# probability maximize expected profit decision model

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The BAC Import Company has decided to market Z-games in the USA. The game, an electronic device the size of a mobile phone, has been a great success in Japan. However, sales of the game in the USA are not expected to last for more than a year; after this period the novelty of the game is likely to have subsided. For simplicity, potential sales levels are categorized as being either high or low. BAC has an initial decision on what price it should charge for the game and two prices are being considered: a low price (\$4) and a high price (\$8). The table below shows the estimated profits that would be achieved for each price and sales level.

 Sales Level (Profits) High Low Low price High price \$2 m \$4 m -\$1m \$1m

If the low price is chosen it is thought that there is only a 0.1 probability that a competitor will enter the market. If there is no competitor then it is thought that the chances of high sales will be 0.9. However, if there is competition then BAC will have to decide whether to respond by either advertising on television or lowering the price even further. Advertising would lower profits by \$1m, but would give an estimated 0.4 probability of high sales. Lowering the price would reduce profits by \$2m, but would give a 0.7 probability of high sales. (Only one of these two responses to competition would be used).

If the high price is chosen then the probability of competition is estimated to be 0.8. In the absence of competition it is thought that there would be a 0.5 probability of high sales. If there is competition then either advertising on television or lowering the price would be carried out, as above. These would have estimated probabilities of generating high sales of 0.1 and 0.3, respectively. (These two responses would have the same effect on profits as before.)

(a)Assuming that BACâ€™s objective is to maximize expected profit, identify the policy that the company should adopt.

(b)Determine how sensitive your recommended policy is to changes in the estimated probability of competition when a low price is initially chosen.

(c)Discuss whether the use of utilities, rather than profits, would have improved your decision model.