferent between E and
F. The consumption bundle F contains more food and more shelter than E. Monotonicity means
that the person prefers F to E, which is a contradiction.
You did not need to use a drawing in your answer, as long as you explained why the indifference
curves could not intersect.
2. Explain in your own words what would happen in a perfectly competitive market if some firms were
making an economic profit.
Solution:
If some firms are making an economic profit, new firms will enter the market causing the short
run supply curve to shift out to the right. The increase in supply will cause the market price to
fall. Firms will continue to enter the market until the price falls so low that firms are earning zero
economic profits.
3. Alice has a utility function over money which is U (M ) = M 2 . She is offered the choice between two
different lottery tickets. The lottery tickets are free. In other words, she does not have to pay to enter
either lottery. One lottery ticket pays $10 with a probability of 0.10 and $20 with a probability of 0.90.
The second lottery ticket pays $100 with a probability of 0.01 and $2 with a probability of 0.99.
(a) What is the expected value of each lottery?
(b) What is Alice’s expected utility from each lottery?
(c) Which lottery would Alice choose? (She can not have both. She must choose only one lottery to
enter.)
Solution:
(a) Expected values are: EV1 = 0.10 ∗ 10 + 0.90 ∗ 20 = 19 EV2 = 0.01 ∗ 100 + 0.99 ∗ 2 = 2.98
(b) Expected utility are: EU1 = 0.10 ∗ 102 + 0.90 ∗ 202 = 370 EU2 = 0.01 ∗ 1002 + 0.99 ∗ 22 = 103.96
(c) Alice will choose the first lottery because the expected utility of lottery 1 is higher than the
expected utility of the second lottery.
4. Sheldon spends all of his income on food and shelter. The price of food is $50 and the price of shelter is
$100. If Sheldon’s marginal utility of food is 4 and his marginal utility of shelter is 10, is he maximizing
his utility? Explain why or why not.
Solution:
If Sheldon is maximizing his utility his marginal rate of substitution between food and shelter is equal
to the ratio of food and shelter prices. In other words, M Uf /M Us = pf /ps . Sheldon’s marginal
rate of substitution between food and shelter is 4/10 or 0.4. The ratio of food and shelter prices is:
50/100 or 0.5 This means that Sheldon is not maximizing his utility.
Page 2
5. (a) Consider a profit maximizing monopolist who produces with the following total cost function:
T C = 0.8Q2 . If the monopolist can not price discriminate and he sells in a market with the following
demand function: P = 10 − 0.2Q how much will he produce, and how much profit will he make?
(b) Now consider a monopolist who sells in two separate markets. The monopolist can charge a different
price in each market. Total demand in the first market is P1 = 200 − 2Q1 . Total demand in the
second market is P2 = 300 − 3Q2 . This monopolist has the same total cost function T C = 0.8Q2 . If
the monopolist wants to maximize his profits, what price does he charge in each market and what
is his total profit?
Solution:
(a) A profit maximizing monopolist chooses output where M C = M R. Marginal cost is M C = 1.6Q
and marginal revenue is M R = 10−0.4Q Proft maximizing output is 1.6Q = 10−0.4Q =⇒ Q = 5
The monopolist charges P = 10−0.2∗5 = 9. Profits are therefore Π = T R−T C = 9∗5−0.8∗52 =
25
(b) To find out what prices the monopolist is going to charge, it is necessary to find out how much
output the firm will produce. A monopolist chooses output where M C = M R. To solve this
equation, we first need to find the aggregate marginal revenue, which is found by adding the
marginal revenue curves horizontally.
200 − M R1
4
300 − M R2
M R2 = 300 − 6Q2 =⇒ Q2 =
6
2400 − 10M R
2400 − 24Q
Q = Q1 + Q2 =
=⇒ M R =
24
10
M R1 = 200 − 4Q1 =⇒ Q1 =
Marginal cost is the same as above M C = 1.6Q. To find Q,
MR = MC
2400 − 24Q
= 1.6Q
10
Q = 60
The firm will produce 60 units in total, and will choose how much to sell in each market by
equating marginal revenue in each market. The output sold in each market is found by solving
the system of two equation where M R1 = M R2 is one equation and Q1 + Q2 = 60 is the second
equation. Solving this system gives: Q1 = 26 and Q2 = 34 We insert these quantities in the
respective demand curves to get the prices charged in each market: P1 = 200 − 2 ∗ 26 = 148 and
P2 = 300 − 3 ∗ 34 = 198
Total profit is Π = T R − T C = T R1 + T R2 − T C = 148 ∗ 26 + 198 ∗ 34 − 0.8 ∗ 602 = 7700
Page 3
6. Suppose total market demand for milk in Denmark can be described by the demand function, P =
155 − 2Q. The market supply function is P = 100 + 3Q. If the government imposes a law which forbids
sellers from charging a price above 115, how much excess demand will there be?
Solution:
If the price is fixed at 115 then demand is 115 = 155 − 2Qd =⇒ Qd = 20 and supply is 115 =
100 + 3Qs =⇒ Qs = 5. That means that excess demand is 20 − 5 = 15
Page 4
Page 1 of 2
Microeconomics, IB and IBP
ORDINARY EXAM with Answers (preliminary)
December 2009
Open book, 4 hours
Question 1
Consider an airline company that knows that there are two different
segments of travelers, namely business and leisure travelers. Estimation of
price elasticities shows that while business travelers have a price elasticity
equal to 1.15, leisure travelers’ price elasticity is 1.52.
1.1 Assuming that the marginal cost for the two types of travelers is the
same, find how much higher the airline will charge the business travellers compared to the leisure travellers, i.e. find the PB /PL , where
PB , PL are respectively the business and leisure ticket prices.
1.2 If the marginal cost for the airline is $1000 for both types of travelers,
find the actual ticket prices for each segment.
1.3 If the marginal cost of the business segment is 1.5 times the marginal
cost of the leisure segment, and if the latter is $1000, find the actual
ticket prices, and determine how much higher the business ticket price
is compared to the leisure ticket price.
Answer 1
1.1 When a firm faces two different segments of the market, it is profit
maximizing to charge different prices, i.e. to practice third degree price
discrimination. We treat each segment as a different market, and we set
marginal revenue in each segmend equal to (the common) marginal cost.
This will result in
1
) = MC
εB
1
= PL (1 − ) = M C
εL
M RB = PB (1 −
M RL
1
Taking the ratio of these two equations, we get
1 − ε1L
PB
=
PL
1 − ε1B
Substituting the values for the elasticities given to us, we have
1−
PB
=
PL
1−
1
1.52
1
1.15
= 2.6
that is, the price of the business tickets should be 2.6 times higher than the
price of the leisure tickets.
1.2 For M C = 1000, and using the above marginal revenue equal to
marginal cost expressions, we have
1
) = 1000 =⇒ PB = 7, 692, 3
1.15
1
) = 1000 =⇒ PB = 2, 923.9
PL (1 −
1.52
PB (1 −
1.3 We do the same as above but now for M CB = 1.5M CL , where
M CL = 1000. Thus, we have
1
) = 1500 =⇒ PB = 11, 538, 4
1.15
1
) = 1000 =⇒ PB = 2, 923.9
PL (1 −
1.52
PB (1 −
which means that business tickets are 3.94 (=
than leisure tickets.
11,538,4
2,923.9 )
times more expensive
Question 2.
A current debate in the U.K. is how to encourage people eat healthy food.
Some have claimed that many consumers are simply too poor to purchase
healthy food. This leads poorer people to be more prone to various health
problems such as diabetes and heart disease. As a result, a voucher system
(where additional money can only be spend on healthy food – beware: this
is not a price subsidy!) and an income support system (a cash check) have
been proposed to encourage consumers to purchase and eat healthy foods.
Use consumer theory to explain which of the two systems you would support
and why.
Answer 2
See page 142 in the book for something similar (school vouchers).
2
Basically what the voucher system does is to create a kink on the budget
constraint line. Providing a voucher means that you refund the money that
the consumers have used on healthy good, and this money would not be given
to you otherwise – in other words, and in some cases (as we will see below)
you force the consumption of these goods. The alternative income support
system just raises the budget constraint to a higher level, as consumers get
the extra money and they can use them as they please. The figure below
illustrates:
Other goods
Income+cash
A
I’1
Income
I1
I’0
I0
B0
F’0 F’1 F0 F2
B1
Healthy Food
F1
The initial budget contraint is B0. , i.e. if they did not buy any healthy
food, they have "income" and that will go to all other goods. Assume that
the preferences of the poor people are I0 . In that case, the optimal choice
will be to consume F0 healthy food.
This consumption of healthy food is now seen as way too little, and
the authorities want to induce more consumption of healthy food. They
can do it in two ways: (i) voucher system, or (ii) income support. Assume
that authorities want to induce a consumption level of F2 or more. Then
a voucher system will imply a new budget constraint that it is flat from
"income" to point A (which corresponds to F2 ), and then slopes with the
same slope as before (after all we have not changed any prices). An income
support system will just shift the budget contraint to B1 , which is a parallel
shift of the old budget constraint.
