ECON 100 Tutorial: Week 8
www.lancaster.ac.uk/postgrad/murphys4/
s.murphy5@lancaster.ac.uk
office: LUMS C85
Question 1
Match each of the three types of price discrimination to
the following definitions:
(a) When a firm charges a consumer so much for the first
so many units purchased, a different price for the next so
many units purchased and so on.
(ii) Second-degree price discrimination
(b) When a firm divides consumers into different groups
and charges a different price to each group, but the same
price to all the consumers within a group.
(iii) Third-degree price discrimination
(c) When a firm charges each consumer for each unit the
maximum price the consumer is willing to pay for that
unit.
(i) First-degree price discrimination
Question 2
Under what circumstances can a monopolist practice price
discrimination? Illustrate your answer with appropriate
examples.
– Firms must be price setters, not price takers
– There must be no possibility for resale between segments
– Consumers must have different price elasticities in separate
markets
• This will ensure that optimal price is different in the different markets
• Examples:
– Discounts to the elderly for entry to theatres, meals in restaurants
and travel on buses and rail
– Different prices for kids and adults for sporting and other
attractions
– Gender pricing in some bars/clubs (lower prices for females
entering some night clubs)
– EuroRail pass for student travel - compared to standard fares for
business users
– Length of stay in airline tickets
Question 3(a)
£
A 20
15
AC1 = MC1
B
C 12
Dm
MR
O
4
8
Q
In the diagram above what is the price and quantity if
there is perfect competition?
P = £12 and Q = 8 units
In a perfectly competitive market, there are zero profits ,
so firms choose to produce where AC = AR.
Question 3(b) and (c)
£
A 20
15
AC1 = MC1
B
C 12
Dm
MR
O
4
8
Q
(b) If the firm could
act as a monopolist
selling at a single
price what would be
the equilibrium price
and output?
P = £15, Q = 4 units
(c) What would
supernormal profit
be at this position?
Profit = (P – AC)Q =
(£15 – £12) × 4 = £12
Question 3(d) and (e)
(d) If the monopolist
could sell to each customer
according to their
willingness to pay, what
would their revenue be?
Shade in this area on the
diagram.
TR =(£12 × 8) + 0.5(£8 × 8 )
TR = £128
(e) What name is given to
this practice
First degree price
discrimination
Question 3(f)
Is this (first degree price discrimination) better for society than
selling at a single monopoly price? Briefly explain.
Some consumers are better off because they receive the good at
prices below the single monopoly price of £15, though others are
worse off because they have paid in excess of £15. The monopolist
has captured the consumer surplus of these consumers because it
has worked out their willingness to pay for this good.
Overall, a successful first-degree price discrimination strategy is
equivalent to a perfectly competitive outcome except that the
monopolist captures the entire consumer surplus shown by triangle
ABC.
Question 4
Define natural monopoly.
A natural monopoly is characterized by falling
AC in the relevant industry output range. This
makes production cheaper for one firm than for
two or more firms.
Question 4(a)
Use a diagram to explain the equilibrium position if there
is a single monopoly producer.
A monopoly has optimal
production where MR=MC, at Qm
and sets price where Qm crosses
AR, at Pm, so profit will be the
blue-shaded rectangle.
Question 4(b)
Use the diagram to explain why a duopoly industry
structure will be inefficient.
At any level of total
production, in a
duopoly, the cost to
each firm will be
higher and the profit
for each firm will be
lower than the cost
and profit for a
monopoly producing
at that same total
level of production.
Question 4(c)
Show on the diagram the equilibria when MC
and AC pricing policies are adopted,
indicating any profits/losses that are
obtained.
MC Pricing is when
Price is set where
D=MC.
If MC < AC, a
monopolist would
want some sort of
subsidy to keep prices
at this level.
AC Pricing is when
Price is set where
D=AC. At this price
level, a monopolist will
earn zero profit
because P=AC, making
this a more sustainable
solution than MC
Pricing.
Question 5
A single firm delivers all the water to a set of
households in an area – in total Q units.
Suppose costs consist of fixed costs, F, and a constant
MC of m per unit, so total cost is given by C = F + mQ.
If an entrant would have the same costs does the
incumbent firm have a natural monopoly?
If each firm delivers to half of the households, then
each firm would have costs equal to C = F + mQ/2,
So then, the combined costs of two firms would be:
2F + mQ
The combined costs of the two firms is greater than
the costs under the monopoly (C = F + mQ) – so it's a
natural monopoly
Question 6(a)
Allergan is the monopoly producer of Botox, a wrinkle
treatment - well, it was originally a successful treatment
for an eye condition that led to blindness and they noticed
that wrinkles disappeared!
A vial of Botox costs $25 to produce and this MC is
constant. Beauty technicians buy vials at a price of $400
each. Sales revenue is $400m.
This tells us:
MC = $25, P = $400,
Total Revenue = PQ, so Q = TR/P
Q = $400 mil./$400, so Q = 1 (where Q is in millions)
What is the price elasticity of demand?
