Download ECON 102 Tutorial: Week 7

ECON 102 Tutorial: Week 7
Ayesha Ali
www.lancaster.ac.uk/postgrad/alia10/econ102.html
[email protected]
office hours: 8:00AM – 8:50AM tuesdays LUMS C85
Ch. 8, Problem 2(a)
True or False: In a perfectly competitive industry the
industry demand curve is horizontal, whereas for a
monopoly it is downward-sloping.
False.
The industry demand curve is downward sloping in
both cases, but from the individual perfectly
competitive firm’s point of view, the demand curve
is horizontal.
Because the individual firm is too small to affect the
market price, it can sell as many units as it wishes at
that price. (that’s why we say it is a price taker)
Ch. 8, Problem 2 (b)
True or False: Perfectly competitive firms have no
control over the price they charge for their product.
True.
If they try to charge a higher price they will lose all
their business; if they try to charge a lower price,
they will not be maximizing profit.
Ch. 8, Problem 2 (c)
True or False: For a natural monopoly, average cost
declines as the number of units produced increases
over the relevant output range.
True.
This is the essential feature of natural monopoly.
Ch. 8, Problem 3
A single-price profit-maximising monopolist:
a. Causes excess demand, or shortages, by selling too few units of a
good or service.
b. Chooses the output level at which marginal revenue begins to
increase.
c. Always charges a price above the marginal cost of production.
d. Also maximises marginal revenue.
e. None of the above statements is true.
The answer is c. The monopolist chooses the output level at which
marginal revenue equals marginal cost and then charges a price
consistent with demand at that level of output. Since price always
exceeds marginal revenue, price is greater than marginal cost. There
is no shortage: at the output chosen, demand and supply coincide.
And the monopolist has no reason to maximize marginal revenue
(which would require producing zero units of output).
Ch. 8, Problem 4
If a monopolist could perfectly price discriminate:
a. The marginal revenue curve and the demand curve would coincide.
b. The marginal revenue curve and the marginal cost curve would
coincide.
c. Every consumer would pay a different price.
d. Marginal revenue would become negative at some output level.
e. The resulting pattern of exchange would still be socially inefficient.
The answer is a. The demand curve and the marginal revenue curve
would coincide, because the monopolist would sell each successive
unit of output at exactly its reservation price, so that unit would
generate revenue identical to the reservation price. The final unit of
output would be sold at a price equal to marginal cost, so e is wrong:
the outcome would be socially efficient. Because two or more
consumers might have the same reservation price, c is wrong.
Ch. 8, Problem 6
What is the socially desirable price for a natural monopoly to charge? Why
will a natural monopoly that attempts to charge the socially desirable price
invariably suffer an economic loss?
What do we mean by socially desirable price? This just means the
equilibrium price when there is no deadweight loss. It’s basically the same
thing as the equilibrium price in a perfectly competitive market, when S = D,
or when P = MC.
The textbook solution is given in the next slide.
Ch. 8, Problem 6
What is the socially desirable price for a natural monopoly to charge? Why
will a natural monopoly that attempts to charge the socially desirable price
invariably suffer an economic loss?
The socially desirable price to charge is the one at which the marginal
benefit to consumers equals the marginal cost of production. However,
natural monopolies are usually characterized by very large fixed costs and
relatively low marginal costs. The high fixed costs mean that average cost is
greater than marginal cost, so that charging a price equal to marginal cost
implies economic losses. An example is the London Underground, which
incurred huge fixed costs tunneling, laying railway line, building stations and
acquiring rolling stock. However, this transport system incurs virtually no
additional cost when an additional passenger travels from Heathrow airport
to Trafalgar Square. Charging a price equal to the marginal cost would thus
fail to cover the average cost of a ride.
One way the London Underground deals with this problem is by selling a
rail-card that entitles customers to unlimited travel within a certain period.
With this card, the marginal cost to the consumer of an additional journey is
zero.
