Week 13

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Week 13

• Managerial Economics

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Order of Business

• Homework
• Assigned Lectures
• Other Material
• Lectures for Next Week

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Homework-Last Week
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Pashigian, Chapter 10, Exercise 3
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Since marginal cost is zero, I assume each firm
can produce the entire market demand. This sounds
to me like a "winner take all bidding situation".
The demand curve for firm A for instance would be
equal to zero when its price was above that of
firm B, and equal to 60-P when its price was
below B's. That means a Nash Equilibrium at a
price of zero, with the firms splitting the
market of 60 each firm would produce 30. Each
firm then loses 50, assuming fixed costs of 50.
If the firms merged, they would act like a
monopoly and force the price to 30, and market
demand to 30.
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Now suppose you were working with the FTC. If
the merger does not go through, neither firm will
stay in the business. No consumer surplus will
be generated. But if the merger goes through,
there will be consumer and producer surplus
generated. Thus I would support the merger as
the lesser of two evils.
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Pashigian, Chapter 10, Exercise 4
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If they build plants of fixed and limited
production capacity, then they can effectively
prohibit their customer from employing a winner
take all strategy against them. For example,
suppose the competitive solution would have
production of 20 units and the monopoly solution
would have production of 10 units. If each
builds a plant capable of producing 5 units, then
they cannot be subject to a price war. Between
them, they will only build 10 units for that is
all they can produce.
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Pashigian, Chapter 10, Exercise 10
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No just because you have a dominant strategy does
not mean that strategy will maximize profits. .
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The demand curve for a particular product is
given by Q 630000-300p. The marginal cost of
producing the product is 400. Two firms produce
the product, working as a Cournot Duopoly. Plot
their reaction functions. Given their reaction
functions, calculate the quantity produced and
the market price for the product.
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A
510,000
Each firm produces 170,000 Market price is 93.33
Accept a lot of round off
A
255,000
B
B
510,000
255,000
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The industry demand curve for widgets is given
by Q 240 - 10 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). Nine of the
ten plants have a cost function 16 q2
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The tenth plant (Acme) has an exemption from
environmental laws so that its cost function is
9 q2
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• Assuming initially that only these ten
  firm/plants may produce widgets, determine the
  equilibrium price and quantity of widgets, as
  well as the profits of each firm, including Acme.
  

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Each firm has a MC 2q, so each firms supply is
q P/2. Since there are 10 firms total industry
supply is 10(P/2) 5P. Since supply and demand
must equal 240-10P 5P Solving P 16. Total
quantity demanded is 80, each firm produces 8.
Profits. Each firm has revenue of 144. Nine
firms have costs of 16 82 80, or profits of
64. Acmes profits are 71.
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• 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
  nine plants. 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, including Acme.

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Lets find the minimum of the AC function. AC is
16/q q, and MC 2q. Since MC AC at the
minimum of the AC function, we solve 16/q q
2q, and get q 4. At that level of output MC
AC 8. That will be the price. Total demand is
240-10(8) 160. Since each firm produces 4, there
must be 40 firms. Each firm except Acme will
have zero profits Acme will have profits of 7.
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• Now suppose that Acme Widgets, the owner of the
  first plant, is given a legal monopoly to produce
  widgets, but is also given the right to open as
  many other plants 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.
  (Break on 1 plant)

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LRMC 8 (we see that from the previous
problem). We want to know MR. To get that, note
that the monopolists revenue function is R PQ
(24-0.1Q)Q 24Q 0.1Q2 Thus MR 24 -
0.2Q Since MR MC for a monopolist, we can solve
to get Q 80. It will sell at a price of 16.
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To get profits, remember that revenues are
(80)(16) 1440. Costs are 8 each or 640. So
profits are 800. EXCEPT for the 7 extra profit
Acme makes on its first plant, so profits turn
out to be 807.
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• Now suppose that widgets are subject to a 1 tax.
  What happens to Acme's supply curve?

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• Now suppose that widgets are subject to a 1 tax.
  What happens to Acme's supply curve?

Silly! A monopolist does not have a supply curve
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Homework-Due this Week
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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.
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(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?
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(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?
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(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 dont forget the
fixed cost).
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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.
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(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.
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(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.
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(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 Acmes supply curve.
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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.
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(a) Assuming initially that only these ten
firm/plants may produce widgets, determine the
equilibrium price and quantity of widgets.
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(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.
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(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?
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(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).
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Lectures for This Week

• Agency Problems
• Expense Preference

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• Agency Problems

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• Expense Preference

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Lectures for Next Week

• Price Discrimination-A Primer
• Price Discrimination with Self Identification
• Price Discrimination in Action
• Three Discrimination Problems
• Solution to Three Discrimination Problems

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