3
The effects of the two systems depends on the preferences that poor
people have.
If preferences are I0 then the new optimal choice will be at F1 no matter whether authorities give a voucher or an income support (new optimal
consumption is F1 ).
However, if preferences are I00 (the red-colored curves) then it matters a
lot whether the support is given as a voucher or an income support. While
the income support leads to a small increase of healthy good consumption
(from F00 to F10 ), the voucher support leads to a larger consumption of healthy
food (from F00 to F2 ). However, and as it is seen in the figure, in this situation
the consumer obtains a higher indifference curve by the income support
system (I10 ) than with the voucher support system (the indifference curve
then is the thick red line that is tangent on the kinked budget constraint at
point A). Still, the authorities have managed to indice more consumption
of healthy food, which will have positive extrenalities in the future.
All in all, and given that we do not know how exactly the preferences
look like, the voucher system perfoms best if the target is to increase as
much as possible the healthy food consumption.
Question 3
3.1 For a linear demand curve, what is the price elasticity for a monopoly
that maximizes revenues and not profits? – explain!
3.2 "A profit maximizing monopolist always operates in the inelastic part
of the linear demand curve". True or false? – explain!
3.3 Does a Cournot duopolist have a supply curve? – explain!
Answer 3
3.1 See figure 12.7 at p.383. Basically, a revenue maximizing monopolist
is like a monopolist that maximizes priofits when its marginal costs are
zero. Using the marginal revenue equal the marginal cost expression for
profit maximization, we write
1
P (1 − ) = 0
ε
which implies that ε = 1. (one can also draw the linear demand curvbe as
in figure 12.7 in the book)
4
3.2 False. The explanation is in the book – see page 385. One can also
prove that by looking carefully at the Lerner Index formula – however the
intuition for that is in the book at page 385.
3.3 A Cournot duopolist faces a negatively sloped residual demand curve.
Given that demand curve, he behaves as any other firm, by equalizing marginal revenue to marginal cost. Thus, like a monopolist, he does not take
prices as given. In that sense, a duopolistic firm does not have a supply
curve — the latter defined as combinations of prices and quantities. For the
monopoly case, see page 388 in the book.
Question 4
Samsung and Lucky Goldstar (LG) are Korea’s two main producers of
DRAM chips. The domestic market demand curve for DRAM chips is given
by P = 100 − QS − QLG , where QS , QLG are respectively the amount of output Samsung and LG produces. Moreover, the marginal cost of producing
a DRAM chip for both companies is $10.
4.1 What is the Cournot equilibrium quantities, price, and profits?
4.2 What would have been the equilibrium price, quantities, and profits if
the two companies were competing in prices and not quantities?
4.3 What would the equilibrium price, quantities, and profits be if the two
companies cooperated and acted as a single company?
Answer 4
4.1 To find the Cournot equilibrium, we first derive the residual demand
(RDi ) for each firm. Given that residual demand, we derive the marginal
revenue and set it equal to marginal cost. This procedure will derive the reaction function for each firm. The Cournot equilibrium will be characterised
when the two reaction functions cross each other.
Let us do the above for one of the two firms, say Samsung.
RDS = (100 − QL ) − QS =⇒ M RS = (100 − QL ) − 2QS
Setting M R = M C, we get
100 − QL − 2QS = 10 =⇒
90 − QL
QS =
2
which is the reaction fucntion for Samsung.
5
A similar procedure for LG will result into
QL =
90 − QS
2
We can now solve these two equations with two unknowns and get QL and
QS . However, a simpler way is to notice that the two firms are symmetrical
(have the same costs), which will result into the same outputs, i.e. QL = QS .
Using this equality in one of the above equations, we have:
QL =
90 − QL
=⇒ QL = 30.
2
Thus, each firm will produce 30 units at equilibrium. Given these equilibrium quantities, the price will be:
P = 100 − 30 − 30 = 40.
The profits can then be derived as:
Π = P · Q − MC · Q
= 40 · 30 − 10 · 30 = 900
4.2 If competition between these two symmetrical firms was in terms
of prices and not quantities then the Betrrand paradox will take place, i.e.
prices will come down to the marginal cost. This implies that
P = 10
and
QL + QS = 100 − P = 100 − 10 = 90
Symmetry will imply QS = QL = 45. Finally, profits will of course be zero.
4.3 If the two firms cooperate, they will behave as a monopoly. They
will choose the monopoly output and then share it. Solving for that output,
we set (total, and not residual) marginal revenue equal to marginal cost:
100 − 2QT otal = 10 =⇒
QT otal = 45 and thus
Deriving profits :
P = 100 − 45 = 55,
ΠT otal = 55 · 45 − 10 · 45 = 2025
Thus, each firm will produce 22.5 units, they will both charge $55, and they
will each earn 1012.5 as profit. As expecetd, the cooperative equilibrium is
better than the Cournot equilibrium (lower output, higher prices and higher
profits).
6
Page 1 of 2
Microeconomics, IB and IBP
RE-TAKE EXAM, January 2010
Open book, 4 hours
Question 1
Suppose that the market demand function for corn is Qd = 15−2P while
the market supply function for corn is QS = 5P − 2.5, both measured in
billions of bushels per year. Suppose that the government imposes a $1.40
tax on each bushel of corn.
1.1 What will be the effects on consumer, producer, and aggregate surplus,
and what will be the deadweight loss caused by the tax?
1.2 What is the economic incidence of taxes. Provide an intuition for the
resulting tax incidence.
Answer:
1.1 We start by inverting the functions given, so that it is easier to draw
them.
Qd = 15 − 2P =⇒ P = 7.5 − 0.5Qd
QS = 5P − 2.5 =⇒ P = 0.5 + 0.2QS
We calculate the equilibrium before taxes. Since demand equals supply, and
since at equilibrium Qd = QS = Q, we write:
7.5 − 0.5Q = 0.5 + 0.2Q =⇒
Q = 10
and thus P
= 2.5
At this price and quantity, the consumer surplus is calculated as the area
under the demand function and above the price, while the producer surplus
is the area above the supply functions and below the price:
CS =
PS =
(7.5 − 2.5)10
= 25
2
(2.5 − 0.5)10
= 10
2
1
We now introduce the tax t = 1.4. Since the market is competitive, it
does not matter where it applies to. Below, we assume that it applies to
consumers, and thus it shifts demand function inwards (although we could
easily have assumed that it applied to producers, in which case it would
have shifted the supply function to the left).
P + 1.4 = 7.5 − 0.5Qd =⇒ P = 6.1 − 05Qd
Solving for the equilibrium quantity, we get
6.1 − 05Qd = 0.5 + 0.2QS =⇒
Q = 8
Going back to the demand function, we can derive that P = 2.1 (the producer price) and P + 1.4 = 3.5 (the consumer price). Calculating the new
CS and PS, we have
CS =
PS =
(7.5 − 3.5)8
= 16
2
(2.1 − 0.5)18
= 6.4
2
At this tax equilibrium there are also tax revenues collected by the government which are equal to T R = tQ = 1.4 · 8 = 11.2.
Comparing the pre- and post-tax equilibria, we see that total welfare
has fallen from 25 + 10 = 35 to 16 + 6.4 + 11.2 = 33.6. The resulting loss of
1.4(= 35 − 33.6) is the so-called deadweight loss (DWL) of taxes.
1.2: Tax incidence: that is, who pays the tax: the consumer or the
producer?
From the above calculations we saw that the consumer paid 3.5 after
taxes, while she was paying 2.5 before taxes were applied. The producer
instead, got 2.1 for its product, while before taxes she was getting 2.5.
Clearly the biggest part of the 1.4 tax is paid by the consumer. More
precicely, the consumer pays
3.5 − 2.5
= 0.71, i.e. 71%
1.4
while the producer pays
2.5 − 2.1
= 0.29, i.e. 29%
1.4
2
of the tax. The intuition for such a result builds on the fact that the agent
with the most inelastic function bears the tax heaviest. In the above example, it is the consumer that has the most inelastic function.
Question 2.
A local video rental monopoly faces the weekly demand function Q =
1000 − 50P. The marginal cost of a rental is $1. Suppose that the town
government places a $1 tax on a video rental.
2.1 What effects will the tax have on the price the monopolist charges?
2.2 What subsidy would persuade the monopolist to sell the same quantity
of rentals that would be sold in a competitive video rental industry?
Answer:
Q
.Given this
2.1: We first invert the demand function to P = 20 − 50
(inverted) demand function, the marginal revenue has the same slope and
Q
Q
= 20 − 25
.
double the slope, i.e. M R = 20 − 2 50
Since the monopolist always set M R = M C, the pre-tax equilibrium is
characterised by the following quantity and price:
Q
25
and thus P
20 −
= 1 =⇒ Q = 475
= 10.5
When taxes apply, the marginal cost of the monopolist will increase
by the amount of tax, i.e. M C = 2. (one can also assume that the tax
falls on the consumers, in which case the demand shrinks inward - such an
assumption is also fine - below, I continue with assuming that the tax falls
on the producer). The new equilibrium is now
Q
25
and thus P
20 −
= 2 =⇒ Q = 450
= 11
Thus, the price the monopolist charges increases.
