LIBRARY OF THE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN «T\ol>74- -579 Cop. 2. The person charging this material is re- sponsible for its return to the library from which it was withdrawn on or before the Latest Date stamped below. Theft, mutilation, and underlining of books are reasons for disciplinary action and may result in dismissal from the University. To renew call Telephone Center, 333-8400 UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN DEC 2 9 19d0 m «0I L161— O-1096 Digitized by the Internet Archive in 2013 http://archive.org/details/economicsofmilit378davi Jfbr ' / to*-^- 7 RERPORT NO. 378 THE ECONOMICS OF MILITARY ALLIANCES by CARL WAYNE DAVIS January 15, 1970 NOV 91972 «' u R8ANA-CHAMPAtGN DEPARTMENT OF COMPUTE.. UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN URBANA, ILLINOIS REPORT NO. 378 THE ECONOMICS OF MILITARY ALLIANCES by CARL WAYNE DAVIS January 15, 1970 Department of Computer Science University of Illinois Urbana, Illinois 6l801 This work was submitted in partial fulfillment of the Master of Science degree in Computer Science. TABLE OF CONTENTS Page INTRODUCTION 1 I. ECONOMIC THEORY OF ALLIANCES - INDEPENDENT PROGRAMS 3 A. Indifference Curves and Related Concepts 3 B. Elasticity 7 C. Reaction Curves 10 D. Disproportionality 12 II. ECONOMIC THEORY OF ALLIANCES - MARGINAL COST-SHARING 17 A. Infrastructure Funding 17 B. Operating Accounts 22 C. Consortium Arrangements 23 III. SUMMARY 2k LIST OF REFERENCES 25 APPENDIX 26 in LIST OF FIGURES Figure Page 1. Indifference schedule and indifference map h 2. Indifference map for defense 6 3. Elasticity of goods 9 h. Nation i's indifference map 11 5. Reaction curves 13 6. Evaluation curves for two countries 1^ 7. Distribution of infrastructure construction by country (Iceland and Luxembourg omitted) 21 IV INTRODUCTION Today, many Americans are expressing dissatisfaction at United States participation in international organizations. This paper is concerned with NATO to which the United States contributes a substantial military force. The main complaint is that the United States is bearing a dispropor- tionate share of the burden because the smaller nations contribute smaller percentages of their national incomes to defense. The stated purpose of defense alliances is to deter aggression by a common enemy. Defense is a collective good in economic theory since it satisfies the following two properties: 1. If the common goal is achieved everyone who shares this goal automatically benefits, or non-purchasers cannot feasibly be kept from consuming the goods. 2. If the good is available to any one entity in a group, it is or can be made available to the other members of the group at little or no marginal cost. A two-pronged analysis developed by M. Olson, Jr. and R. Zeckhauser [2] will be used in this paper. The two parts are described in Chapters I and II, respectively. Part 1. In independent programs, the more affluent nations will bear a disproportionately large share of the total burden. (National military budgets are good examples of independent programs.) 2 Part 2. Marginal cost sharing will tend to work against disproportion in "burden sharing. (Marginal cost sharing here simply means common funding of proposed additional programs; it involves a measure of negotiated agree- ment among the partners to share the costs of a community endeavor. ) Data in the appendix clearly explain the problem in part 1 and part 2. I. ECONOMIC THEORY OF ALLIANCES - INDEPENDENT PROGRAMS A. Indifference Curves and Related Concepts A nation deciding its precise contribution to an alliance must consider the value it places on collective defense to the non-defense goods it must sacrifice. An indifference schedule will be used to indicate various com- binations of defense and non-defense goods which will yield a nation the same total satisfaction. This schedule is then plotted as an indifference map, the dollar value of non-defense goods on the vertical axis and the value of defense on the horizontal axis. The curve connecting the various points is known as an indifference curve . The curve shows nothing about the absolute amounts of satisfaction obtained but merely indicates the various combinations which will yield equal satisfaction. Indifference curves slope downward and measure the marginal rate of substitution between defense and non-defense goods. In other words, for a particular indifference curve plotted in the x-y plane, the ratio -Ax/ Ay, or its limit -l/slope of tangent, is called the