SMALL WARS JOURNAL
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Guns and Money: A Microeconomic Perspective on
Weapons Buy-Back Programs
by Jed Medlin
Editor’s Note. See also Chad Machiela’s Gun Control in Counterinsurgency for a game theory
perspective on guns and money in counterinsurgency.
Often cited benefits of weapons buy-back programs include getting “guns off the street.”
A Special Operations Team Leader stated that such a June 2011 program in Afghanistan’s
Uruzgan Province would “help improve security, stability and development by getting these
weapons out of insurgents’ hands.”1 The following analysis investigates this claim and evaluates
the ability of weapons buy-back programs to remove weapons in an area by using
microeconomic theory. Further, it suggests that, unless accompanied with security measures that
prevent the free movement of weapons into the targeted area, weapons buy-back initiatives will
likely be ineffective.
Since weapons can be moved into or out of an area in response to changes in in demand,
the effectiveness of weapons buy-back programs is dependent on the elasticity of supply (Es). Es
is the relationship between a change in quantity and a change in price. When applied to weapons
buy-back programs, Es is determined by the ease of transporting weapons into the area affected
by the program. The ability to move weapons freely results in a perfectly elastic, horizontal
supply curve while the complete inability to do so results in a perfectly inelastic, vertical supply
curve. The more inelastic or vertical that the supply curve becomes due to security measures
which make any movement of weapons more difficult, the more successful the weapons buyback program. The graph below depicts how a perfectly elastic supply curve (S) results in an
ineffective weapons buy-back program and represents an initiative that is not coordinated with
any security measures to limit the free flow of weapons into the program area.2
SPC Ashley Bowman, “Small Rewards Weapons Buy Back Program Successful in Deh Rawud.”
Defense Video and Imagery Distribution System, July 2, 2011. Available online at
http://www.dvidshub.net/news/73156/small-rewards-weapons-buy-back-program-successful-dehrawud#.TiogQhrCudg; accessed 22 July 2011.
2
The graphs used in this analysis are not to scale and all numbers are notional. These numbers are used to
assist in understanding and do not suggest actual numbers of any previous or future program. Developing
actual supply and demand equations for particular programs would be necessary in order to provide
precise estimates for any particular program. Regardless, an understanding of microeconomic theory and
Es can assist in planning for effective weapons buy-back programs.
1
© 2011, Small Wars Foundation
August 15, 2011
Perfectly Elastic Supply 3
In the graph above, the notional price of a weapon is $100 which occurs at (a) which is
the intersection of S, the supply curve, and D1, the original demand curve before the buy-back
program. At this price (P*) and before program implementation, the notional quantity of
weapons sold in the market is 1000 or Q*.
The initiation of the buy-back program increases the demand for weapons; therefore, D2
represents demand upon program implementation and the intersection of S and D2 at (b) results
in an increase in quantity sold on the market from Q* to Q1, a notional increase of 250 weapons
supplied. Therefore, a perfectly elastic supply curve (S) that reflects the inability to prevent
weapons from entering into the area results in buy-back programs that merely purchase the
additional supply of weapons that the programs’ increased demand initiated. The supply of
weapons at equilibrium remains the same both before and after the program. As a result, any
weapons buy-back program that is implemented in an area where security forces cannot prevent
the inflow of any additional weapons is ineffective and fails to get any “guns off the street.” Such
programs that are not coordinated with security efforts only increase the supply of guns coming
into the area for the implementing unit to buy. To break even, the implementing unit must buy
this additional supply of weapons. Buy-back programs in an area with perfectly elastic supply
increases the available weapons by an amount that the unit’s buy-back capability cannot exceed,
resulting in an increased quantity of weapons sold on the market which is likely contrary to
security objectives. With perfectly elastic supply, units can buy as many guns as they would like,
but the inability to increase the market price results in the inability to remove any “guns off the
street.”4
3
Tyler Cohen and Alex Tabarrok, Modern Principles: Microeconomics (New York: Worth Publishers,
2010), 63-64.