2.2: First of all, we need to find how much it would be produced if the
market was perfectly competitive (and without taxes). In that case firms
will charge a price equal to their marginal cost, i.e. P = 1(= M C). It is
then easy to see that
Q = 1000 − 50 · 1 = 950.
3
To induce such an output, a subsidy is considered. To find this subsidy,
we write
M R = M C − s =⇒
950
= 1 − s =⇒ s = 19.
20 −
25
Thus the subsidy will have to be $19 per rental before a monopoly is induced
to produce the competitive output.
Question 3
"Competitive firms can easily have profits – the real question is for how
long they can keep these profits". Discuss this statement: is it true or false
and why? Make sure to develop your arguments both with diagrams and
with economic intuition.
Answer:
The statement is true, if one assumes short run profits not disappearing
instantaneously. One should refer to short run (i.e. before entry) and long
run (after entry) equilibria that a competitive firm faces. Please see pp.350354 at the textbook.
It is important to discuss the fact that the theory of perfect competition
assumes that entry and exit occurs instantaneously, while in reality such
entry and exit takes time, and thus short run profits are not competed away
instantaneously.
Question 4
Noah and Naomi have decided to start a firm to produce garden tables.
If Noah and Noami have √
at least 500 square meters of garage space, their
weekly production is Q = L, where L is the amount of labour they hire, in
hours. The wage rate is $12 an hour, and a 500 square-meter garage rents
for $250 per week.
4.1 What is the weekly cost function for producing garden tables? Graph
it.
After some time Noah and Noami want to expand. They now want to
produce 100 garden benches per week in two production plants A and B.
Assume that the cost functions at the two plants are CA = 6000QA −3(QA )2
and CB = 650Q2 + 2(QB )2 .
4.2 What is the best assignment of output between the two plants? (that
is, how many to produce at A and how many at B).
4
Answer:
4.1: The weekly cost function has two elements; the variable cost and
the fixed cost. The variable refers to the workers hired, while the fixed to
the rent paid for the garage space. Thus
TC = w · L + F =
= 12 · L + 250
To find the demand for labour (L), i.e. how many workers Noah and Naomi
√
1
will want to hire, we solve Q = L = L 2 as L = Q2 . Thus, the cost function
(i.e. total costs as a function of output) is
T C = 12 · Q + 250
We can easily graph such a function in the figure below.
TC
250
Q
4.2: There is typo in the exam question. The cost function of plan B
should be CB = 650Q2B +2(QB )2 and not CB = 650Q2 +2(QB )2 . While some
assumed that, some assumed that it should have been CB = 650QB +2(QB )2
and did their calculations based on that. No matter what, I graded the
calculations and reasoning given the assumption that the student has chosen,
and not the actual result. Below, I present the answer key for the CB =
650Q2B + 2(QB )2 .
In order to solve for the best assignment of outputs, we know that the
equilibrium should be characterised by M CA = M CB , i.e. the marginal
costs should be the same in both places. Thus we have
M CA = 6000 − 6QA = 1304QB = M CB
5
Given that QA + QB = 100, we write
6000 − 6(100 − QB ) = 1304QB
which implies that QB = 7.6 and QA = 92.4.
6
Page 1 of 2
Microeconomics, IB and IBP
RETAKE EXAM, January 2009
Open book, 4 hours
Question 1
1.1 De…ne price ceilings and price ‡oors and rationalize their use, i.e. why
do governments use such measures. In doing that discuss who gains
and who losses from such measures.
1.2 De…ne and explain the notion of "tax incidence", and discuss the factors that a¤ect it, i.e. what are the important parameters that one
has to know in determining tax incidence?
Answer:
1.1 Please see p. 34-36 of the textbook. Here it is important to explain
what price …xing (either above or below equilibrium prices) is doing.
Explain excess demand and supply and the forces that are created to
by-pass the …x prices (black and shadow markets). Also refer to who
gain and who loses from these price interventions - aftre all this is what
explains the price intervention in the …rst place. Clearly the people
that are able to buy (sell) at the low (high) prices are bene…ted while
the ones that left out of the market are loosing out.
1.2 Please see p.4750 of the textbook. Explain the di¤erence betweeen
legal tax incidence (where the tax is levied) and economic tax incidence
(who is paying the tax). We care about the latter, and there one should
mention the formula (A.2.2) in the book and discuss what a¤ects it,
i.e. demand and supply elacticities.
1
Question 2
2.1 Set up (by choosing your own numbers) a simple — 2 agents with each
having 2 choices — prisoner’s dilemma type of game and determine
the Nash equilibrium. In doing that show that there exists another
solution which although is Pareto dominating, it cannot be reached.
What changes do we have to make to this simple game in order for the
Pareto solution to be an equilibrium?
2.2 De…ne the marginal rate of technical substitution (MRTS) and explain
why …rms should operate where
M PL
M PK
=
w
r
where M PL ; M PK denote respectively the marginal product of labour
and capital, and where w; r are respectively the factor prices for labour
and capital.
Answer:
2.1 Please see p. 214-222 of the textbook. It is important to present a
game where the equilibrium (Nash) is not the best possible solution for
the agents, i.e. there should exist another equilibrium (Pareto) that
the agents cannot coordinate towards to. For the latter to be possible
either some communication must be possible (threats, commitment
devices), or som repeated game interactions, and thus in…nitive time
dimensions, must be added.
2.2 Straight out of the textbook. See p.276-277 for the de…niton of MRTS
and 311-314 for the rationality behind the given formula.
Question 3
Consider a monopoly gas station in a small town that sells both regular
and premium gasoline. The demand functions for the two gasolines are
QR = 10; 000
QP
1; 000PR + 50PP
= 350 + 50PR
100PP
where quantities and prices for Regular and P remium gas are denoted by
QR ; QP and PR ; PP .
2
3.1 Are these products substitutes or complements?
3.2 If the price of regular gas PR is $3.00 per gallon, its constant marginal
cost M CR is $2.95, and the constant marginal cost of premium gas
M CP is $3.05, what is the pro…t-maximizing price of premium gas
PP ?
Answer:
3.1 The products are substitutes as increasing the price of the one increase
the quantity sold of the other. Mention the cross price elasticity formula.
3.2 Since PR = 3; QP = 50 100PP : This implies that PP = 5 (1=100)QP
and that M RP = 5 (2=100)QP (since marginal revenue has the
same intersection and double the slope of a linear (inverse) demand).
Equating marginal revenue to marginal cost gives:
2
Q = 3:05 =) Q = 97:5
100
and thus P = 4:025
5
Question 4
The market demand and supply functions for corn are respectively
Qd = 15
S
Q
= 5P
2P
2:5
4.1 Draw carefully the above demand and suppy functions and calculate
the equilibrium price and quantity.
4.2 Suppose the government imposes a 2.10 per unit tax on corn consumption. What will be the e¤ects on consumer surplus, producer surplus,
and deadweight loss?
Answer:
3
4.1 In drawing the functions one has to re-write them as
0:5Qd
P
= 7:5
P
= 0:5 + 0:2Qs
and then plot the 7.5 and 0.5 points in the vertical axis as the points
where the demand and supplu functions start, respectively. The demand then is negatively slopped and ends up to point 15 in the horizontal axis (since the slope is 0.5). The supply is positive sloped and
‡at (with a slope much smaller than the 45 degree line - which has
slope 1).
In calculating the equilibrium, we use the given demand functions1 and
write Qs = Qd which gives
15
2P
= 5P
2:5 =)
P
= 2; 5
and thus
Q = 10
At this equilibrium point we can calculate the CS and PS as
CS =
PS =
(7:5
2:5)10
= 25
2
(2:5 0:5)10
= 10
2
i.e. the CS is the area of the triangle below the demand function and above
the price, while the PS is the area of the triangle above the supply function
and below the price.
4.2 The imposition of consumption tax at t = 2:1 per unit shifts the
demand function inwards. Thus the new inverse demand function is
P + 2:1 = 7:5
0:5Qd () P = 5:4
0:5Qd
Equating this new demand function with the supply function gives
(given Qs = Qd )
5:4
0:5Q = 0:5 + 0:2Q =)
Q = 7; P = 1:9 and P + t = 4
1
We can also use the inverse demand functions and set them equal to each other. This
is what I do later on.
4
The new CS and PS surplus is thus
CS =
PS =
(7:5
4):7
2
(1:9
= 6:125
0:5)7
2
= 4:9
Moreover, the government’s tax revenue is T R = t:Q = 2:1 7 = 14:7:
The deadweight loss is measured as the drop of the quantity (from
10 to 7 - which represents the height of the DWL triangle) times the
consumer minus producer price, i.e. the tax (which represents the base
of the DWL triangle) divided by 2, i.e.