marginal rate of substitution (MRS) of x for y. The same level of satisfaction is maintained as we move along the curve if every unit of y is replaced by MRS units of x (see Figure l). Assuming the "Principle of Diminishing Marginal Rate of Substitution" applies, indifference curves are convex to the point of origin, so that as additional units of defense are acquired, the MRS of non-defense goods for defense increases. For every nation, there is an indifference map for defense and non- defense goods showing a family of indifference curves, where different 3 INDIFFERENCE SCHEDULE NON-DEFENSE DEFENSE (Dollars in millions) (Dollars in millions) 100 = National Income 95 6 90 15 80 50 75 95 50 595 MRS (Dollars in millions) 0.83 0.55 0.23 0.11 0.05 0.00 $ of Non-Defense Goods 100 95 $ of Defense INDIFFERENCE MAP Figure 1. Indifference schedule and indifference map. 5 curves indicate different levels of satisfaction given by combinations that lie on separate indifference curves. A schedule only shows that combinations on one curve yield more or less satisfaction than combinations on another. If a given combination on one curve contains more of both defense and non-defense goods than any combination on another curve, the curve containing the first combination gives more satisfaction. Therefore, the indifference curve that lies to the northeast of another indifference curve will represent greater satisfaction. In Figure 2, curve C shows that the nation is indifferent to any point on it, for example P and Q. At P all of the national income is spent on non-defense goods; whereas at Q, only an amount E is spent on non-defense goods and the balance is applied to defense. Similarly, points R and S lie on curve C which is preferred to C if feasible. Note that if R is attained some alliance is making a contribution of D units of defense. Likewise D and even D might require side payments to be obtainable. A certain fixed amount of money to be spent on goods A and B may be spent all on A, all on B, or any feasible combination of A and B. These alternatives will lie on a straight line in the A-B plane which depends only on the fixed amount of money and is called a budget restraint line . For a fixed national income there is by convexity one indifference curve tangent to the budget restraint line at one point. In order to maximize satisfaction, the highest indifference curve attainable with the above fixed national income must be reached. The highest indifference curve which can be reached is the one to which the budget restraint line is tangent. Any other possible combination of A and B would either be on a lower indifference curve and thus yield less satisfaction, or would be unattainable with this amount of national income. '1 2 Figure 2. Indifference map for defense. 7 As national income changes, the budget restraint line moves and for each position of the budget restraint line there is a uniquely best indifference curve and therefore a unique point of tangency. The locus of these tangency points is called the income-consumption line and is assumed to be unbroken. B. Elasticity If the income-consumption line is plotted on log paper (both axes), its slope at a point is called income elasticity and represents exactly the limiting case of percentage change in defense demanded divided by the percentage change in national income. For a given class of goods we may plot the amount spent on this class of goods against total income. Around a certain income level we compare small absolute and relative changes in income with the corresponding changes in the amount spent on that good. If increased income causes decreased expenditure on the goods, they are called inferior goods . If increased income causes a higher absolute increase in expenditures on the goods, they are called superior goods . If neither of the above holds, then only part of an absolute increase in income is applied to buy more of the class of goods. In this case the percentage increase in expenditures for the class of goods may be more or less than the percentage change in total income and we call these elastic and inelastic goods respectively. Table 1 and Figure 3 show the ranges and income-consumption lines for these classes of goods respectively. Figure k is provided as an example. If nation i is not a member of an alliance then its budget restraint line B is shown tangent to an indif- ference curve at (D , E ). This means that acting alone, nation i must pay PNI-E for an amount D of defense and these two quantities are equal. CLASS INCOME ELASTICITY CHARACTERISTIC Inferior E < Expenditure on the good decreases or is unchanged as income increases. Inelastic < E < 1 Expenditure on the good increases, but by a smaller percentage than income increases. Elastic 1 < E < Y /S ( Expenditure on the good increases by a percentage that is as great or greater than the percentage by which income increases, but by a smaller absolute amount, Superior E > Y /S Expenditure on the good increases faster than income increases. Note S is the expenditure on the good when income is Y . E = dx/x dy/y Table 1. Elasticity range. y. ELASTIC INELASTIC b a x INFERIOR SUPERIOR Figure 3. Elasticity of goods. 