# Solutions seminar 5 micro 2021 ```Seminar 5 solutions
Ethan O’Leary∗
September 2021
1
Q1
1.1
Part a)
Our given market demand curve is P = 12−Q for yeast and there is one present
firm *Gestur.* The total revenue obtained by *Gestur* for any quantity at any
given price is hence:
T R = (12 − Q) &middot; Q
T R = 12Q − Q2
The marginal revenue is hence defined by:
MR =
d(T R)
= 12 − 2Q
dQ
Since monopolistic firms produce the profit maximising quantity, Q∗ , defined
by the point at which the marginal revenue is equal to the marginal cost, we
compute:
MR = MC
12 − 2Q∗ = 0
Q∗ = 6
According to the market demand equation, the profit maximising price, P ∗ ,
is given by:
P ∗ = 12 − Q∗ = 12 − 6 = 6
∗ 41643@student.hhs.se
1
Hence the maximised profit is π ∗ = T R − T C = P ∗ Q∗ − c = 36 where c is
C)
some constant such that d(T
= 0. In other words, there is only a fixed cost
dQ
equal to some constant c (which could be zero). From herein, we assume for
simplicity that c = 0. See below for a diagram.
1.2
Part b)
The producer surplus in this case is defined by the profit (P ∗ − M C) &middot; Q∗ which
is computed above to be 36. From the diagram below, one can see that the
consumer surplus is defined as the triangle above the price set P ∗ that is bounded
above by the market demand curve. The area of such is 12 (P M AX − P ∗ )Q∗ =
1
M AX
is the price at which the demand curve intersects
2 &middot; 6 &middot; 6 = 18 where P
the vertical axis (here it is 12). Further, the deadweight loss is computed as the
remaining triangle such that DW L = 12 &middot; P ∗ &middot; (QM AX − Q∗ ) = 18 where QM AX
is the point at which the market demand curve intersects the horizontal axis.
The presence of this non-zero deadweight loss is a signal of market inefficiency
caused by a price setting monopolist. A diagram is included below.
2
1.3
Part c)
In a Cournot duopoly we have two firms producing homogeneous (the same)
goods facing a common market demand with individual cost functions. Thus
firms form reaction functions which intuitively show **the profit maximising
quantity the firm should produce given the quantity produced by the other
firm**. Clearly then we expect the reaction function (RF) to be a function
in the form qi∗ = f (qj ). We formulate this by incorporating the two firms’
individual outputs into the market output such that Q = qG + qJ i.e. the
market output is the output of *Gestur* plus the output of *Jaer.* This allows
us to rewrite the market demand curve as:
P = 12 − Q = 12 − qG − qJ
As per our assumption in part a), we assume no fixed costs such that T CG =
T CJ = 0. Thus both firms facing the same demand and cost functions will
face the same profit maximisation problem where Profit π for firm i is defined
as πi = (12 − Q) &middot; qi . To solve this for *Gestur,* we acknowledge the profit
maximisation problem which can be written as:
max πG = (12 − qG − qJ )qG
qG ≥0
To find a maximum point, we differentiate the profit function subject to the
variable which *Gestur* is choosing: it’s output quantity, and set this to equal
zero:
∂πG
= 12 − 2qG − qJ = 0
∂qG
[NOTE: the keen eyed among you will wonder why I have used the symbol
∂ above instead of d. The reason is that there is more than one variable in the
equation for profits of *Gestur.* The ∂ symbol states that we differentiate the
profit function with respect to some variable (here qG ) while keeping all other
variables constant (so we can treat qJ in this example just like a constant)].
∗
, we have:
Rearranging the above equation to compute qG
∗
2qG
= 12 − qJ
1
∗
qG
= 6 − qJ
2
Which tells us the optimal profit maximising quantity that *Gestur* should
produce given any output produced by *Jaer.* Note that since *Jaer* has an
identical profit maximising problem, we can write *Jaer’s* reaction function as:
1
qJ∗ = 6 − qG
2
We can draw these two reaction functions on one diagram to show our optimal point at where these two cross:
3
Substituting this into the reaction function for *Gestur*, we can compute:
1 ∗
1 ∗
1
∗
) = 3 + qG
qG
= 6 − (6 − qG
2
2
4
3 ∗
q =3
4 G
∗
qG
=4
Since we have symmetrical problems, we also have qJ∗ = 4 and thus market
price is P ∗ = 12 − qG − qJ = 4. Thus each individual firm has a profit of
πiC = P ∗ &middot; qi∗ = 16 which is less than the monopolisation profit. In this case, we
expect that the deadweight loss is reduced from the previous diagram.
From the below diagram, we allow *Gestur* to produce 4 units as it would
want to according to its marginal revenue curve. This leaves the rest of the
market demand curve open for *Jaer* to conquer. Since the two firms are
colluding they both price at P ∗ = 4 given the output level set individually at 4
units per firm and thus the consumer surplus has increased while the deadweight
loss has decreased. Note that the producer surplus has also decreased in whole
C
and has decreased for each individual firm πG
+ πJC = 32 &lt; 36.
4
marginal cost
changes for Jaer,
meaning that his
profit is no longer
(P x Qj)Qj, but (P x
Qj)Qj—2Qj
This is because the
cost changes for
one firm, and their
reaction function
will change. And
there is a new
Cournot eq.