4
Ibid., 64.
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The graph below shows how a weapons buy-back program that is accompanied with
security measures that reduce the free flow of weapons into an area, causing a more inelastic
supply curve, increases the effectiveness of the program.
More Inelastic Supply 5
In the graph above, a more inelastic supply is represented by a more upright S, or
supply curve. The implementation of the program still causes an increase in demand represented
by the shift of D1 to D2. The more inelastic S causes the equilibrium to shift from point (a) before
the program to point (b) after program implementation causing the price to increase from P* to
P1. Security measures that provide an ability to prevent some weapons from entering the program
area result in only a notional 350 weapons entering the program area (represented by the increase
of supply to Q1) while a notional 550 weapons are purchased by the implementing unit (Q1-Q2).
In this example, coordinating the buy-back program with security measures that prevent some
weapons from entering the program area yields a notional 200 (Q*-Q1) “guns off the street” and
800 (Q2) remaining which corresponds to P1 at point (c). Therefore, the more security measures
initiated to create a more inelastic supply curve, the more efficient the weapons buy-back
program will be in getting “guns off the street.” Regardless, implementing units should be
cautious in using any metrics that equate the number of weapons purchased with an equal
number of “guns off the street.” Unless supply is perfectly inelastic because the implementing
unit is able to prevent the inflow of all weapons into the program area, the number of weapons
purchased will not equal the number of “guns off the street.”
The graph below depicts a perfectly inelastic supply where security forces are able to
completely prevent weapons from entering the program area.
5
Ibid., 67.
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Perfectly Inelastic Supply 6
In the graph above, the vertical or perfectly inelastic supply curve (S) caused by the
ability to prevent weapons from flowing into the program area results in a reduction in the
number of “guns on the street” equal to Q*- Q1. The intersection of S and D1 at point (a)
represents the original price (P*) and quantity of weapons supplied (Q*) before program
initiation. Security measures that prevent all weapons from entering the buy-back area result in a
perfectly inelastic supply curve (S). Once the buy-back program begins, demand increases to D2
and a new equilibrium is reached at point (b) which represents the intersection of S and D2. Due
to effective security measures, the quantity of weapons supplied remains at Q*, but the increased
demand from the buy-back program is able to increase the price from P* to P1. In the diagram
above, this results in a notional 510 weapons bought and taken off the street (Q*-Q1) and a
notional 490 remaining (Q1) which is reflected by point (c) or the intersection of the new price
(P1) and the original, pre-program demand (D1). The ability to achieve a perfectly inelastic
supply curve (S) by the implementation of effective security measures which prevent all
weapons from entering the program area results in weapons purchased by the program actually
translating to an equal number of “guns off the street.”
In conclusion, weapons buy-back programs have the potential to be inefficient if they are
not accompanied by security measures that reduce the ability of outsiders to bring weapons into
the program area. Effective security measures that are implemented in conjunction with the
program to disrupt the free flow of weapons into the area result in a more inelastic supply (S) and
a more successful weapons buy-back program. Therefore, a weapons buy-back program is not a
stand-alone initiative and must be accompanied with supporting efforts aimed at achieving as
6
Ibid., 66.
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close to a perfectly inelastic or vertical supply curve (S) as possible to be most effective. Areas
where this is not feasible are likely to host inefficient programs that buy weapons, but do not
actually get an equal number, or any “guns off the street” in the targeted area. If coordinated
security measures were implemented with the program in Uruzgan, then perhaps the Special
Operations Team Leader was correct. If not, he likely bought weapons, but probably did not
reduce and perhaps even increased the quantity of weapons flowing into the buy-back area.
Jed Medlin holds a B.S. in Political Science from the U.S. Military Academy at West Point, a
M.A. in Management & Leadership from Webster University, and both a Master of International
Studies and a Graduate Certificate in Public Policy from North Carolina State University. His
research interests include Democratization and Consolidation, Development, and Political
Economy.
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