10 If nation i becomes a member c f an alliance and if it evaluates the cost of the contributions of the other members as M, then its budget re- straint line is given by B and its share of the cost is D -M, which in the example pictured is less than D . By joining the alliance, it decreases its defense expenditures. The amount M, the actual contribution of its allies, can be found by the following iterative procedure: Each country first assumes that its allies contribute to the alliance the same amount as they would spend alone. Each country then recomputes its own contribution via a budget restraint line. Each country then tells its partners its new tentative alliance contribution and each ally revises its budget restraint line and again recomputes its contribution. This process converges to the actual contributions each country will pay when in equilibrium. C. Reaction Curves Another method is to plot a nation's reaction curve which depicts a nation's contribution when the other members contribute given amounts. The intersection of the reaction curves is the point of equilibrium. The follow- ing shows this technique: Consider a two nation alliance, A and B, where A's defense expenditures when alone is Y and B's is X. In Figure 5, A's indifference map and budget restraint lines give its defense expenditures when it considers the amount the other member is spending on defense. If B spent nothing on defense then A would spend y on defense; if B spent v on defense then A would spend u on defense; and if B spent w on defense then A would spend o on defense. B would determine his reaction curve in a similar manner. 11 PNI+N PNI+M PNI PNI = Present National Income Defense in dollars Figure k. Nation i's indifference map. 12 The intersection of the reaction curves at point (s, t) gives the expenditures of A and B of s and t respectively when the nations are in equilibrium. If the reaction curves do not intersect, then the nation with the higher reaction curve would pay for all of the defense. D. Disproportionality It will now be shown why more affluent nations bear a disproportionate amount of the common burden. To determine how the burden of costs will be shared, consider first the valuation of defense neglecting the relation between defense and non-defense goods. This is done in Figure 6, which shows the evaluation curves that two nations, big A and little a_, have for common defense. Nation A has a higher, steeper evaluation curve because it places a higher absolute value on defense than nation a. The cost curve, CC, shows the cost of providing defense to each nation, assuming that the cost of defense for each nation is the same and linear. In isolation, nation A would buy B amount of defense and nation a_ L, since at these levels of defense their respective evaluation curves are parallel to their cost curves. If the two nations maintained these levels, the level of defense for the alliance would be L+B. But since each nation values a marginal unit of defense at less than its marginal cost, nation A will start reducing its defense spending when the sum of defense supplied by the two nations equals B. But when any amount greater than L is available, nation a_ will start reducing its defense expenditures. Therefore, the two nations will be in equilibrium only when nation A provides B amount of defense and nation a_ provides no defense. In such a case, it may be said that nation A provides a disproportionate share of the costs. 13 A Expenditures t x w Figure 5. Reaction curves. 11* Figure 6. Evaluation curves for two countries. 