The Centers for Disease Control and Prevention (CDC) recommended against vaccinating the whole population against the smallpox virus because the vaccination has undesirable, and sometimes fatal, side effects. Suppose the accompanying table gives the data that are available about the effects of a smallpox vaccination program.

a. Calculate the marginal benefit (in terms of lives saved) and the marginal cost (in terms of lives lost) of each 10% increment of smallpox vaccination. Calculate the net increase in human lives for each 10% increment in population vaccinated.
b. Using marginal analysis, determine the optimal percentage of the population that should be vaccinated.

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Percent of population vaccinated Deaths due to Deaths due to smallpox vaciation side effects 0% 10 20 30 40 50 60 200 180 160 140 120 100 80 0 4 10 18 50 74