1.4
Part d)
In part d, firms no longer have homogeneous cost functions. As such while
*Gestur*’s profit function remains at πG = (12 − Q)qG , the profit function of
*Jaer* is now πJ = (12 − Q)qJ − 2qJ = (12 − qG − qJ )qJ − 2qJ since total cost is
2qJ for *Jaer.* Hence, we reaction function for *Gestur* is unchanged, but we
must compute a new reaction function for *Jear* by differentiating the profit
function and setting it to the value of zero:
∂πJ ∂qJ = 12 − qG − 2qJ − 2 = 0
Rearranging the right hand side, one obtains:
2qJ∗ = 10 − qG
1
qJ∗ = 5 − qG
2
By substituting this into the original reaction function for *Gestur* computed in part c, one obtains the profit maximising output for *Gestur:*
1
1 ∗
∗
qG
= 6 − (5 − qG
)
2
2
5
∗
qG
=
7 1 ∗
+ q
2 4 G
14
&gt;4
3
Further, the profit maximising output of *Jaer is now:*
∗
qG
=
1 14
7
8
=5− = &lt;4
2 3
3
3
Hence since *Jaer* faces a higher per unit cost than *Gestur, Gestur* is able
to capture a higher market share. This reflects the notion of economic efficiency
- since it is cheaper for *Gestur* to produce yeast, it is a more efficient use of
resources to allocate a greater share of production to *Gestur.*
8
14
∗
− qJ∗ = 12 − 14
Here the market price will be P ∗ = 12 − qG
3 − 3 = 3 &gt; 4
thus since the total quantity supplied to the market is less than the case in part
c, the market price set is higher and the aggregate profits are:
qJ∗ = 5 −
8
266
14 14 8 14
+
−2 =
&lt; 32
3 3
3 3
3
9
Thus profits are lower in this case indicating a reduction in the producer
surplus. In this case, the deadweight loss increases also indicating that the
greater the marginal cost of firms, the greater the inefficiency in the case of
collusion power (price setting).
π = πG + πJ =
6
7
2
2.1
Q2
Part a)
In the case where a low income country (e.g. Thailand) demands a small quantity of goods at every price but a higher income country (e.g. Germany) demands a proportionally larger quantity of goods at every price, a market-set
price formed by an aggregated demand function will favour consumers in higher
income countries. Suppose the efficient market price in the Thai market is pT
and the efficient market price in Germany is pG . The price set by *Econdork*
will be some price pT &lt; p∗ &lt; pG . This means that the price will be above
equilibrium price for Thai consumers reducing the total welfare in that market
- Thai consumers would be willing to buy more units of the good at a lower
price. On the other hand, the price will be below equilibrium price for German consumers. This unfairly gives consumers in higher income countries a
greater consumer surplus and increased equilibrium quantity of goods. Thus
the argument is valid on both efficiency and equity fronts.
2.2
Part b)
If we ignore at first the prospect of in-game purchases, this is precisely 2nd degree
highly and as such setting a high price for removal of ads will allow the firm to
cover the marginal cost for providing the game and thus can extract consumer
surplus from this set of individuals. Another set of consumers may not value
the absence of advertisements. As such, the firm can lower its marginal cost
to zero by displaying paid advertisements and can efficiently charge nothing for
line of thinking is a little nuanced since the consumers are not transferring some
8
of their surplus to the producer in the form of price discrimination but it does
describe precisely the concept of ’self-sorting’: where consumers choose which
product to purchase according to their preferences to transfer optimal producer
surplus to *Econdork.*
From another view: imagine the world where only the paid version is supplied: only the set of individuals who value the absence of advertisements enough
in the game will purchase the good and because of the monopolistic power of
*Econdork,* there will be a deadweight loss. By introducing another free product which is funded by advertisement revenue, the firm has been able to increase
its revenue (overall producer surplus) while a) capturing a bigger share of the
market and b) allowing both sets of users to access in-game purchases thus
increasing opportunity for further revenue.
2.3
Part c)
First, lets compute the total revenue and marginal revenue for Äppstore:
T RÄ=20Q
MR
Ä= dQ
Ä−Q
Ä2
d(T R
Ä)
=20−2Q
Ä
Ä
The firm will produce where the marginal revenue is equal to the marginal
cost:
M RÄ=M C
Ä
20 − 2QÄ=2
QÄ∗ =9
PÄ∗ =11
∗
πÄ
= Q∗Ä &middot; PÄ∗ − 2QÄ = 99 − 18 = 81
Now we have the case of a tariff which is applied in order to capture a
greater part of consumer surplus. In fact, this question describes a special case
of the two-part tariff which does not have any per-unit cost. Hence in this case,
Spåttifaj will want to price their subscription such that they capture the entire
consumer surplus when the price per unit is equal to their marginal cost.
If they were to price per unit at their marginal cost (P = M C = 2), consumers would consume 18 songs and have a consumer surplus of 18&middot;(20−2)/2 =
162. Hence if Spåttifaj were to charge a subscription price of 162, then consumers would still demand the subscription but would not have any consumer
surplus. This would give a producer surplus (profit) of 162 − 18 &middot; 2 = 126.
9
The problem with this analysis is that if the consumer purchases the subscription, **there is nothing to stop them downloading more songs since the
marginal cost to the consumer is effectively zero.** Hence it is always logical to
think that the consumer will download 20 songs (since this is their maximum
demand) which increases the cost to the firm. A predatory firm could notice
this and price the subscription assuming that at whatever price they set, the
consumer surplus will be equal to the entire triangle under their demand curve.
This gives a maximum willingness to pay for a subscription of 200 which gives
a profit of 160. Which is now the final answer.
3
Q3
When companies merge or acquire other competitors, it is only permitted by
Anti-Trust laws if it leads to synergies - this means that by combining resources,
firms are able to cut costs, combine technologies and the end result is a better
product at a lower price to the consumer. Thus the merger must be beneficial
to the end-consumer. In the case of Facebook, the podcast argues that the company’s executives acquired Instagram and Whatsapp in order to suppress their
competitive potential and thus increase the market power of Facebook. This