Transcript ECON 100 Tutorial: Week 7

ECON 100 Tutorial: Week 7
www.lancaster.ac.uk/postgrad/murphys4/
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Office: LUMS C85
Question 1
From the list of points below select those which distinguish a monopolistically
competitive industry from a perfectly competitive industry.
a) There are no barriers to the entry of new firms into
the market.
b) Firms in the industry produce differentiated
products.
c) The industry is characterised by a mass of sellers,
each with a small market share.
d) A downward sloping demand curve means the firm
has some control over the product's price.
e) In the long run only normal profits will be earned.
f) Advertising plays a key role in bringing the product
to the attention of the consumer.
Question 1
From the list of points below select those which distinguish a monopolistically
competitive industry from a perfectly competitive industry.
a)
b)
There are no barriers to the entry of new firms into the
market.
Perfectly competitive
Firms in the industry produce differentiated products.
Monopolistically competitive
c)
d)
The industry is characterised by a mass of sellers, each with a
small market share.
Perfectly competitive
A downward sloping demand curve means the firm has some
control over the product's price.
Monopolistically competitive
e)
In the long run only normal profits will be earned.
Perfectly competitive
f)
Advertising plays a key role in bringing the product to the
attention of the consumer.
Monopolistically competitive
Question 2
Draw a diagram depicting a firm in a monopolistically
competitive market that is making profits. Use diagrams to
show what happens to this firm in the long run as new
firms enter the industry.
The short run equilibrium
– a firm under monopolistic
competition is similar to that of a
monopoly.
• Firm is in equilibrium
– Q is where MR = MC
• But AR>AC
– Profit is area of PXYZ rectangle
– But unlike in a monopoly, other
firms may enter
• So, in the long run:
– This lowers price
– And reduces market share
• Shifting demand to the left
– The long run demand curve will be more
inelastic than the short run demand
curve
• Firm is in equilibrium
– Q is where MR=MC
• Industry is in equilibrium
– AR = AC
Question 3
Draw the average revenue and marginal revenue curves for a monopolist. Why does
the marginal revenue curve lie below the average revenue curve for a monopolist?
Note: Because the monopoly’s price equals its average revenue, the demand curve is
also the average revenue curve.
Question 3 (ctd.)
Question 4
Marginal revenue is the addition to total revenue as a
result of the sale of one extra unit of output. Given this
definition, explain how marginal revenue can be negative.
Marginal revenue is negative when the price effect on
revenue is greater than the output effect.
This means that when the firm produces an additional unit
of output, the price falls by enough to cause the firm’s total
revenue to decline, even though the firm is actually selling
more units.
Question 5(a)
Describe the Sylos Postulate using diagrams where
appropriate.
Sylos Postulate: Potential entrants believe that if
they were to enter the market, a monopolistic
incumbent firm would maintain its pre-entry output
level.
– The addition of the new entrant’s production would
result in a market with an increased quantity of the
product – and thus a lower market clearing price.
– At this low price, both firms would be losing money,
deterring new entry into the market.
Question 5(b)
Suggest a firm/industry that you believe may use a limit
pricing strategy.
In a situation with no potential new entrants, a monopolist
sets price where MC=MR to maximize profits. This price may
be well above the monopolist’s ATC.
If potential entrants are present, the monopolist may have a
lower cost curve than potential entrants. Rather than
maximizing profits, the monopolist now may wish to set a
price to deter new entry.
Limit pricing strategy: When a monopolist sets prices equal to
the Average Total Cost that potential entrants may face, in
order to prevent new firms from joining the market.
Question 6
£
80
MC
70
60
50
AC
40
30
20
AR
10
0
0
100
200
300
400
500
600
-10
-20
MR
Quantity
(a) What is the maximum-profit output?
200 units (where MC = MR)
(b) What is the maximum-profit price?
£60
(given by AR curve at 200 units)
(c) What is the total revenue at this price
and output?
TR = (AR)(Q)
TR = £60  200 units
TR = £12,000
(d) What is the total cost at this price and
output?
