Download Week 2 - personal.kent.edu

Week 14
Managerial Economics
Order of Business
•
•
•
•
Homework
Assigned Lectures
Other Material
Lectures for Next Week
Homework-Last Week
Problem 1
• The demand for a product is
Q = 600-2p.
• The marginal cost of producing a product is
zero, but each firm in the business has a
fixed cost of $20.
(a) Initially two firms are producing the
product in a Cournot Duopoly. How many
units are being produced? At what price are
they being sold? What is each firm's profit?
(a) Initially two firms are producing the product in a
Cournot Duopoly. How many units are being
produced? At what price are they being sold?
What is each firm's profit?
Q = 600 – 2P
Competition: 600
Cournot = (2/3)(600) = 400
400 = 600 – 2P  P = 100
 = PQ – FC = (100)(200) – 20 = 19980
(b) Now suppose a third firm enters the
business. We know this is not technically a
Cournot duopoly, but we know how to extend
the model. With three firms, how many units
are being produced? At what price are they
being sold? What is each firm's profit?
(b) Now suppose a third firm enters the business. We
know this is not technically a Cournot duopoly, but
we know how to extend the model. With three firms,
how many units are being produced? At what price
are they being sold? What is each firm's profit?
Q = 600 – 2P
Competition: 600
Cournot = (3/4)(600) = 450
450 = 600 – 2P  P = 75
 = PQ – FC = (75)(150) – 20 = 11230
(c) These profits will be a signal to other
firms to enter the business, so a fourth firm
will enter. And so on. How many firms will
eventually enter? When firms stop entering,
what price will the product be sold for? How
many firms will there be? (Hint: don’t forget
the fixed cost).
(c) These profits will be a signal to other firms to
enter the business, so a fourth firm will enter. And
so on. How many firms will eventually enter?
When firms stop entering, what price will the
product be sold for? How many firms will there
be? (Hint: don’t forget the fixed cost).
N=4
Cournot = (4/5)(600) = 480
480 = 600 – 2P  P = 60
 = PQ – FC = (60)(120) – 20 = 7180
(c) These profits will be a signal to other firms to enter the
business, so a fourth firm will enter. And so on. How many
firms will eventually enter? When firms stop entering, what
price will the product be sold for? How many firms will
there be? (Hint: don’t forget the fixed cost).
# Firms
50.0
Q
588.2
P
R
5.9
69.2
Profit
49.2
(c) These profits will be a signal to other firms to enter the
business, so a fourth firm will enter. And so on. How many
firms will eventually enter? When firms stop entering, what
price will the product be sold for? How many firms will
there be? (Hint: don’t forget the fixed cost).
# Firms
93.0
94.0
Q
593.6
593.7
P
3.2
3.2
R
20.4
19.9
Profit
0.4
-0.1
Problem 2
The industry demand curve for widgets is given by
Q = 600 - 10 P. Initially there are forty plants
producing widgets. Each plant belongs to a
different firm. (Indeed, there is a law restricting
each firm to one plant). Each plan has costs equal
to
27 + 3q2
where q is the number of widgets produced by each
plant.
(a) Assuming initially that only these
forty firms/plants may produce widgets,
determine the equilibrium price and
quantity of widgets, as well as the profits
of each firm.
(a) Assuming initially that only these forty firms/plants
may produce widgets, determine the equilibrium price
and quantity of widgets, as well as the profits of each
firm.
C = 27 + 3q2
MC = 6q  q = p/6
Industry Supply = 40 times firm supply = 40p/6
Supply = Demand 600-10p = 40p/6  p = 36
Q = 240, each firm produces 6
 = PQ – C = (36)(6) – [27+3 62]= 216- 135 =81
(b)
Now assume that other firms may
open a (single) plant and produce widgets
if they wish. If they do, their cost
function will be the same. Now
determine the equilibrium price of
widgets, the number of firms in the
industry, the quantity of widgets produced
by each firm, and the profits of each firm.
(b) Now assume that other firms may open a (single)
plant and produce widgets if they wish. If they do, their
cost function will be the same. Now determine the
equilibrium price of widgets, the number of firms in the
industry, the quantity of widgets produced by each firm,
and the profits of each firm.
MC
AC
Min occurs where
MC = AC, so
6q = 27/q +3q 
q =3 &AC = 18
Equilibrium price
with entry
(b) Now assume that other firms may open a (single)
plant and produce widgets if they wish. If they do, their
cost function will be the same. Now determine the
equilibrium price of widgets, the number of firms in the
industry, the quantity of widgets produced by each firm,
and the profits of each firm.
P = 18, Q = 600-10(18) = 420
Each firm produces 3, so N = 140
=0
(c)
Now suppose that Acme Widgets is
given a legal monopoly to operate
widgets, but is also given the right to open
as many plans as it wishes. Determine
how many plants Acme will operate, the
number of widgets it will produce at each
plant, the price it will charge for widgets,
and its profits.
(d) Derive Acme’s supply curve.