Slide 16 from Prof. Rietzke’s Week 6 Slides:
MR and the Monopolist
• Useful fact: If demand is given by: p = a – bQ,
then MR is given by the equation: p = a – 2bQ.
Note: We use this rule to find the Marginal Revenue in Problem 8.
Ch. 8, Problem 8 (a)
Suppose that a university student cinema is a local monopoly whose
demand curve for adult tickets on Saturday night is P = 12 – 2Q, where
P is the price of a ticket in euros and Q is the number of tickets sold in
hundreds.
The demand for children’s tickets on Sunday afternoon is P = 8 – 3Q,
and for adult tickets on Sunday afternoon, P = 10 – 4Q.
On both Saturday night and Sunday afternoon, the marginal cost of an
additional patron, child or adult, is €2.
What is the marginal revenue curve in each of the three sub-markets?
Finding the equation for the marginal revenue curve is
straightforward, we will apply the rule from the previous slide:
If demand is given by: p = a – bQ,
then MR is given by the equation: p = a – 2bQ
Ch. 8, Problem 8 (a)
Suppose that a university student cinema is a local monopoly whose
demand curve for adult tickets on Saturday night is P = 12 – 2Q, where P is
the price of a ticket in euros and Q is the number of tickets sold in hundreds.
The demand for children’s tickets on Sunday afternoon is P = 8 – 3Q, and for
adult tickets on Sunday afternoon, P = 10 – 4Q.
On both Saturday night and Sunday afternoon, the marginal cost of an
additional patron, child or adult, is €2.
What is the marginal revenue curve in each of the three sub-markets?
The demand curve for adult tickets on Saturday night: P = 12 – 2Q
We can apply our rule: If demand is given by: p = a – bQ, then MR is given by the
equation: p = a – 2bQ
So then,
Marginal revenue curve for adult tickets on Saturday night: P = 12 - 4Q
Similarly:
Marginal revenue curve for kids’ tickets on Sunday afternoon P = 8 - 6Q
Marginal revenue curve for adult tickets on Sunday afternoon P = 10 - 8Q
Ch. 8, Problem (b)
What price should the cinema charge in each of the three sub-markets if its
goal is to maximise profit?
To maximise profit, they should set marginal revenue equal to marginal cost
in each market.
We know MR from part (a); And we are told that on both Saturday night and
Sunday afternoon, the marginal cost of an additional patron, child or adult,
is €2.
Ch. 8, Problem (b)
What price should the cinema charge in each of the three sub-markets if its goal is to
maximise profit?
To maximise profit, they should set marginal revenue equal to marginal cost in each
market.
We know MR from part (a); And we are told that on both Saturday night and Sunday
afternoon, the marginal cost of an additional patron, child or adult, is €2.
Let’s look at the Saturday night adult tickets; MR is given by P = 12 – 4Q.
So we set
MR = MC
12 – 4Q = 2
And solve for Q:
-4Q = -10
Q = 2.5
But, remember, Q is in terms of hundreds of tickets, so actually the profit maximizing
number of tickets will be 250.
To find profit-maximizing price, we can plug Q in to our equation for Demand:
P = 12 – 2(2.5)
P = 12 – 5
P = €7
Doing the same thing in the other two markets, we should get:
Sunday Children tickets; Q = 100 tickets, P = €5
Sunday Adult tickets; Q = 100 tickets, P = €6
Ch. 8, Problem 9 (a)
Suppose you are a monopolist in the market for a specific video
game. Your demand curve is given by P = 80 – Q/2, and your marginal
cost curve is MC = Q. Your fixed costs equal €400.
Graph the demand and marginal cost curve.
Ch. 8, Problem 9 (a)
Suppose you are a monopolist in the market for a specific video
game. Your demand curve is given by P = 80 – Q/2, and your marginal
cost curve is MC = Q. Your fixed costs equal €400.
Graph the demand and marginal cost curve.