15 Now, considering the relation between non-defense goods and defense, the disproportionality in the sharing of burdens will be less extreme. Consider the above two nations where nation A and nation a are identical in every respect except that nation A's gross national product, GNP, is k times that of nation a; per capita and individual tastes are the same in both nations; the population of nation A is k times that of nation a. Assume that at present nation A is providing k times as much defense as nation a just as proportionality would require. In equilibrium the marginal rate of substitution of money for defense must equal the marginal cost of each nation, MRS = MRS = MC, assuming the cost of defense is the same for both nations and linear. But since both nations enjoy the same amount of defense and nation A provides k times as much, its MRS is k times MRS . To show that nation A will provide a disproportionate share of the cL common burden in equilibrium, the following is a mathematical proof: Let x' be the amount of money spent on defense by a nation not in an alliance, d be the amount of defense obtained with x' , D be the amount of defense enjoyed by a member in an alliance, x be the contribution of a member in an alliance, so that x! = kx' where k > 1 ,t x l = kx 1 a d A = kd a MRS a x' - X a a D-d a MRS X k~ X A D-d, In equilibrium: a A 16 Cross-multiplying and rearranging X a (D - d A ) ^ (D - d a ) ^a CD - d A ) X A (D - d ) (D - d ) " (D - d ) a a a substituting for x' and d and simplifying X A = D - kd a D-d x + kx' - x' cL a. a* D - kd D-d X A = r D - d (1 - k)d a a D - d D-d a a (x - x' ) + kx' cl cl EL x = x - x' + kx' + .A. cl cL ct ' 1 - k)d a Let C = (1 - k)d^ c D-d D-d x - x' ,X - X' Since a member's expenditures decrease when it joins an alliance, x - x' will be negative and 1 - k will be negative since k > 1. Therefore a a C > 0. x A = x + x' (k - 1) + C A a a Since x* > x then a a x + x '(k - l) > x + (k - l)x = kx £13, 3, a Ql Therefore x A > kx . A a In words, the contribution of nation A, x , is greater than k times the contribution of nation a, x . ' a [3] II. ECONOMIC THEORY OF ALLIANCES - MARGINAL COST-SHARING 1 JJ Common funding in NATO may be divided into three parts: infrastructure, operating accounts, and consortium arrangements. These constitute from our viewpoint a small hut interesting part of NATO funding in as much as expenditures are shared equitably. A. Infrastructure Funding Infrastructure funds are capital investments for fixed military facil- ities. These funds are the largest and most important category and its name was derived from a French term meaning the embankments, bridges, tunnels, and other structures supporting the bed of a railroad. Table 2 shows the commitments denoted slices in NATO for infrastructure funds since NATO's birth. The main thing to note is that the principle of cost sharing was used by the five Brussels Treaty powers before the principle was adopted by the larger alliance. There are two main reasons why infrastructure funds were confined to fixed facilities such as airfields, pipelines, and missile sites. First, if infrastructure funds could be used to buy mobile equipment, major con- tributors like the United States preferred to build, buy, and operate these items themselves instead of contributing to a common pool. Second, major contributing nations wanted to make sure that the installations they financed were employed solely for the purposes intended; mobile equipment, such as aircraft and missiles, could be too easily diverted to other uses. Several exceptions have been granted to this general rule, however, including mobile war headquarters and tactical airfield equipment. 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CO VO l/N -J- t- rH -3- J" vo CM • • • • • oo 1 1 Lf> 1 1 1 o oo 1 1 1 t— 1 rH 1 1 -=r 1 bO o H CO c H 1 ■g 1 CVI 1 O bO •H 1 CO CD -P cd p en 3 cd ^ CD § CD 43 rH >, bD >> Id T3 •H -o cd O O >> cd P CD CD CD bO a) g S i OJ H CD 43 t P M P p H § 2 CD a B •P U J i •H •H £ CD h & rH p CD o o y (3 d o Q ft o H j Si a ft Eh P P o •H P cd b0| •H ■P CO > S3 cd cd > M -P •rH H -H M 43 H X O O CD 43 P cd o En >>< ■ s 03 o •H (1) *H ft CO -P co CD cd 43 co U bD| o r, ft cd cd 43 P -p cd co CD O O Cd in H ft ft CD Ti U CD rH •H Pi g a o co ■H cd 1 o ft ■a d o •H cd P •i i o •H I ' Sh a ;<> ft co CO CD u bO S3 O O 43 P On CO co S3 o •H P cd rH CD P, O -P (3 CD 1 rH o ft bO S3 ■H rH cd 43 co -P CO o o -p o d rH P CO cd ^ ft S3 •H 43 ft CM CD H ■3 EH 19 The country in which the facility is located is called the "host" country and the country occupying the facility is called the "user." The host country is responsible for maintenance and operation of a facility, but it is free to make contractual arrangements with the user country or countries. Three