TC = (AC)(Q)
TC = £30  200 units = £6,000
(e) What is the level of profit at this price
and output?
π = TR – TC
π = £12,000 - £6,000
π = £6000
Question 6
£
80
(f) If the monopolist were
ordered to produce 300
units, what would be the
market price?
MC
70
60
£50 (where AR curve = Q)
50
AC
(g) How much profit would
now be made?
π = TR – TC
AR
π = (AR – AC)Q
π = (£50 - £35)  300
π =£15  300
π =£4500
40
30
20
10
0
0
100
200
300
400
500
600
-10
-20
MR
Quantity
Question 6
(h) If the monopolist were faced with
the same demand, but average costs
were constant at £60 per unit, what
output would maximise profit?
100 units
(where AC = MC = MR = £60)
(i) What would be the price now?
£70
(given by AR curve at 100 units)
(j) How much profit would now be
made?
π = TR – TC
π = (AR – AC)Q
π = (£70 - £60)  100
π = £10  100
π = £1000
Question 6
£
80
MC
70
60
50
AC
40
30
20
AR
10
0
0
100
200
300
400
500
600
-10
-20
MR
Quantity
(k) Assume now that the monopolist
decides not to maximise profits, but
instead sets a price of £40. How much
will now be sold?
400 units
(given by AR curve)
(l) What is the marginal revenue at
this output?
MR = 0
(m) What does the answer to (l)
indicate about total revenue at a
price of £40?
Total Revenue is Maximised
When MR = 0, TR is no longer
increasing, so it has reached a
maximum point.
(Note MR is the derivative of TR)
Question 6
£
80
MC
70
60
50
AC
40
30
20
AR
10
0
0
100
200
300
400
500
600
-10
-20
MR
Quantity
(n) What is the price elasticity
of demand at a price of £40?
Hint: You do not need to do a
calculation to work this out:
think about the relationship
between MR and TR.
When P = £40, Unit elastic
(When Q<400, MR>0, elastic
When Q>400, MR<0, inelastic
When Q=400, unit elastic
because MR=0)
Question 7
When the iPad was introduced Apple engineers reckoned that
the MC was about $200 and the fixed costs were about $2
billion. Apple’s econometricians estimated that the inverse
demand function was P = 800 -10 Q where Q is in millions although at the time they were working in the dark. Its hard
to figure out what the demand curve was likely to be for what
was effectively a new product in the market. In fact they
relied on information from selling their old “Newton”
touchpad (never a big seller and now a museum piece) and
estimates of the price differentials associated with the
various features of the iPad that could be found on other
machines. Apple was effectively a monopolist in the sale of
high end tablets at this time – there have been many entrants
since of course, but Apple retains a strong cost advantage.
Question 7(a)
When the iPad was introduced Apple engineers
reckoned that the MC was about $200 and the fixed
costs were about $2 billion. Apple’s econometricians
estimated that the inverse demand function was P =
800 -10 Q where Q is in millions - although at the time
they were working in the dark.
What was the AC function?
AC = TC/Q
AC = (FC + VC)/Q
We know: FC = $2bil and VC = MC * Q
TC = $2bil + $200 * Q
AC = $2bil/Q + $200
Question 7(a) ctd.
When the iPad was introduced Apple engineers reckoned that
the MC was about $200 and the fixed costs were about $2
billion. Apple’s econometricians estimated that the inverse
demand function was P = 800 -10 Q where Q is in millions although at the time they were working in the dark.
Assuming that Apple maximised profits, what was MR?
Average revenue is the demand curve for a monopolist (both
give price received for a given quantity), so AR = 800 – 10 Q.
TR = AR*Q
TR = 800Q – 10Q2
MR =
𝑑𝑇𝑅
𝑑𝑄
(Note: MR is the derivative, or slope, of TR)
MR = 800 – 20Q
Question 7(b)
Use Excel to draw the AC, MC, Demand and MR
curves (over the range of Q from 0 to 40).