Ch. 8, Problem 9 (b)
Suppose you are a monopolist in the market for a specific video game. Your
demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC
= Q. Your fixed costs equal €400.
Derive and graph the marginal revenue curve.
Ch. 8, Problem 9 (b)
Suppose you are a monopolist in the market for a specific video game. Your
demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC
= Q. Your fixed costs equal €400.
Derive and graph the marginal revenue curve.
Using our rule to find the MR curve, we get: MR=80 - Q.
Ch. 8, Problem 9 (c)
Suppose you are a monopolist in the market for a specific video game. Your
demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC = Q.
Your fixed costs equal €400.
Calculate and indicate on the graph the equilibrium price and
quantity.
Ch. 8, Problem 9 (c)
Suppose you are a monopolist in the market for a specific video
game. Your demand curve is given by P = 80 – Q/2, and your marginal
cost curve is MC = Q. Your fixed costs equal €400.
Calculate and indicate on the graph the equilibrium price and
quantity.
Profit is maximized where MR = MC; looking at the graph, this is when q = 40.
Because we are a monopolist, we will produce at this quantity, but set the price where
q = 40 is equal to our Demand curve. So, Price will set at €60.
P
MC=Q
80
p*=60
q*=40
80
160
Q
Ch. 8, Problem 9 (d)
Suppose you are a monopolist in the market for a specific video game. Your
demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC = Q.
Your fixed costs equal €400.
In part (c), we found that P* = 60 and Q* = 40.
What is your profit?
Ch. 8, Problem 9 (d)
Suppose you are a monopolist in the market for a specific video game. Your
demand curve is given by P = 80 – Q/2, and your marginal cost curve is MC = Q.
Your fixed costs equal €400.
What is your profit?
In part (c), we found that P* = 60 and Q* = 40.
We know that Profit = total revenue - total cost
And that TR = PQ and TC = FC + VC. We are told FC = 400.
And, we should have been given VC = ½(Q)2
So we can plug all of this in to our equation for profit:
π = total revenue - total cost
π = (P)(Q) – FC – VC
π = (60)(40) - 400 - (40)(40)/2
π = 1200
Ch. 8, Problem 9 (e)
Suppose you are a monopolist in the market for a specific video
game. Your demand curve is given by P = 80 – Q/2, and your marginal
cost curve is MC = Q. Your fixed costs equal €400.
P
What is the level of consumer surplus?
MC=Q
80
p*=60
q*=40
80
160
Q
Ch. 8, Problem 9 (e)
Suppose you are a monopolist in the market for a specific video
game. Your demand curve is given by P = 80 – Q/2, and your marginal
cost curve is MC = Q. Your fixed costs equal €400.
What is the level of consumer surplus?
Consumer Surplus is the difference between what
consumers are willing to pay (the demand curve)
and the actual price that they do pay.
So, it is the area of this triangle here:
We use the equation: area = ½(b)(h) to find the area
of a triangle.
So, Consumer Surplus = (½)(40)(20)
CS = 400
P
MC=Q
80
p*=60
q*=40
80
160
Q
Ch. 8, Problem 10 (a)
Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban
neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no
fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand
each day are listed in the table below:
Person A
Reservation price (€) 1.00
B
0.90
C
0.80
D
0.70
E
0.60
F
0.50
G
0.40
H
0.30
I
0.20
J
0.10
Beth knows the distribution of reservation prices (that is, she knows that one person is
willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s
reservation price.
Ch. 8, Problem 10 (a)
Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban
neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no
fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand
each day are listed in the table below:
Person A
Reservation price (€) 1.00
B
0.90
C
0.80
D
0.70
E
0.60
F
0.50
G
0.40
H
0.30
I
0.20
J
0.10
Beth knows the distribution of reservation prices (that is, she knows that one person is
willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s
reservation price.
Calculate the marginal revenue of selling an additional cup of lemonade.