DW L =
3 2:1
= 3:15
2
Clearly, the PS will fall, the PS will also fall, the government will
increase its tax revenue, and the overall e¤ect will be negative (i.e. a
positve DWL).
5
Page 1 of 2
Microeconomics, IB and IBP
RE-TAKE EXAM, January 2008
Open book, 4 hours
Question 1
Encouraged by the recent shift of preferences towards environmental products, Aqua A/S has decided to raise capital by going
public, i.e. by issuing shares. After a long debate, the managing
team of Aqua A/S decides to issue 50:000 shares.
1.1 Given that the demand for Aqua A/S shares (QD ) turns out
to be
5:000:000
P2 =
QD
determine the price of these shares and the capital that Aqua
A/S manages to raise.
1.2 Could Aqua A/S had raised more capital if they had issued
a larger number of shares?
Answer:
1.1 The 50:000 shares represents a vertical supply curve, i.e. QS =
50:000. Equating the supply and the demand for shares QD = QS , we
write:
5:000:000
P2 =
=) P 2 = 100 =) P = 10
50:000
Thus the price is 10 Euros per share and the capital that Aqua A/S manages
to raise is P Q = 10 50:000 = 500:000 Euros.
(One can easily depict the demand and supply function in a diagram.)
1.2 The question can be answered by checking whether the revenues P Q
can increase if we increase Q (or if we reduce P ). This is easily done by
checking whether the elasticity of the demand curve is above or below unity.
We write:
P
=
=
5:000:000 2P P
dQ P
=
dP Q
p4
Q
5:000:000
5:000:000
2
= 2
=
P 2Q
5:000:000
1
2
Given that j P j = 2 > 1, we know that this demand function is iso-elastic
and that its elasticity is larger than unity. Thus, a large increase of the
quantity would only produce a small reduction of its price (or, better said, a
small reduction of the price will lead to large increase of the quantity). This
on the whole will lead to an increase of the revenues P Q: Thus, the answer is
positive: Aqua A/S could had raised more capital if they had issued a larger
number of shares (given that demand that it was revealed in the market).
Question 2
Consider a monopolistic …rm that faces the following demand
and total cost functions
P
= 20
2Q
T C = 10 + 4Q + 2Q2
where P is the price, and Q is the quantity sold.
2.1 Under the assumption that the monopolist maximizes pro…ts,
…nd the price (P ), quantity (Q), pro…ts ( ) and consumer
surplus (CS).
2.2 Calculate the deadweight loss that the monopolist creates.
What will the deadweight loss be if the monopolist could
perfectly price discriminate all the consumers (explain your
answer).
Answer:
2.1 To …nd the optimal choices, and thus the equilibrium values, for
the price and quantity, we set M R = M C: First, we derive M R by noting
that the demand is lenear and that thus the M R has the same intersect
and double the slope, i.e. M R = 20 4Q: Moreover, we derive the M C by
di¤erentiating T C with respect to Q, i.e. M C = 4 + 4Q: We can now write
20
4Q = 4 + 4Q =) Q = 2
From the demand function we can then derive
P = 20
2 2 = 16
The pro…ts can be derived by writing
= PQ
T C = 16 2
10
2
4 2
2 (2)2 = 6
The consumer surplus is found by writing
CS =
(20
P )Q
=
2
(20
16)2
2
=4
2.2 To calculate the deadweight loss we need to know what the quantity
would have been if the market was perfectly competitive. Under perfect
competition P = M C and thus we write
20
8
2Q = 4 + 4Q =) Q = (= 2 + 2=3)
3
As seen in the …gure below, we now need to calculate the value of the M R
when Q = 2, i.e. when the …rm is a monopoly. We write
M RM = 20
P
20
4 2 = 12
MC
PM
MRM
P
4
MR
Q Q
M
PC
5
10
3
Q
We can now derive the DWL (=the area of the triangle with thick lines):
DW L =
=
(P M
(16
M RM )(QP C QM )
2
14)(2 + 2=3 2)
= 2=3
2
In the case where the monopolistic …rm was able to perfectly discriminate
the consumers (charge precise the price that each consumer is willing to pay)
there will be no deadweight loss, as the whole consumer surplus will fall on
the hands of the producer. Moreover, the producer will produce exactly the
output that it would had produced if there was perfect competition. (see
more on this on p. 431-433 in the book).
Question 3
3.1 What is tax incidence, and what determines the distributional consequences of it?
Answer:
Tax incidence is how much of the tax-induced price increase is payed by
the consumers and how much is payed by the producers. In other words, who
ends up paying the higher prices that taxes give rise to. The distributional
e¤ects of a tax are measured by the tax incidence which is turn depends on
how elastic the demand (consumers) and the supply (producers) function
is. The general rule is that the tax falls more heavily on the most inelastic
side of the economy (consumption vs production). The inutition is that the
inelastic agents of the economy (consumers or producers) are the ones that
can not reduce their demand/supply of the good as prices change (see more
on this issues at p. 51-55 of the book).
3.2 How do we de…ne public goods, and how can they be …nanced?
Answer:
Public goods satisfy two properties: (i) they are non-diminishable, and
(ii) they are no excludable. (see more on this at p. 608)
Public goods are …nanced by taxes if they are produced by the public
sector. However, it can easily be the case that there is private provision
of public goods, i.e. the public good is not …nanced by taxes. In these
situations the public good can be …nanced either by
4
1. voluntary contributions,
2. sale of by-products,
3. developments of new means to exclude nonpayers,
4. private contracts,
5. constructing clubs (and thus using the insights from the economics of
clubs).
(see more on this at p. 653-657).
Question 4
4.1 What do we mean by imperfect competition? Which market
structures can we have under imperfect competition and how
can we distinguish between them?
Answer: Imperfect competition captures all the market structures that
are not perfectly competitive. In all these cases, the …rm has some power
in determining the price in the market. There are 3 cases of imperfect
competition: (i) monopolistic competitive, (ii) oligopoly, and (iii) monopoly.
In a monopolistic competitive market there are many producers all producing a di¤erent variety of a product, i.e. there is product di¤erentiation.
The producer has power in determining the price of its product, but can
not in‡uence the price that the other producers set /because there are too
many of them).
In an oligopoly there are few producers of the same product (but product di¤erentiation may also exist). This low number of producers implies
that each …rm can calculate what the other producer will do and thus each
producer’s decision has an e¤ect on the other producers. In other words
there is strategic interaction among them.
In a monopoly, the producer is the sole supplier of a product and there
are substantial barriers to enter that market. It is important to note that it
is these barriers of entry that create the monopolist. If these barriers are not
important, then a single producer may not behave as a monopolist (charge
a high price and produce a small quantity) - the fear of entry will be enough
to discipline the supplier.
(see more on these issues at ch.12 - monopoly and ch13 - imperfect
competition. )
5
4.2 Describe the Cournot model of an olipopolistic market.
Answer: The Cournot model describes the situation where two or few
suppliers compete by choosing the output that they want to put in the
market. Most of the times, such a decision is amde by choosing the capacity
that the …rm has (a decision that occurs in an early stage of the production
process). Such decisions are seen by other …rms, and can thus be used in
strategic behaviour.
In describing the Cournot model attention has to be given to as to how
a …rm decides its optimal output. For example in the case of two …rms, it is
important to understand that each …rm calculates its residual demand (i.e.
the demand that it faces after the other …rm has decided a hypothetical
output). Having that, the …rm will then decide its pro…t maximising output
which will clearly depend on how much the other …rm produces. This is
what is called the reaction, or best-responce, function, as it describes how
much will …rm 1 produce given …rms 2’s output. The point where the two
reaction functions meet is the point where the …rm’s expectations will be
realised - this is the Nash equilibrium, i.e. the equilibrium where both …rms
act simultaneously.
(see more on this at p. 467-470).
6
Microeconomics, IB and IBP
ORDINARY EXAM, December 2007
Open book, 4 hours
Question 1
Suppose the supply of low-skilled labour is given by
w=
LS
10
where LS is the quantity of low-skilled labour (in million of persons
employed each year), and w is the wage rate (in dollars per hour).
The demand for low-skilled labour is given by
w=8
LD
10
1.1 What will be the perfect competitive market wage rate and
employment level? Suppose the government sets a minimum
wage of $5 per hour. How many people would then be employed and how many will be unemployed?
To …nd the equilibrium employment level we set demand equal to supply.
First we rewrite the above demand and supply functions in terms of LD and
LS and get
LS = 10w
LD = 80
10w
Setting LD = LS we get,
10w = 80
10w ) w = 4
Substituting this into the demand or the supply function gives us the equilibrium level of employment LD = LS = 40: The following …gure depicts the
1
above functions.
w
9
8
5
4
A
B
L-supply
L-demand
40
30
50
80 L
45
The point where the demand for labour equals the supply gives L = 40 and
w = 4:
Consider now the case where the government sets a minimum wage equal
to 5, i.e. the wage can not fall under 5: In that case it is easy to see from the
above …gure that the demand for labour is at point A, while the supply is
given at point B. Given that the labour demanded is smaller than the labour
supplied, it is the demand side that determines the level of employment.
