A state highway safety agency must allocate its budget for the next fiscal year. A total funding of $32 million has been granted for reducing fatalities and property damage due to automobile accidents. However, detailed funding decisions concerning specific programs remain to be made. The table lists pertinent data on four major programs.
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Expected Fatalities
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Expected Reduction
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Prevented per
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in Property Damage
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Upper Limit
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Millions of
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per Millions of
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Project on Expenditures
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Dollars Expended
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Dollars Expended
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Seat-belt
advertising $14,000,000 1.0 $0 Research in
improved
highway safety 12,000,000 .2 3,200,000 Research in
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improved auto
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design
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9,000,000
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.5
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1,500,000
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Dollars spent
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lobbying for
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tougher drunk-
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driving penalties
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16,000,000
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.75
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200,000
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To solve its budget problem, the council still must formulate a trade- off between lives saved and property damage prevented. The council is aware that a certain government agency employed $4.8 million as the value of a life saved. To make a start on its decision, members of the council have agreed to use this figure, enabling it to put a dollar value on the total benefits (from lives and property saved) of a given expenditure on each program.
a. Find the budget allocation that generates the greatest total benefits. (Hint: Where should the first dollars be spent, the next dollars, and so on?)
b. Suppose the council increases the value of a life to $7.2 million. How does the value placed on a life influence the council's budget allocation? Explain briefly.