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 software’s present form, the firm’s 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 < 600, choose Supplier B • If Q > 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 π = (P*)(Q*) – (1200 + 2Q*) π = (5)(600) – (1200 + 2x600) π = 3,000 – 2,400 π = 600 For Supplier B: Q* = 400, P* = 6 π = (P*)(Q*) – (4Q*) π = (6)(400) – (4x400) π = 2,400 – 1,600 π = 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 airline’s 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.