Setting w = 5 into the demand equaltion we get:
LD = 80
10w = 80
10 5 = 30
Thus, the …rms will employ 30 workers at that minimum wage. At the same
time there are LS = 10 5 = 50 wanting to work. This excess supply implies
that there are 50 30 = 20 workers that there are unemployed.
(In a way, the minimum wage changes the supply curve in the market.
With a minimum wage at 5; the supply curve is horizontal until it hits the
positive LS curve at point B: After that point, the supply curve follows the
positive part. The interaction point of this new supply curve and of the
demand curve is at point A:)
1.2 Suppose that instead of a minimum wage, the government
pays employers a subsidy of $1 per hour for each employee.
What is the total level of employment, the wage workers
receive, and the wage …rms pay?
2
If the government provides a wage-subsidy of 1$ per hour, the employers
will pay a 1$ less per hour, i.e. the labour demand function will now be
w
10w
LD
)
10
10 = 80 LD )
1 = 8
LD = 90
10w
This new demand function is depicted in the above …gure as the thick negative line that starts at 9 (and stops at 90 - not shown in the …gure). Equating
this demand with original supply curve gives the equilibrium wage and employment:
10w = 90
10w ) w = 4:5
and thus L = 10 4:5 = 45
Note that while the worker receives 4:5$ per hour, the …rm only pays 3:5$
per hour (the di¤erence is the 1$ subsidy that the government pays - these
wages are not depicted in the above …gure).
(One could also get the same results by saying that the supply of labour
will shift to the right - since it is a competitive market, it does not matter
to what side of the market we o¤er the subsidy. The way to do it then is to
S
say that w + 1 = L10 , i.e. the workers will get 1$ more per hour.)
Question 2
Consider a monopolist that is deciding how to allocate output
between two geographically separated markets. Demand for the
two markets are given by the following functions:
P1 = 15
Q1
P2 = 25
2Q2
Moreover the monopolist’s total cost is given by:
T C = 5 + 3(Q1 + Q2 )
Determine the following variables: price, output, pro…ts, consumer surplus, if
2.1 the monopolist can price discriminate.
2.2 the monopolist can not price discriminate.
3
First of all, we …nd the marginal revenue in each market. Since the
demand curves are linear, we know that the marginal revenue curves have
the same intersection and double the slope, i.e..
M R1 = 15
2Q1
M R2 = 25
4Q2
Moreover, knowing the total cost function, we can determine the marginal
cost for producing an extra unit: M C = 3:
2.1: When the …rm can price discriminate, i.e. charge each market a di¤erent price, it should set M C = M R1 and M C = M R2 : This will give
3 = 15
2Q1 =) Q1 = 6 and thus P1 = 15
3 = 25
4Q2 =) Q2 = 5:5 and thus P2 = 25
6=9
2 5:5 = 14
Since we have found the prices and the quantities sold in each market it is
easy to calculate the consumer surplus in each market. This is de…ned by
the triangle that is created under the demand function and above the price
charged in that market. It is easy to see that the consumer surpluses can
be calculated as
CS1 =
CS2 =
(15
9) 6
2
(25
= 18
14) 5:5
= 30:25
2
Total consumer surplus is then CS = 48:25:
The total pro…ts earned are = P1 Q1 + P2 Q2 3(Q1 + Q2 )
tuting the values of prices and quantities from above, we get:
= 9 6 + 14 5:5
3(6 + 5:5)
5: Substi-
5 = 91:5
2.2: When the …rm can not price discriminate, i.e. charges the same price
in both markets, then it treats the two markets as one. In that case what
is interesting is the total demand. To …nd that we …rst write Q1 = 15 P1
and Q2 = 12:5 P22 : Given that the price in the two markets is the same
(P1 = P2 = P ), we add these two demands into Q = Q1 + Q2 = 27:5 3P
2 :
Solving for P gives:
55 2Q
P =
3
3
4
It is easy then to see that the total marginal revenue is:
M RT otal =
55
3
4Q
3
To maximize pro…ts the …rm sets M C = M RT otal and thus
3=
55
3
4Q
55
=) Q = 11:5 and thus P =
3
3
2 11:5
32
=
3
3
Pro…ts will then be
= P Q 3Q 5 = 83:1 (i.e. lower than the pro…ts
in case 2.1 above). To …nd the consumer surplus, we need …rst to see how
much output is sold in each market. From the demand functions and with
P = 32=3 we get Q1 = 4:3 and Q2 = 7:1: The consumer surplus is then
CS1 =
CS2 =
(15
(25
32=3)4:3
= 9:3
2
32=3)7:1
= 50:8
2
Thus, total CS = CS1 + CS2 = 60:1 (i.e. higher that the consumer surplus in case 2.1 above - note that consumers in market 1 bene…t from price
discrimination while consumers in market 2 are harmed from price discrimination).
These results …t perfectly with what is known about price discrimination:
it bene…ts the …rm and hurts the consumers as a whole (it bene…ts though
the consumers with the most elastic demand).
(Please note that simple calculation mistakes are not taken into account
- it is the method that matters.)
Question 3
3.1 Draw and explain the shape of an indi¤erence curve when
products are (i) perfect complements and (ii) perfect substitutes. Explain what is the marginal rate of substitution
(MRS) and what values it takes on the above two cases. Finally, describe the income and substitution e¤ects in these
two cases.
The …gures below depict indi¤erence curves for substitutes (left panel)
and complement goods (right panel)
5
X
X
3
B
1
3
B
2
2
A
Y
A
1
Y
Starting from the left panel, we draw the indi¤erence curve as a line, i.e.
the two goods X and Y are substituted at a constant rate. This is only the
case when the two goods are perfect substititutes, i.e. a one unit less of the
one good is always substituted by, say, a one untit of the other good. In this
one-to-one example, the M RS = 1: The important point is that in perfect
substitutes the M RS is constant. We can not tell anything more about the
value that the M RS takes - we only know that it is constant - the particular
value depends on the substitution pattern, i.e. one-to-one, or one-to-two,
or...... etc.
Given these indi¤erence curves and given a budget constraint, say 1,
in the …gure, the optimal consumption choice is at the point where the
budget constraint meets the highest indi¤erence curve - in the …gure point
A, where the consumer buys zero units of good X and A units of good Y: If
the price of good Y increases and the budget constraint is now given by line
2, the optimal bundle is now at point B, where the consumer consumes zero
units of good Y and B units of good X. To separate the income from the
substitution e¤ect, we draw a hypothetical budget constraint that has the
same slope as the new budget constraint (line 3) and leads to the original
indi¤erence level. It is then easy to see that the income e¤ect is zero and
that the substitution e¤ect is equal to the total price e¤ect (see also the
discussion in the book around …gure 4.11, page 116).
Moving to the right panel of the above …gure, we see that the situation
for the perfgect complement goods is very diiferent. When goods are perfect
complements their consumption pattern is quite particular. the two goods
6
are consumed in a …xed ratio, i.e. one unit of X goes with, say, one unit
of Y . No other consumption pattern can exist. This is also depicted in the
L-shaped indi¤erence curves where the M RS takes the value of in…nity at
the vertical part and the value of zero in the horizontal part - no substitution
takes place!
Given a budget constraint (say line 1), the optimal choice is at point A:
An increase of the price of good Y will shift the budget constraint say at line
2 and will move the optimal choice at point B. To separate the income and
substituion e¤ects we draw a hypothetical budget constraint that has the
same slope as the new budget constraint and reaches the original indi¤erence
level - in the …fure line 3. It is then easy to see that now the substituition
e¤ect is zero (logical, since the goods are perfect complements) and that
income e¤ect is equal to the total price e¤ect. (see also the discussion in the
book around …gure 4.10, page 115.)
3.2 Consider a consumer that has the following utility function
U = X + Y; where U denotes utility/satisfaction level and X; Y
are the two goods that she consumes. Assuming that the
consumer has an income equal to 100 and faces prices PX = 2
and PY = 1, draw the indi¤erence map and determine the
optimal consumption bundle.
Given the above utility fucntion, we can write X = U
draw this indi¤erence curve in the …gure below.
Y and we can
X
100
X=U-Y
50
50
100
Y
The indi¤erence curves are drawn as one-to-one relationships, i.e. with a
M RS = 1: The budget constraint instead is drawn more ‡at. To see
7
why, we write the budget constraint 100 = 2 X + Y and determine the
intersection points with the two axes: at axis X, PMX = 100
2 = 50 and at axis
100
M
Y; PY = 1 = 100: It is clear that the opimal bundle is at point 100 of the
horizontal axis, where the budget constraint meets the highest indi¤erence
curve, i.e. the consumer consumes zero of good X and 100 units of the good
Y . This is also logical, as the two goods are substitutable in a one-to-one
basis and good X is more expensive that good Y:
Question 4
4.1 What methods do we use in order to measure welfare changes?
Draw and explain your answers.
