Question

A toy company is making a decision about ordering a new toy to sell during the holiday season. They are deciding whether or not to undertake market research to evaluate the potential market for the product. They have only one opportunity to order the product for this season and are committed to making either a small order or a large order.
If they choose not to undertake the research, they can make one of two choices: place a large order or place a small order. If they place an order the probability that demand is high is 50% and that demand is low is 50%. If they undertake the market research, the chance that they will get favourable results is 45% and unfavourable results is 55%. If they get unfavourable results, the probability of high demand is 25% and of low demand is 75%. If they get favourable results, the probability of high demand is 80% and of low demand is 20%. The cost of doing the research is $10,000.
If they place a small order and demand is low the net return is $10,000. If they place a small order and demand is high the net return is $100,000. If they place a large order and demand is low the return is $-50,000. If they place a large order and demand is high the net return is $200,000.
What are the right decisions for the firm to make relative to the market research and the size of the order?

Answer 1

The decision tree for the given situation is as follows:

(the payoff’s is in $’000)

(the payoff of -10 is assigned to decision of conducting research, since it cost $10,000 for conducting research)

6 200 7 wlo reserach 2 8 100 Small 5 Event 4 9 10 16 200 12 Low 17 Favorable 10 18 100 13 Low 19 10 conduct reserach 3 20 20O 10 Low 21 Unfavorable 22 100 15 Low 23 10

By conducting backward calculation, the expected payoffs for decision and event nodes is as follows:

Hi 6 200 EMV 200 Low EMV 75 wlo reserach ENAV 50 Hi EMV 75 8 100 Small EM-100 Event 4 EMV-55 9 10 (0.5)(100)+(0.5)(10) EMV-10 16 200 12 EMV-200 Low EMV-75.38 - Max(75, 75 38) EM-150 Favorable 10 EMV-50 EMV-150 18 100 Max(150, 82) Small EMV-100 Low ENAV弌2 19 10 conduct reserach EMV 10 EMV-85.38 20 200 EMV-85.38 -10 ENAV 75.38 EMV 200 Low (.75 EMV-12.5 21 Unfavorable EMV -50 EMV-32.5 22 100 Small 15 EMV-100 Low (.75 EMV-32.5 23 10 EMV-10

The EMV is shown in Blue letters

The sample calculation of event and decision nodes is shown in red letters.

The blue lines represent best decisions under given conditions.

If research is not be conducted, placing large order maximizes the EMV of $75,000

As the EMV of the conducting research is more than not conducting research, the best decision is to conduct the research. If research is conducted and the result is favorable, the best decision is to place large order. If research is conducted and the result is unfavorable, the best decision is to place small order.

EMV of decision is 75,380