This is expected payoff for selling coffee without perfect information, calculated as ($1,900 × .40) + ($2,000 × .60).
This is the profit for selling coffee in hot weather ($1,900) plus the profit for selling coffee in cold weather ($2,000). This payoff is not possible, as the beverage stand can obtain only one profit payoff. Furthermore, the maximum profit the beverage stand can obtain is $2,500. That would occur if the weather is hot and it sells soft drinks.
This is the expected payoff for selling soft drinks when the weather is cold multiplied by the probability of cold weather of .60, plus the expected payoff for selling coffee when the weather is hot multiplied by the probability of hot weather of .40. However, if the vendor has perfect information, it would not sell soft drinks on a cold day, nor would it sell coffee on a hot day. It would do just the opposite.
With perfect information about whether the weather will be hot or cold, the company would be able to choose in advance the correct drink to supply for each of the types of weather. If the beverage stand knew in advance that the weather would be hot, it would supply soft drinks and make $2,500. If it knew in advance that the weather would be cold, it would supply coffee and make $2,000. Therefore, given that for each type of weather, the company will choose the best supply alternative, the expected payoff is the weighted average of the best payoff that can be achieved on a cold day and the best payoff that can be achieved on a hot day, with the probabilities of each weather condition as the weights. Since the probability of cold weather on a given day at this time is 60%, we know that the probability of hot weather is 40%. So the beverage stand's expected profit if it has perfect information is ($2,000 × .6) + ($2,500 × .4), which is $2,200.
|