There are 3 methods: (i) consumer surplus, (ii) use of the equivalent or
compensating variation method, and (ii) use of overall welfare comparisons
that ony determine whether the consumers are better o¤ or not.
(i) is best when we have information of only the particular market of a
good, e.g. the demand function - partial equlibrium
(ii) is best in the case that we have information for more markets, e.g.
indi¤erence curves - general equlibrium, typical a computable general equlibrium approach.
(iii) is used when the only information that we have is about the orginal
consumption bundle and the budget constraint (i.e. income and prices)
(see discussion in the book at pages 156-166).
4.2 What is the condition for an optimal choice of inputs (say,
capital and labour) in a long-run production situation? Provide the intuition behind this condition.
The optimal choice of inputs should full…l the following condition
M PL
w
=
M PK
r
M PL
M PK
=
w
r
or
An intuition for this condition can be given from the latter expression. Given
that M PL is the output a marginal worker produces and given that w is the
wage of this worker, the above conditions says that the overall surplus of
using a marginal labour inlput (output over costs) should be the same to
the overall surplus of using capital (output over costs) - see the discussion
in the book at page 340.
One could provide details of how we reach that condition, see pages
338-339, but this is not necessary for answering the question.
8
Page 1 of 2
Microeconomics, IB and IBP
ORDINARY EXAM, December 2006
Open book, 4 hours
Question 1 (25%)
1.1 Consider a market equilibrium where demand equals supply. Explain
what e¤ects are created in the market if the government imposes a
maximum amount of units that can be sold in the market, i.e. a quota.
How do you think agents will react to such a government intervention?
Could the government create the same equilibrium with a di¤erent
type of intervention? (draw diagrams and use them to explain).
1.2 What do we mean by deadweight loss and what possible forces can
create it? In what way is the deadweight loss created by monopoly
power related to the price elasticity of demand?
Question 2 (25%)
2.1 (i) Explain what an indi¤erence curve represents, and what information its slope provides.
(ii) How does the indi¤erence curve look like if only one of the two
goods is unwanted, i.e. its consumption reduces satisfaction?
(iii) Draw the indi¤erence curve between two goods that are both
"unwanted".
(iv) Draw an indi¤erence curve of two goods that …rstly are "wanted"
goods, but eventually, i.e. after their consumption "satiation" point is
reached, they become "unwanted" goods.
2.2 (i) Describe diagramatically cases where the income e¤ect works against
the substitution e¤ect.
(ii) What is the practical importance of distinguishing between the
uncompensated (ordinary) demand curve and the income-compensated
demand curve?
1
Page 2 of 2
Question 3 (25%)
Take a perfectly competitive industry that has a number of identical
…rms. A, so-called, representative …rm from this industry has the following
total cost function:
T C = 2q 2 + 50q + 50
3.1 Find the equilibrium price (P ) in this industry, and the quantity (q)
that each …rm is able to supply.
3.2 Assuming now that the market demand is given by the following function (where Q represents the total quantity supplied in that market)
P = 210
Q
derive the number of …rms (n) that will produce in that industry.
Question 4 (25%)
Consider a monopolistic …rm that faces the following linear demand function,
P = 400 30Q
and the following total cost function,
T C = 200Q + 20Q2 + 1000
4.1 Under the assumption that the …rm maximizes its pro…ts, derive the
equilibrium quantity (Q), price (P ), pro…ts ( ), and consumer surplus
(CS).
The government considers in giving a subsidy (S) to the …rm. There are
two proposals: (i) to cover the …xed cost of the …rm, or (ii) to reduce the
…rm’s total cost by 300 per unit of output, i.e. S = 300Q.
4.2 Derive, under each proposal, the equilibrium consumer surplus (CS),
and pro…ts ( ) and determine under which proposal the sum of the
two (CS + ) is highest. Please provide some intuition for your answer.
2
Answers to
ORDINARY EXAM, December 2006
Question 1 (25%)
1.1
Consider …gure 1, where demand equals supply at the equilibrium price
P and quantity Q . A quota Q is imposed by the government, which to be
bounding has to be below Q . That level of output can be sold at the price
PD — at the same time, producers would had supplied it at price PS : Thus,
in a way, the government has created a wedge between the price consumers
want to pay and the price suppliers want to sell, i.e. an implicit tax, t;
also called the quota rent: The revenues from such an intervention is given
by the shaded rectangular area. Such a revenue would be realised if the
governmnet sold the licences for producing the restricted amount of output
to producers.
In a way, the imposition of a quote changes the supply curve from being
a positive curve to a curve that is positive until the quota level and then
totally vertical.
Obviously, the government could instead had imposed a tax t on the
consumption side of the economy, reducing thereby the demand to D0 : Again,
the producers will get PS while the consumersr will pay PD : Everything is
the same, a fact that is known as the equivalence between quotas and taxes
3
in a perfect competitive market.
P
S
Pd
t
P*
Ps
D’
Q
Q*
D
Q
1.2
DWL is related to the reduction of output that is created by the existence
of some distortion/intervention. Taxes, quotas, are the typical interventions
that distort the market equilibrium, while existence of monopoly power is
the typical distortion that we refer to in the class. DWL refers to some loss
of surplus/welfare that these departures from the market equilibrium result
to (diagrams should be drawn for each of the cases).
The DWL created by the monopoly is highly in‡uenced by the elasticity
of demand. The higher the elasticity the lower the power of the monopolist
to set a price above the MC, and thus the higher the quantitiy that the monopolist will sell. Clearly, the elasticity of demand is high when consumers
can …nd other substitute goods to buy when the price of the monopolist’s
good increases Using the Lerner Index to show how the p-MC margin is
a¤ected by the elasticity is good. Diagrams can also help in illustrating this
relation.
Question 2 (25%)
4
2.1
(i) An indi¤erence curve is the locus of points where a consumer remains
at the same satisfaction level. There are several axioms that we use
to draw an indi¤erence curve - for two typical goods, we draw the
indi¤erence curve as a negative curve in a X-good,Y-good space. The
slope of an indiference curve is called the MRS and it represents the
rate at which the consumer is willing to exchange the one good with the
other while retaining the same satisfaction level. (Figures; mentioning
the axioms; details about MRS are all welcome).
(ii) The indi¤erence curve is positive sloped - it can either concave or
convex depending of how much of the "good" good we have.
(iii) If both goods are "bad", then the indi¤erence is again negatively
slopped but now it welfare increases as we move towards the origin.
(iv) Here we basically draw a circles with the vertical and horizontal diagonal depicting the satiation consumption levels (see …gure below).
At levels of consumptiuon below Q1 and Q2 the indi¤erence curve is
a normal one. Above Q1 or Q2 (but not both) the indi¤erence curve
is as in (ii) above, where only of the goods is unwanted. When we
are above both Q1 and Q2 then the indi¤erence curve looks like (iii)
above.
Good 1
D
Q1
A
C
B
Q2
Good 2
5
2.2
(i) Here we basicaly require drawing and explaining a …gure as …gure 4.8
at p. 113 of the book, i.e. where the income e¤ect goes against the
substitution e¤ect for an inferior good whose price increases.
(ii) A price change leads to a so-called total price e¤ect, which can be
decomposed to a substitution e¤ect and an income e¤ect. The former
is an e¤ect that takes place immediately, while the second is based on
the realization that prices changes a¤ect also the real value of income.
This latter e¤ect may not be realised immediately and may take time
before the consumers take that e¤ect account. In the possible situation
that this is indeed the case, market surveys that collect data about demand changes only capture the so-called income compensated demand
function, i.e. the demand without any income e¤ect. Knowing that a
good is, e.g., normal would then imply that the total demand will be
even more elastic after some time. Thus, the practicality of including
or not the income e¤ect becomes clear when we are trying to estimate
how demand is a¤ectd by price changes.
Question 3 (25%)
3.1 We know that in the long run (i.e. after entry and exit of …rms has
taken place), a perfectly competitive …rm operates at the minimum
e¢ ciency scale point where P = min LAC (it is best that you explain
why this is the case - …gures will help).
Given this, and given the fact that we have been given a T C function,
we start by deriving the AC as:
TC
50
= 2q + 50 +
AC =
q
q
To …nd the minimum point of that function, we take the …rst derivative wrt
q and we set equal to zero (while the second derivative should be positive).
dAC
dq
50
= 0 =) 2q 2 = 50
q2
=) q 2 = 25 =) q = 5
=
0 =) 2
At quanity equal to 5; the AC will be equal to
50
AC = 2 5 + 50 +
= 70
5
Thus, since P = min LAC; we have that P = 70:
6
3.2 Since we have found the price in the market, we can now use the given
market demand to …nd the total quantity supplied in the market Q.
