We can demonstrate this issue mathematically numerically using a table and

# We can demonstrate this issue mathematically

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We can demonstrate this issue mathematically, numerically (using a table), and graphically.
Recall from Figure “Demand for Pure Public Goods” that the marginal social benefit for a pure public good is the sum of the individual marginal benefits. That is: MSB = MB. Efficient output is therefore: MSB = MB = MSC.
Suppose we have three people who are discussing the issue of hiring security guards. Note that each person places a different value on the levels of security. 26
Number of Security Guards per Week 1 2 3 4 MB A \$300 \$250 \$200 \$150 MB B \$250 \$200 \$150 \$100 MB C \$200 \$150 \$100 \$50 MB \$750 \$600 \$450 \$300 If the cost of security guards is \$450 per week, then no individual will hire even one guard, even though to group one is worth \$750. The group should hire three. If they pay their marginal benefit, then three guards are hired. Person A pays \$600 (\$200 per guard), person B pays \$450 (\$150 per guard) and person C pay \$300 (\$100 per guard). 27
28 Security Guards per Week E 100 200 300 400 500 600 700 800 Marginal Benefit (Dollars) 0 1 2 3 4 5 MB A MB B MB C D A = MB A = MSB MC = AC = MSB
National Defense is the classic pure public good. Defense spending as a percentage of GDP Fell from above 8 percent during the Vietnam era to just above 5 percent in the late 1970s; Grew during the Reagan defense buildup of the 1980s; Fell below 5 percent with the demise of the Soviet Union. 29
30 1966 11 10 9 8 7 6 5 1971 1976 1981 1987 1999 1993 Year Percentage of GDP
The amount each person contributes, ti, depends on their individual desires for the public good. The sum of the contributions equals the total cost of the public good. StiQ* = MC(Q*) = AC(Q*) Sti = MC = AC All individuals agree to pay their share. 31
Freeriding occurs when people are not honest in stating their Marginal Benefit because if they understate it, they can get a slightly reduced level of the public good while paying nothing for it. 32
Anonymity: If everyone knows who contributes, there can be powerful social stigmas applied to shirkers. Large numbers of people: It’s easier to determine the shirkers in a small group and the punishment is more profound when people close to you shun you. 33
Under the premise that defeating Iraq in the Gulf War was a public good to be consumed by the industrialized economies and Arab nations, each nation was expected to contribute. The U.S. and UK contributed the bulk of the fighting forces. Saudi Arabia, Kuwait, the UAE, Japan, and Germany voluntarily paid \$54 billion of the estimated \$61 billion cost. 34

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