94: (20 points) The Thompson Company is considering how to produce a new produll
ID: 376877 • Letter: 9
Question
94: (20 points) The Thompson Company is considering how to produce a new produll production is chosen, it will earn $200,000 when the product sells well, but will lose $180,000 when the product sells bad. If small production is chosen, it will earn $100,000 when the product sells well, but will lose $20,000 when the product sells bad. The manager of Thompson Company estimates that the new product has the same probabilities for selling well and bad. In order to more accurately understand survey, usua survey are "positive" or "negative". Based on past experience, the accuracy of market survey is as follows: P(survey positive l sell well 0.7 and P(survey negative l sell bad)-08. Assuming the manager is risk-neutral, please: Q4.1: If the company does not perform market survey, how to choose? Q4.2: What is the maximal budget for the market survey? 04.3: If the accuracy of market survey is perfect, what is the maximal budget for it? (2 points) Q4.4: Please draw the integrated decision tree of the above problem. surey, usualy t a prie, to get aditional informnation pror to making decisions. The results of the market outlets, the Thompson Company has the option to perform market The results of the (3 points) (10 points) (5 points)Explanation / Answer
Given that there are two states based on market conditions resulting sell well or sell bad.
There are two options to produce new product or go for small production, the payoffs are mentioned as $200,000 (sell well) and loss of $180,00 (sell bad) for new product and in case of small production respective figures are $100,000 and $20,000.
Data is represented in the following table:
Expected gains (Sigma xipi) in case of small production is more than the other option, therefore choose small production.
Given that P(survey positive/ sell well) =.7 so P(survey negative/ sell well) = .3 and P(survey negative/ bad sell)=.8 so P(survey positive/ bad sell) = .2
Prior P(sell well) = .5, P(sell bad)=.5
P(Survey positive) = .7*.5 + .2*.5 =.45 and P(survey negative) = .5*.3 + .8*.5=.55
Therefore P(sell well/survey positive) = .35/.45 and P(sell bad/survey positive) = .10/.45
P( sell bad/ survey negative) = .40/.55 and P(sell well/ survey negative) = .10/.55
Therefore in case report is positive, expected Gain for New Product = 200000*7/9 -180000*2/9=115,555.56
whereas for Small production = 100000*7/9 - 20000*2/9 = 73,333.33
Therefore in case Survey is positive expected gain is $115,555.55 for New PProduct
Without survey maximum gain was for small production having value $40,000 only
Therefore survey may be justified for a cost less than (115,555.55-40,000), say $75555.
Options Sell-well Sell-bad Expected value New Product 200000 -180000 10000 Small Production 100000 -20000 40000 Probability 0.5 0.5Related Questions
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