Note: for a monopolist, (P-MC)/P=-1/.
Question 6(a)
We know:
MC = $25, P = $400,
Total Revenue = PQ, so Q = TR/P
Q = $400 mil./$400, so Q = 1 million
What is the price elasticity of demand?
We are told that for a monopolist,
(P-MC)/P=-1/.
We can re-arrange to solve for :
 = - P/(P-MC)
 = -400/(400-25)
 = -1.067
Question 6(b)
Note that the firm is a profit maximiser and sets MR =
MC. Assuming that demand is linear, then work out
the equation of the inverse demand curve and the
corresponding MR curve.
We know that if inverse demand is linear, it will be in
y=mx+c form (slope-intercept). So, our inverse
demand curve will be P = a + bQ, where a and b are
the intercept and slope, respectively.
From the previous slide, we know the following:
MC = $25, P = $400, Q = 1 and  = -1.067
We can use our equation for elasticity to solve for a
and b to get our inverse demand equation.
From the previous slide, we know the following:
MC = $25, P = $400, Q = 1 million and  = -1.067
And we know that our inverse demand curve will be in the form P = a + bQ
First, we’re going to re-arrange the inverse demand curve, solving for Q:
P = a + bQ
-bQ = a – P
Q = (a – P)/(-b)
so, 𝑄 =
𝑃−𝑎
,
𝑏
which we can re-write as 𝑄 =
If we take the derivative with respect to P, we get:
We know that our equation for elasticity is:
𝜕𝑄
𝜕𝑃
−
𝑎
𝑏
= 1/b
𝜕𝑄
𝜀 = 𝜕𝑃 ∙
𝜕𝑄
𝑃
𝑏
𝑃
𝑄
We can plug in 𝜕𝑃 , P, Q, and 𝜀, into the elasticity equation, in order to solve for b:
𝜕𝑄 𝑃
𝜀=
∙
𝜕𝑃 𝑄
1 𝑃
𝜀= ∙
𝑏 𝑄
1 400
−1.067 = ∙
𝑏
1
400
b = -−1.067
b = -375
Question 6(b) ctd.
From the previous slide, we know the following:
MC = $25, P = $400, Q = 1 and  = -1.067
We also know that our inverse demand curve will be in
the form P = a + bQ and b = -375
Now, we can plug b back into our inverse demand
function, plug in P and Q, and solve to get a.
P = a + bQ
400 = a - 375 * 1
Solving for a, we get: a = 400 + 375 = 775.
So the inverse demand curve is P = 775 – 375 Q.
Question 6(b) ctd.
From the previous slide, we know the following:
MC = $25, P = $400, Q = 1 and  = -1.067
And the inverse demand curve is P = 775 – 375 Q.
To find MR, it helps to know about the relationship
between MR and AR for a monopolist firm.
(Note: AR is the inverse demand curve)
MR has twice the slope of AR. The Y-intercept is the
same for both.
From this, we can write our MR curve as:
MR = 775 – 750Q
Question 6(c)
Work out the CS, profits and DWL.
To find these, we first need to find the profit
maximising P & Q.
From part B, we have MC=25 and MR = 775 – 750 Q
To find profit-maximizing Q, we’ll set MC = MR:
775 – 750 Q = 25
Q=1
From part B, we have P = 775 – 375Q We can plug Q in
and solve for P:
P = 775 – 375(1)
P = 400
Question 6(c) ctd.
Once we find P and Q, we can
solve for CS, profits, and DWL.
CS = area A
CS = ½ (1m)(775-400)
CS = $187m
profits = area B
profits = (1m)(400-25)
profits =$375m minus an FC
DWL = area C
DWL = ½ (2m-1m)(400-25)
DWL = $187m
Question 6(d)
If Allergan could perfectly
price discriminate what
would happen to profits?
Profits would be the entire area of the triangle under the
demand curve, above MC: A+B+C= $750m
Some notes on study skills
If you are having questions about lecture slides, visit Ian or Caroline during their
office hours – they are there to answer questions about their material. Don’t put
it off – ask right away.
Also, if you weren’t pleased with your marks on the exam or with the way that
you prepared for the exam, then get help with your study skills. Email your faculty
student learning advisor (Most of you will be in either FASS or Management
School) and let them know what your concerns are or what you need help with.
Faculty Student Learning Advisors:
1.) Faculty of Arts & Social Sciences - Joanne Wood
Email studyadvice.fass@lancaster.ac.uk
Web: https://modules.lancs.ac.uk/course/view.php?id=283
2.) Faculty of Sciences & Technology and Faculty of Health & Medicine - Robert Blake
Email studyadvice.fstandshm@lancaster.ac.uk
Web: https://modules.lancs.ac.uk/course/view.php?id=282
3.) Management School - Gill Burgess and Sharon McCulloch
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Web: https://modules.lancs.ac.uk/course/view.php?id=281
Don’t put it off for the week before Exam 2!