(Start by figuring out the price Beth would charge if she produced only one cup of lemonade, and calculate the total
revenue; then find the price Beth would charge if she sold two cups of lemonade; and so on.)
Quantity
Price
1
€1
2
€.90
3
€.80
4
€.70
5
€.60
6
€.50
7
€.40
8
€.30
9
€.20
10
€.10
Total Revenue
€1
€1.80
€2.40
€2.80
€3.00
€3.00
€2.80
€2.40
€1.80
€1
Ch. 8, Problem 10 (a)
Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban
neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no
fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand
each day are listed in the table below:
Person A
Reservation price (€) 1.00
B
0.90
C
0.80
D
0.70
E
0.60
F
0.50
G
0.40
H
0.30
I
0.20
J
0.10
Beth knows the distribution of reservation prices (that is, she knows that one person is
willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s
reservation price.
Calculate the marginal revenue of selling an additional cup of lemonade.
(Start by figuring out the price Beth would charge if she produced only one cup of lemonade, and calculate the total
revenue; then find the price Beth would charge if she sold two cups of lemonade; and so on.)
Quantity
Price
Total Revenue
1
€1
€1
2
€.90
€1.80
3
€.80
€2.40
4
€.70
€2.80
5
€.60
€3.00
6
€.50
€3.00
7
€.40
€2.80
8
€.30
€2.40
9
€.20
€1.80
10
€.10
€1
Marginal Revenue
€1
€.80
€.60
€.40
€.20
€0
€-.20
€-.40
€-.60
€-.80
Ch. 8, Problem 10 (b)
Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban
neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no
fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand
each day are listed in the table below:
Person A
Reservation price (€) 1.00
B
0.90
C
0.80
D
0.70
E
0.60
F
0.50
G
0.40
H
0.30
I
0.20
J
0.10
Beth knows the distribution of reservation prices (that is, she knows that one person is
willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s
reservation price.
In part (a), we calculated the marginal revenue for selling an additional cup of lemonade:
Price
Quantity
Total Revenue
€1
1
€1
€.90
2
€1.80
€.80
3
€2.40
€.70
4
€2.80
€.60
5
€3.00
€.50
6
€3.00
€.40
7
€2.80
€.30
8
€2.40
€.20
9
€1.80
€.10
10
€1
Marginal Revenue
€1
€.80
€.60
€.40
€.20
€0
€-.20
€-.40
€-.60
€-.80
What is Beth’s profit-maximising price?
Profit is maximised where MR=MC. We know that Beth’s MC = 0.20, so her MR = 0.20 at a
price of €.60.
Ch. 8, Problem 10 (c)
Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban
neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no
fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand
each day are listed in the table below:
Person A
Reservation price (€) 1.00
B
0.90
C
0.80
D
0.70
E
0.60
F
0.50
G
0.40
H
0.30
I
0.20
J
0.10
Beth knows the distribution of reservation prices (that is, she knows that one person is
willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s
reservation price.
In part (a), we calculated the marginal revenue for selling an additional cup of lemonade:
Price
Quantity
Total Revenue
€1
1
€1
€.90
2
€1.80
€.80
3
€2.40
€.70
4
€2.80
€.60
5
€3.00
€.50
6
€3.00
€.40
7
€2.80
€.30
8
€2.40
€.20
9
€1.80
€.10
10
€1
Marginal Revenue
€1
€.80
€.60
€.40
€.20
€0
€-.20
€-.40
€-.60
€-.80
In part (b) we found Beth’s profit-maximising price is €.60.
At that price, what is Beth’s economic profit?
Profit = TR – TC → Profit = (AR – ATC)*Q → Profit=5*(.6 - .2) → Profit = €2.
Ch. 8, Problem 10 (c)
Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban
neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no
fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand
each day are listed in the table below:
Person A
Reservation price (€) 1.00
B
0.90
C
0.80
D
0.70
E
0.60
F
0.50
G
0.40
H
0.30
I
0.20
J
0.10
Beth knows the distribution of reservation prices (that is, she knows that one person is
willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s
reservation price.
