The average demand for a vaccine for a newly discovered disease is 1 million dos

Question

The average demand for a vaccine for a newly discovered disease is 1 million doses, with a standard deviation of 1 million (nobody knows if there will be an epidemic). Each dose costs $200 to produce. If there is not enough vaccine for all the people who want to be vaccinated, the estimated gross cost to society is $300 per person (i.e., this is the weighted average cost not considering the cost of the vaccine - at one extreme a person who isn't vaccinated may not even get sick while at the other extreme the person may die). What is the socially-optimal number of doses to produce? Assume that when the epidemic hits, it is too late to produce more, and left-over doses are worthless. Hint: think of this just as you would if you were a retailer buying a product at some cost, then selling it at some higher price, without any salvage value.

   569,000

   1,253,000

   1,566,000

   747,000

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