(c)
Now suppose that Acme Widgets is given a legal
monopoly to operate widgets, but is also given the right
to open as many plans as it wishes. Determine how
many plants Acme will operate, the number of widgets
it will produce at each plant, the price it will charge for
widgets, and its profits.
D
MR
LRMC = 18
210
420
(c)
Now suppose that Acme Widgets is given a legal
monopoly to operate widgets, but is also given the right
to open as many plans as it wishes. Determine how
many plants Acme will operate, the number of widgets
it will produce at each plant, the price it will charge for
widgets, and its profits.
Q = 210  P = 39
Widgets at each plant = 3, N = 70
 = (39)(210) – 18(210) = 4410
As to the supply curve….
Problem 3
The industry demand curve for widgets is given by
Q = 650 - 8 P
Initially there are ten plants producing widgets.
Each plant belongs to a different firm. (Indeed,
there is a law restricting each firm to one plant).
Each plant has a cost function
25 + q2
where q is the number of widgets produced by each
plant.
(a) Assuming initially that only these
ten firm/plants may produce widgets,
determine the equilibrium price and
quantity of widgets.
(a) Assuming initially that only these ten firm/plants
may produce widgets, determine the equilibrium
price and quantity of widgets.
C = 25 + q2
MC = 2q  q = p/2
Industry Supply = 10 times firm supply = 5p
Supply = Demand 650-8p = 5p  p = 50
Q = 250, each firm produces 25
 = PQ – C = (50)(25) – [25+ 252]= 625
(b) Now assume that other firms may
open a (single) plant and produce
widgets if they wish. If they do, their
cost function will be the same as the
ten plants.
(b) Now assume that other firms may open a (single)
plant and produce widgets if they wish. If they do,
their cost function will be the same as the ten plants.
Determine the number of firms, price
and quantity
MC
Min occurs where
AC
MC = AC, so
2q = 25/q +q 
q =5 &AC = 10
Equilibrium price
with entry
(b) Now assume that other firms may open a (single)
plant and produce widgets if they wish. If they do,
their cost function will be the same as the ten plants.
Determine the number of firms, price
and quantity
P = 10, Q = 650-8(10) = 570
Each firm produces 5, so N = 114
=0
(c) Now suppose that a new technology
makes it possible to build plants with a
cost of
4 + q2
Once there has been time to adjust,
what will be the equilibrium price of
widgets?
(c) Now suppose that a new technology makes it
possible to build plants with a cost of
4 + q2
Once there has been time to adjust, what will be
the equilibrium price of widgets?
AC
Min occurs where
MC = AC, so
2q = 4/q +q 
q =2 &AC = 4
Equilibrium price
with entry
(d) How many widgets will the old
plants produce?
(e) How many new plants will come
into being? (Assume none of the old
plants leave the industry).
(d) How many widgets will the old plants produce?
(e) How many new plants will come into being?
(Assume none of the old plants leave the industry).
For the old plants:
MC = P, so if P =4, each firm produces
where 2q = 4 implying q = 2
Now if : P=4, Quantity Demanded = 618.
If 114 old plants are producing 2 each, then
total is 228, leaving 390 to be produced by
195 new plants.
HomeworkDue this Week
Pashigian, Chapter
11, Exercise 3
Pashigian, Chapter
11, Exercise 7
Pashigian, Chapter
12, Exercise 2
Acme Widgets has conducted an exhaustive study of its
5,000 customers, and found that each one has a demand
function Q = 15- 3p. Right now, it charges $2 a widget.
The widgets cost essentially nothing to produce. How
much profit is it making per customer? At what price
would you sell widgets to maximize profits? Thomas
Bednarz, a local inventor has come up with a device that
would allow Acme to license widgets, so that they would
not be transferable from one customer to another. Bednarz
has offered to license the device to Acme for $110,000 per
year. Explain why Acme should reject the offer, but
should accept if Bednarz cuts his price to $80,000 per year.
In addition, explain how they should change their selling
policies if they accept his offer.
You have all read about the recent spate of corporate
scandals in which agents fundamentally failed their
duties to principals. Propose a remedy. Be sure to show
how your remedy is thoughtful and realistic and gives
appropriate recognition to the necessity to provide agents
incentives. … Illustrate your proposal by reference to
one of the existing scandals (Enron, World Com, and
Health South come to mind. You can use others but you
must give me a reference to a web site summarizing the
facts so I can familiarize myself with the case. ….
Obviously there is no right or wrong answer to this
question, so I will be looking for thoughtful reasoned
responses. And, sorry no group answers.
Lectures for This Week
• Price Discrimination-A Primer
• Price Discrimination with Self
Identification
• Price Discrimination in Action
• Three Discrimination Problems
• Solution to Three Discrimination
Problems
P
Q
P
Q
Lectures for This Week
•
•
•
•
•
The Free Rider
Asymmetric Information
Asymmetric Information 2
Moral Hazard
Applying the Premium for Honesty
•The Free Rider
•Asymmetric
Information
•Asymmetric
Information 2
•Moral Hazard
•Applying the
Premium for
Honesty