Week 14 Managerial Economics. Order of Business Homework Assigned Lectures Other Material Lectures for Next Week.

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


50.0 588.2 5.9 69.2 49.2

# Firms Q P R Profit


# Firms Q P R Profit

93.0 593.6 3.2 20.4 0.494.0 593.7 3.2 19.9 -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.


ACMC

Min occurs where MC = AC, so

6q = 27/q +3q q =3 &AC = 18

Equilibrium price with entry


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.


LRMC = 18

420

D

210

MR


Q = 210 P = 39

Widgets at each plant = 3, N = 70

= (39)(210) – 18(210) = 4410

As to the supply curve….

Problem 3The 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

ACMC

Min occurs where MC = AC, so 2q = 25/q +q q =5 &AC = 10


P = 10, Q = 650-8(10) = 570

Each firm produces 5, so N = 114

= 0

(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

(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


(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.

Homework-Due this Week

Pashigian, Chapter 11, Exercise 3



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

Week 14 Managerial Economics. Order of Business Homework Assigned Lectures Other Material Lectures for Next Week.

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