Suggested Solution: Instead of finding the slope
using the rule you could draw AR (ie the demand
curve) in Excel and then use excel to calculate the
change in R when output changes by 1 unit) and
then plot this against Q.
Question 7(c)
What was the profit maximising P and Q?
MR = MC
800 – 20Q = 200
-20Q = -600
Q = 30
At Q = 30, the demand function (P = 800 – 10 Q)
gives:
P = 800 – 10 * 30
P = 800 – 300
P = $500
Question 7(c) ctd.
What was its level of profit?
Profit = (P – AC) * Q
Since AC = $2bil/Q + $200,
Profit = P*Q – AC*Q
= P*Q – ($2bil/Q + $200)*Q
= $500*Q – $2bil – $200*Q
= $300*Q – $2bil
Q = 30 million, so:
= $300*30mil – $2bil
= $9bil – $2bil
= $7 billion
Question 8(a)
Suppose a monopolist sells in two countries, 1 and 2, and can prevent resale.
MC=20
The inverse demand equations are:
p1=100-Q1 and p2=100-2Q2.
What does he charge in each country?
We want to find where MR = MC. We are given MC and the inverse
demand equations.
We know that MR is the derivative (or the slope) of TR.
So, we can solve this in three steps:
1) We can plug the inverse demand equations for each country into the
equation for Total Revenue: TR = P*Q
2) Once we have TR, we can take the derivative to get MR, set that equal
to MC and solve for Quantity.
3) Once we have Quantity, we can plug it in to our inverse demand
equation and solve for the price that the monopolist will charge in each
country.
Question 8(a)
In both countries:
MC=20
The inverse demand equations are:
p1=100-Q1 and p2=100-2Q2.
Step 1) We plug the inverse demand equations for
each country into the equation for Total Revenue:
TR = P*Q
Country 1:
TR1 = p1Q1
TR1 = (100-Q1)Q1
TR1 = 100Q1 - Q12
Question 8(a)
We are given: MC=20
p1=100-Q1
p2=100-2Q2
Step 2) We have TR, so we will take the derivative of TR, which is MR; then
we’ll set that equal to MC and solve for Quantity.
Country 1:
TR1 = 100Q1 - Q12
MR1=100-2Q1
Set
MR = MC
100-2Q1 = 20
Solving for Q1:
-2Q1 = -80
Q1=40
Step 3) This how much will be produced in Country 1. To find the price that
will be charged, we will plug Q1=40 into our inverse demand equation:
p1=100-Q1
p1=100-40
p1= 60
Question 8(a)
Given:
MC=20
p1=100-Q1 and p2=100-2Q2
We use the same methods for Country 2:
Step 1) We plug the inverse demand equations for each country into the equation for Total Revenue: TR
= P*Q
TR2 = p2Q2
TR2 = (100-2Q2)Q2
TR1 = 100Q2 - 2Q22
Step 2) We have TR, so we will take the derivative, which is MR; then we’ll set that equal to MC and
solve for Quantity.
TR2 = 100Q2 - 2Q22
MR2=100-4Q2
Set
MR = MC
100-4Q2 = 20
Solving for Q1:
-4Q2 = -80
Q2=20
Step 3) This how much will be produced in Country 2. To find the price that will be charged, we will plug
Q2=20 into our inverse demand equation:
p2=100-2Q2
p2=100-40
p2= 60
So P1=60 and P2=60.
Question 8(b)
Does it price discriminate or not? Why/Why not?
In this case P1 = P2 = 60, so the firm does NOT
discriminate – even though it could.
In this case, it doesn't because its optimal not to.
Note that the two demand curves differ in their slopes
but not their intercepts.
Price discrimination is possible when the monopolist
can prevent resale and it is profitable when different
consumers have different elasticities. In this case, the
first is true, but at optimal P and Q, the two countries
have the same elasticity. So, Price discrimination, while
possible is not profitable and therefore will not occur.
Next Week
Tutorial Worksheet on Moodle.