Having that and having the quantity sold by each …rm q, we can …nd
the number of …rms that exist in equilibrium
70 = 210
Q =) Q = 140
Thus, denoting n the number of …rms in equilibrium, we have
140 = n 5 =) n = 28
Question 4 (25%)
Pro…t maximization for a monopolistic …rm occurs where M R = M C:
Given that the demand function is linear, we know that the M R has the
same interecept and double the slope, i.e. M R = 400 60Q: Thus, the pro…t
maximization condition gives:
400
60Q = 200 + 40Q =)
200 = 100Q =)
Q = 2
From the demand function we can then …nd the price P as
P = 400
30 2 = 340:
Pro…ts then are expressed as
= 340 2
= (340
=
200 2
200
20 22
20 2)2
1000
1000
800
that is, the …rm is making losses (still it covers some of its …xed costs).
Finally, the consumer surplus CS is given the triangle belæow the demand curve and above the price (make a …gure!). The area of that triangle
is equal to
1
1
(hight width) = (400
2
2
= 60
CS =
7
340) 2
4.2 Seeing that the …rm is making losses, the government considers two
subsidy proposals (i) covering the …rm’s …xed cost, and covering some
part of the marginal costs. We examine each proposal aat a time.
(i) With the subsidy given in covering the …xed cost the only thing
that changes is the …nal pro…t of the …rm. While before it was
making a loss of 800; now the …rm is making a gain of 200.
However, all the marginal decisions of the …rm remain unaltered,
as f ixed cost have no in‡unece on these. Thus, the price that
the consumers pay and the quantity suplied in the amrket are
unchanged at P = 340 and Q = 2: Thus the consumer surplus is
still equal to 60: The sum of consumer surplus and pro…ts is now
CS + = 260:.
(ii) If the subsidy reduces the total cost by 300Q; then the new MC
function is M C = 100+40Q and thus the new pro…t maximizing
point is where
400
60Q =
100 + 40Q =)
Q = 5
The price is the derived as P = 400 30 5 = 250; and the pro…t
equals = 250 5 + 100 5 20 52 1000 = 250: The consumer
surplus equals CS = 12 (400 250) 5 = 325: Thus CS + = 575:
Clearly the fact the we see much more surplus generated with subsidies
that a¤ect the marginal decisions of the monopolist has to do with the
fact that such subsidies provide an incentive for more production and thus
smaller DWL. A subsidy to the …xed costs is merely an income transfer from
the government to the monopolist.
8
Page 1 of 2
Microeconomics, IB and IBP
RETAKE EXAM, January 2007
Open book, 4 hours
Question 1 (25%)
1.1 What is an externality and how can we correct it? Mention examples
from both negative and positive externalities.
1.2 What are the special characteristics of a public good? Does existence
of public goods necessiate the existence of a public sector?
Question 2 (25%)
2.1 What is the Production Possibility Frontier? Explain in detail the
reason for drawing it as a concave function.
2.2 Using the Production Possibility Frontier demonstrate that there are
aggregate gains from engaging in international trade.
Question 3 (25%)
Suppose the demand curve for a product is given by
Q = 10 − 2P + PS
where P is the price of the product and PS is the price of a substitute good.
The price of the substitute good is PS = 2.
3.1 Suppose P = 1. What is the price elasticity of demand? What is the
cross-price elasticity of demand?
3.2 Assume now that the supply curve is represented by
Q = 4P
Find the equilibrium quantity (Q) and price (P ), and the corresponding
consumer and producer surpluses. What is the price elasticity of demand
at that equilibrium? What is the cross-price elactisity of demand at the
equilibrium?
1
Page 2 of 2
Question 4 (25%)
Consider a firm with monopoly power that faces the demand curve,
1
P = 100 − 3Q + 4A 2
and has the total cost function,
T C = 4Q2 + 10Q + A
where A is the level of advertising expenditures, and P and Q are price and
output.
4.1 Find the values of A, Q and P that maximize the firm’s profit.
4.2 Calculate the Lerner index LI = (P − M C)/P, for this firm at its
profit maximizing levels of A, Q and P.
2
Microeconomics, IB and IBP
Answer Key for
RETAKE EXAM, January 2007
Question 1 (25%)
1.1 What is an externality and how can we correct it? Mention examples
from both negative and positive externalities.
Def: Anything that affects others and which is not taken into account
by you! Two main ways to correct it: (i) use of the Coase theorem: negotiation under small transaction costs should lead to efficiency solautions,
(ii) government intervention, e.g. standards, taxes, tradable licences etc.
The typical (negative) externality example is environment, while a positive
externality example is education, number of kids etc.
1.2 What are the special characteristics of a public good? Does existence
of public goods necessiate the existence of a public sector?
The special characteristics are two: non-excludability and non-rivalry.
An explanation of these two notions should follow. One can also divide
the producs in generally in Private goods, Public goods, Artificially Scarce
goods, and Common resources according to whether they combine these
two characteristics (see. p. 648 in the textbook). Public goods can be
produced by private markets without the existence of a public sector. The
book mentions (i) private donations, (ii) sale of by-products, (iii) new means
of excluding nonpayers, (iv) private contracts/economics of clubs. (see p.
653-657).
Question 2 (25%)
2.1 What is the Production Possibility Frontier? Explain in detail the
reason for drawing it as a concave function.
The PPF is the locus of points depicted in a production Edgewoth box
(where iso-quants tangent each other) put into a figure where the axes depict
the amount of the two goods. In that sense, the PPF depicts the frontier
of the production possibilities of a country that produces two goods. To
be inside the frontier implies that the allocation of input recourses is not
optimal and that there exists some inefficiency.
3
The concavity of the PPF is based on the fat that there exist decreasing
or constant returns to scale (in the case of increasing returns to scale the PPF
can be no strictly concave. The best way of explaining what is happening
is to start from one of the axes, say the vertical axe, where all recourses
are used in the production of one good, say good X. A release of some
resources will definitely reduce the production of good X and will increase
the production of the other good, say good Y . However, and due to the fact
that the marginal product of these recourses is quite low in the production
of good X (which is not-scarce) and quite high in the production of good Y
(which is scarce), such a release will reduce the production of X by little,
while it will increase the production of Y by much (therefore the flat but
negative curve). Clearly as we keep removing inputs from good X and
transferring them in good Y this relation will change, and at the end we
will have the opposite situation, i.e. a further removal of recourses from X
will reduce its output by much, while it will increase the production of Y by
little (therefore the steep, and negative curve). All in all, such a procedure
leads to a concave curve.
2.2 Using the Production Possibility Frontier demonstrate that there are
aggregate gains from engaging in international trade.
The figure below describes best whjat is happening. Consider a country
that has the PPF depicted below. When the country does not trade, all its
production has to be consumed internally and the efficiency point is depicted
by point P, where the quantities demanded equal the quantities supplied,
viz.X 0 and Y 0 . The price ratio is then depicted by the AA line, i.e. the line
that passes from the tangency of the PPF and of the indifference curve I1
that the representative consumer in the country has.
If the country opens up its trade then the relative prices will change, say
BB, (it is irrellevant whether the price ratio will be steeper or not). Again
it will be tangent to another point of the PPF, here PP, and to a higher
indifference curve, here C. Thus, the country will now produce X 000 and Y 000
and will consume at X 00 and Y 00 .The difference of these points describe the
trade pattern of the coutnry, viz. it will import X 00 − X 000 and it will export
Y 000 − Y 00 . The fact that the indifference curve I2 lies above I1 shows that
trade is overall beneficial, i.e. that there aggregate gains from trade.
4
B
X
A
C
X''
I2
P
X'
I1
X'''
PP
B
O
Y'
Y''
A
Y'''
Y
In p. 602 of the book a different proof is provided - a proof that is based
on overall welfare comparisons as that was shown in p.164 and used in the
classes numereous times.
Question 3 (25%)
Setting Ps = 2 into the demand function given (Q = 10 − 2P + Ps ) we
have Q = 12 − 2P. If we also set P = 1 then we have Q = 10. We are now
ready to answer question 3.1..
dQ
3.1.Since dQ
dP = −2 and dPs = +1, we can directly write the following
1
1
dQ P
= − (−2)
=
dP Q
10
5
2
1
dQ Ps
= (+1) =
= −
dPs Q
10
5
εp = −
εps
3.2: With the given supply curve, equilibrium is derived by setting demand equal supply, i.e.
12 − 2P = 4P =⇒ P = 2
This implies that Q = 12 − 4 = 8.
In deriving the CS and PS, one has to pay attention that the inverse
demand function is P = 6 − Q/2. Then, the consumer surplus is the area
under that inverse demand function and above the price. Thus,
1
CS = (6 − 2)8 = 16
2
5
while the producer surplus is
PS =
1
(2) 8 = 8
2
Finally the εP = 2 28 = 12 and the εPS = 1 28 = 14 .