In part (a), we calculated the marginal revenue for selling an additional cup of lemonade:
Price
Quantity
Total Revenue
€1
1
€1
€.90
2
€1.80
€.80
3
€2.40
€.70
4
€2.80
€.60
5
€3.00
€.50
6
€3.00
€.40
7
€2.80
€.30
8
€2.40
€.20
9
€1.80
€.10
10
€1
Marginal Revenue
€1
€.80
€.60
€.40
€.20
€0
€-.20
€-.40
€-.60
€-.80
In part (b) we found Beth’s profit-maximising price is €.60.
At that price, what is Beth’s total consumer surplus?
Consumer Surplus is the difference between what consumers are willing to pay (i.e. their
reservation price) and the actual price that they do pay.
Consumer surplus = (€1 - €0.60)+ (€0.90 - €0.60)+(€0.80 - €0.60)+(€0.70 - €0.60)= €1.
Ch. 8, Problem 10 (d)
Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban
neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no
fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand
each day are listed in the table below:
Person A
Reservation price (€) 1.00
B
0.90
C
0.80
D
0.70
E
0.60
F
0.50
G
0.40
H
0.30
I
0.20
J
0.10
Beth knows the distribution of reservation prices (that is, she knows that one person is
willing to pay €1, another €0.90, and so on), but she does not know any specific individual’s
reservation price.
In part (a), we calculated the marginal revenue for selling an additional cup of lemonade:
Price
Quantity
Total Revenue
€1
1
€1
€.90
2
€1.80
€.80
3
€2.40
€.70
4
€2.80
€.60
5
€3.00
€.50
6
€3.00
€.40
7
€2.80
€.30
8
€2.40
€.20
9
€1.80
€.10
10
€1
Marginal Revenue
€1
€.80
€.60
€.40
€.20
€0
€-.20
€-.40
€-.60
€-.80
In part (b) we found Beth’s profit-maximising price is €.60.
What price should Beth charge if she wants to maximise total economic surplus?
Total economic surplus is maximised at the perfect competition equilibrium, or where S = D,
or where P = MC.
So if Beth wanted to maximise total economic surplus, she should set P = MC; so P = €.20.
Ch. 8, Problem 10 (e)
Beth is an 8-year-old who old sells home-made lemonade on a street corner in a suburban
neighbourhood. Each paper cup of lemonade costs Beth 20 cents to produce; she has no fixed costs. The
reservation prices for the 10 people who walk by Beth’s lemonade stand each day are listed in the table
below:
Person A
B
C
D
E
F
G
H
I
J
Reservation price (€) 1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
In part (a), we calculated the marginal revenue for selling an additional cup of lemonade:
Price €1
€.90
€.80
€.70
€.60
€.50
€.40
€.30
Quantity
1
2
3
4
5
6
7
8
Total Revenue €1
€1.80
€2.40
€2.80 €3.00 €3.00 €2.80 €2.40
Marginal Revenue
€1
€.80
€.60
€.40
€.20
€0
€-.20
€-.40
0.20
0.10
€.20
9
€1.80
€.10
10
€1
€-.60
€-.80
In part (b) we found Beth’s profit-maximising price is €.60.
In part (c) we found Beth’s economic profit is €2 and total consumer surplus is €1.
Now suppose that Beth can tell the reservation price of each person. What price would she
charge each person if she wanted to maximise profit?
She would sell to each person whose reservation price is below her marginal cost, and she
would charge these people (persons A through I) their respective reservation prices.
Compare her profit to the total surplus calculated in part (c).
Doing so would earn her a profit of €3.60, which is the same as the total economic surplus in
part (d).
Next Week
 Check Moodle for the Week 8 worksheet. It’s on
game theory – Chapter 9 of the textbook should
be helpful if you have not studied game theory
before.
 Exam results should be coming out soon. You can
check on Moodle for your results.