Practice Questions

1
Practice Questions

• Question 1 (Ch. 8, Q5 in Samuelson Marks)
• A firm faces uncertain revenues and uncertain
  costs. Its revenues may be 120,000, 160,000,
  or 175,000 with probabilities 0.2, 0.3, and 0.5,
  respectively.
• Its costs are 150,000 or 170,000 with chances
  0.6 and 0.4, respectively.
• What is the expected profit?
• How much would the firm pay for perfect
  information about its costs?

2
Practice Questions

• Question 1 (Ch. 8, Q5 in Samuelson Marks)
• Expected profit 1,500

3
Practice Questions

• Question 1 (Ch. 8, Q5 in Samuelson Marks)
• Set up the Decision Tree assuming the information
  costs 0
• Expected Value 5.7K
• Added value of information 5.7K - 1.5K
  4.2K

4
Practice Questions

• Question 2 (Ch. 8, Q3 in Samuelson Marks)
• For five years, a firm has successfully marketed
  a package of multitask software. Recently, sales
  have begun to slip because the software is
  incompatible with a number of popular application
  programs. Thus, future profits are uncertain.
  In the softwares present form, the firms
  managers envision three possible five-year
  forecasts Maintaining current profits in the
  neighborhood of 2 million, a slip in profits to
  0.5 million, or the onset of losses to the tune
  of -1 million. The respective probabilities of
  these outcomes are .2, .5, and .3
• An alternative strategy is to develop an open
  or compatible version of the software. This will
  allow the firm to maintain its market position,
  but the effort will be costly. Depending on how
  costly, the firm envisions four possible profit
  outcomes 1.5 million, 1.1 million, 0.8
  million, and 0.6 million, with each outcome
  considered equally likely.
• Which course of action produces greater expected
  profit?

5
Practice Questions

• Question 2 (Ch. 8, Q3 in Samuelson Marks)
• The Alternate Strategy produces greater expected
  profits of 1M.

6
Practice Questions

• Question 3 (Ch. 2, Q6 in Samuelson Marks)
• A television station is considering the sale of
  promotional videos. It can have the videos
  produced by one of two suppliers. Supplier A
  will charge the station a setup fee of 1,200
  plus 2 for each cassette supplier B has no
  setup fee and will charge 4 per cassette. The
  station estimates its demand for the cassettes
  will be given by Q 1,600 200P, where P is the
  price in dollars and Q is the number of
  cassettes.
• If the station plans to give away the cassettes,
  how many cassettes should it order? From which
  supplier?
• Suppose the station seeks to maximize its profits
  from sales of the cassettes. What price should
  it charge? How many cassettes should it order
  from which supplier?

7
Practice Questions

• Question 3 (Ch. 2, Q6 in Samuelson Marks)
• If the station plans to give away the cassettes,
  how many cassettes should it order? From which
  supplier?
• Try to minimize costs, since there are no
  revenues. Which supplier is less expensive? It
  depends Find when the cost of the suppliers is
  equal
• Cost of Supplier A Cost of Supplier B
• 1,200 2Q 0 4Q
• 2Q 1,200
• Q 600
• If Q lt 600, choose Supplier B
• If Q gt 600, choose Suppler A
• If Q 600, indifferent between suppliers

8
Practice Questions

• Question 3 (Ch. 2, Q6 in Samuelson Marks)
• Suppose the station seeks to maximize its profits
  from sales of the cassettes. What price should
  it charge? How many cassettes should it order
  from which supplier?
• Find profit maximizing in price and quantity for
  both MC functions
• Solve for inverse demand P 8 0.005Q
• Revenue 8Q 0.005Q2
• MR 8 0.01Q MCA 2 MCB 4

For MCA 2 8 0.01Q 2 0.01Q 6 Q
600 Since MCA applies when Q 600, this is a
possible solution P 8 (1/200)600 8 3 P
5
For MCB 4 8 0.01Q 4 0.01Q 4 Q
400 Since MCB applies when Q 400, this is a
possible solution P 8 (1/200)400 8 2 P
6
9
Practice Questions

• Question 3 (Ch. 2, Q6 in Samuelson Marks)
• Suppose the station seeks to maximize its profits
  from sales of the cassettes. What price should
  it charge? How many cassettes should it order
  from which supplier?

For Supplier A Q 600, P 5 p (P)(Q)
(1200 2Q) p (5)(600) (1200 2x600) p
3,000 2,400 p 600
For Supplier B Q 400, P 6 p (P)(Q)
(4Q) p (6)(400) (4x400) p 2,400 1,600 p
800

• So, the station should order cassettes from
  supplier B since the profits are highest, and
  sell the cassettes at a price of 6.

10
Practice Questions

• Question 4 (Ch. 2, Q12 in Samuelson Marks)
• As the exclusive carrier on a local air route, a
  regional airline must determine the number of
  flights it will provide per week and the fare it
  will charge. Taking into account operating and
  fuel costs, airport charges, and so on, the
  estimated cost per flight is 2,000. It expects
  to fly full flights (100 passengers), so its
  marginal cost on a per passenger basis is 20.
  Finally, the airlines estimated demand curve is
  P 120 0.1Q, where P is the fare in dollars
  and Q is the number of passengers per week.
• What is the airlines profit-maximizing fare? How
  many passengers does it carry per week, using how
  many flights? What is its weekly profit?

11
Practice Questions

• Question 4 (Ch. 2, Q12 in Samuelson Marks)
• MC 20
• P 120 0.1Q
• Revenue (120 0.1Q)Q 120Q 0.1Q2
• MR 120 2 x (0.1Q) 120 0.2Q
• MC MR
• 20 120 0.2Q
• Q 500
• P 120 0.1(500) 120 50
• P 70
• Profit (P)(Q) (20Q)
• Profit (70 x 500) (20 x 500)
• Profit 35,000 10,000
• Profit 25,000
• The profit maximizing fare is 70. The airline
  will carry 500 passengers per week using 5
  flights, for a weekly profit of 25,000.