Question 4 (25%)
4.1: We first write down the profit function for the firm:
1
Π = (100 − 3Q + 4A 2 )Q − 4Q2 − 10Q − A
To derive the values of Q,A and P that maximize the profits of the firm, we
take the first derivative of the profit function with respect to the two choices
the firm has, viz. Q and A, and set it equal to zero.
∂Π
∂Q
∂Π
∂A
=
1
0 =⇒ 90 − 14Q + 4A 2 = 0
1 1
0 =⇒ 4Q A 2 −1 − 1 = 0
2
1
2Q
− 12
=⇒ 2QA = 1 =⇒ 1 = 1 =⇒ 2Q = A 2
A2
=
This is a system with two equations and two unknowns (Q, A). Substituting
the latter equation into the former can solve for Q.
90 − 14Q + 4 · 2Q = 0 =⇒ Q = 15
1
1
We can then substitute Q into 2Q = A 2 and get 30 = A 2 . Raising both
sides into the power of 2 gives
A = 900
It remains to solve for P
P = 100 − 3 · 15 + 4 · 30 = 175
4.2: The Lerner index gives us how much the price is above the marginal
cost of producing a unit of output. At equilibrium the firm charges a price
equal to 175 and its marginal cost is M C = 8Q − 10 = 8 · 15 − 10 = 130.
Thus the Lerner Index is
LI =
175 − 130
P − MC
=
= 0.27
P
175
i.e. the price is set 27% higher than the marginal cost.
6
Page 1 of 2
Microeconomics, IB and IBP
RE-TAKE EXAM, January 2008
Open book, 4 hours
Question 1
Encouraged by the recent shift of preferences towards environmental products, Aqua A/S has decided to raise capital by going
public, i.e. by issuing shares. After a long debate, the managing
team of Aqua A/S decides to issue 50:000 shares.
1.1 Given that the demand for Aqua A/S shares (QD ) turns out
to be
5:000:000
P2 =
QD
determine the price of these shares and the capital that Aqua
A/S manages to raise.
1.2 Could Aqua A/S had raised more capital if they had issued
a larger number of shares?
Answer:
1.1 The 50:000 shares represents a vertical supply curve, i.e. QS =
50:000. Equating the supply and the demand for shares QD = QS , we
write:
5:000:000
P2 =
=) P 2 = 100 =) P = 10
50:000
Thus the price is 10 Euros per share and the capital that Aqua A/S manages
to raise is P Q = 10 50:000 = 500:000 Euros.
(One can easily depict the demand and supply function in a diagram.)
1.2 The question can be answered by checking whether the revenues P Q
can increase if we increase Q (or if we reduce P ). This is easily done by
checking whether the elasticity of the demand curve is above or below unity.
We write:
P
=
=
5:000:000 2P P
dQ P
=
dP Q
p4
Q
5:000:000
5:000:000
2
= 2
=
P 2Q
5:000:000
1
2
Given that j P j = 2 > 1, we know that this demand function is iso-elastic
and that its elasticity is larger than unity. Thus, a large increase of the
quantity would only produce a small reduction of its price (or, better said, a
small reduction of the price will lead to large increase of the quantity). This
on the whole will lead to an increase of the revenues P Q: Thus, the answer is
positive: Aqua A/S could had raised more capital if they had issued a larger
number of shares (given that demand that it was revealed in the market).
Question 2
Consider a monopolistic …rm that faces the following demand
and total cost functions
P
= 20
2Q
T C = 10 + 4Q + 2Q2
where P is the price, and Q is the quantity sold.
2.1 Under the assumption that the monopolist maximizes pro…ts,
…nd the price (P ), quantity (Q), pro…ts ( ) and consumer
surplus (CS).
2.2 Calculate the deadweight loss that the monopolist creates.
What will the deadweight loss be if the monopolist could
perfectly price discriminate all the consumers (explain your
answer).
Answer:
2.1 To …nd the optimal choices, and thus the equilibrium values, for
the price and quantity, we set M R = M C: First, we derive M R by noting
that the demand is lenear and that thus the M R has the same intersect
and double the slope, i.e. M R = 20 4Q: Moreover, we derive the M C by
di¤erentiating T C with respect to Q, i.e. M C = 4 + 4Q: We can now write
20
4Q = 4 + 4Q =) Q = 2
From the demand function we can then derive
P = 20
2 2 = 16
The pro…ts can be derived by writing
= PQ
T C = 16 2
10
2
4 2
2 (2)2 = 6
The consumer surplus is found by writing
CS =
(20
P )Q
=
2
(20
16)2
2
=4
2.2 To calculate the deadweight loss we need to know what the quantity
would have been if the market was perfectly competitive. Under perfect
competition P = M C and thus we write
20
8
2Q = 4 + 4Q =) Q = (= 2 + 2=3)
3
As seen in the …gure below, we now need to calculate the value of the M R
when Q = 2, i.e. when the …rm is a monopoly. We write
M RM = 20
P
20
4 2 = 12
MC
PM
MRM
P
4
MR
Q Q
M
PC
5
10
3
Q
We can now derive the DWL (=the area of the triangle with thick lines):
DW L =
=
(P M
(16
M RM )(QP C QM )
2
14)(2 + 2=3 2)
= 2=3
2
In the case where the monopolistic …rm was able to perfectly discriminate
the consumers (charge precise the price that each consumer is willing to pay)
there will be no deadweight loss, as the whole consumer surplus will fall on
the hands of the producer. Moreover, the producer will produce exactly the
output that it would had produced if there was perfect competition. (see
more on this on p. 431-433 in the book).
Question 3
3.1 What is tax incidence, and what determines the distributional consequences of it?
Answer:
Tax incidence is how much of the tax-induced price increase is payed by
the consumers and how much is payed by the producers. In other words, who
ends up paying the higher prices that taxes give rise to. The distributional
e¤ects of a tax are measured by the tax incidence which is turn depends on
how elastic the demand (consumers) and the supply (producers) function
is. The general rule is that the tax falls more heavily on the most inelastic
side of the economy (consumption vs production). The inutition is that the
inelastic agents of the economy (consumers or producers) are the ones that
can not reduce their demand/supply of the good as prices change (see more
on this issues at p. 51-55 of the book).
3.2 How do we de…ne public goods, and how can they be …nanced?
Answer:
Public goods satisfy two properties: (i) they are non-diminishable, and
(ii) they are no excludable. (see more on this at p. 608)
Public goods are …nanced by taxes if they are produced by the public
sector. However, it can easily be the case that there is private provision
of public goods, i.e. the public good is not …nanced by taxes. In these
situations the public good can be …nanced either by
4
1. voluntary contributions,
2. sale of by-products,
3. developments of new means to exclude nonpayers,
4. private contracts,
5. constructing clubs (and thus using the insights from the economics of
clubs).
(see more on this at p. 653-657).
Question 4
4.1 What do we mean by imperfect competition? Which market
structures can we have under imperfect competition and how
can we distinguish between them?
Answer: Imperfect competition captures all the market structures that
are not perfectly competitive. In all these cases, the …rm has some power
in determining the price in the market. There are 3 cases of imperfect
competition: (i) monopolistic competitive, (ii) oligopoly, and (iii) monopoly.
In a monopolistic competitive market there are many producers all producing a di¤erent variety of a product, i.e. there is product di¤erentiation.
The producer has power in determining the price of its product, but can
not in‡uence the price that the other producers set /because there are too
many of them).
In an oligopoly there are few producers of the same product (but product di¤erentiation may also exist). This low number of producers implies
that each …rm can calculate what the other producer will do and thus each
producer’s decision has an e¤ect on the other producers. In other words
there is strategic interaction among them.
In a monopoly, the producer is the sole supplier of a product and there
are substantial barriers to enter that market. It is important to note that it
is these barriers of entry that create the monopolist. If these barriers are not
important, then a single producer may not behave as a monopolist (charge
a high price and produce a small quantity) - the fear of entry will be enough
to discipline the supplier.
(see more on these issues at ch.12 - monopoly and ch13 - imperfect
competition. )
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4.2 Describe the Cournot model of an olipopolistic market.
Answer: The Cournot model describes the situation where two or few
suppliers compete by choosing the output that they want to put in the
market. Most of the times, such a decision is amde by choosing the capacity
that the …rm has (a decision that occurs in an early stage of the production
process). Such decisions are seen by other …rms, and can thus be used in
strategic behaviour.
In describing the Cournot model attention has to be given to as to how
a …rm decides its optimal output. For example in the case of two …rms, it is
important to understand that each …rm calculates its residual demand (i.e.
the demand that it faces after the other …rm has decided a hypothetical
output). Having that, the …rm will then decide its pro…t maximising output
which will clearly depend on how much the other …rm produces. This is
what is called the reaction, or best-responce, function, as it describes how
much will …rm 1 produce given …rms 2’s output. The point where the two
reaction functions meet is the point where the …rm’s expectations will be
realised - this is the Nash equilibrium, i.e. the equilibrium where both …rms
act simultaneously.
(see more on this at p. 467-470).
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