basic factors working in favor of infrastructure funding are: 1. the military value of the installation; 2. the economic benefits to the host country and to the country that manufactures the equipment; 3. the advantages to the user country. The major factor working against it is the fact that each country has to pay some part of the cost of every project. This is keenly felt by nations such as Canada, the United Kingdom, and the United States who receive little or no home construction and is felt somewhat by nations like the Netherlands, Denmark, and Belguim, which come out less than even. Military necessity underlies the entire process since the infrastructure was established to provide things needed by the military authorities. No longer can any nation go its own way by establishing its own communications channels, warning network, or air-weapon control system. Unless all nations support a project, it either will not operate or will have gaps that mar its performance. The economic appeal is probably the most influential factor to host countries. Construction activity increases employment and demand for local goods and if the facility is occupied by foreign users, there will be a continuing external stimulus to the local economy. Some installations, like telephone lines and airfields, will have a dual military and commercial use. 20 Although the host country is : esponsible for making certain contribu- tions that reduce its profits, the net advantage of being host to infra- structure projects can be seen by the effort each country makes to get projects assigned to its territory. Norway was the only exception when it was supposed to man the early warning stations in its territory. A manning compromise was arranged, however. Figure 7 shows how infrastructure construction has been distributed among the NATO members. It should be noted that Germany's returns in excess of contributions is misleading because of unrecorded monies spent before Germany entered the alliance. These were occupation funds taken from the local economy by occupying powers to build facilities they needed. Germany now contributes more than twenty percent of the input. Under the rule of unanimity, one might expect that small nations, each holding a veto power, would sell their consent dearly and receive payments out of proportion to their contributions. This does not appear to have happened, at least not across the board. Norway, Greece, and Turkey, being in a militarily exposed position, could be expected to receive a great deal of aid from the other members who would want to help fortify their borders and install early warning radar sites, short range missiles, and emergency airfields. Italy and Denmark, both somewhat exposed, do not appear to have exploited their bargaining position either. The advantage of the infrastructure to the user is sometimes overlooked, especially by the United States. The fact that the United States has been the most extensive user has been a key factor in American acceptance and support of the infrastructure system. It has been argued that the Europeans should provide the facilities since the United States is there at European 21 ^5. o -3 on o on o C\J LTN ■65. O LTN hssssK wnKwwK-wn n 1 \ \ \ i , \\ \k\ v\K \~X5 -P W o & Tl en 0) •H f> U •H -P a; a o o a) o Fh -p -P a a Pn Ph n J one NV\\\\\ ^ s JS c£ ess KWvW £ \\w ww \\ \ £S K\\\\ \> None k\ W\NV ^ ■65. ■&S. V5. Ts^. Tss. ^5. ■65. feS. O LTN O LTN O LTN O LT\ -3" on on CVI CVJ H H ■A 4> c^ w o e ^ # <* .V ,# 5>-' ^ TV ^ -v ^ ^ e „>* Figure 7. Distribution of infrastructure construction "by country (Iceland and Luxembourg omitted). 22 request in the role of protector. Whether the United States is there to protect Europe or to extend its external security is a subjective question, but a comparison of United States arrangements in non-NATO countries shows the advantages of the infrastructure. In non-NATO countries the United States usually has to lease land and pay all of the construction costs and sometimes it must also provide utilities (power and heating). It may be argued that the United States acquires some title to the bases built in non-NATO countries whereas in NATO the bases belong to the host country. But surely this argument is invalid since bases in Morocco are no longer available, the Libyan base is under severe restrictions, and the rights to Spanish bases have to be periodically renegotiated. Regardless of the "fairness" of the infrastructure system, the United States stands to lose by not using it whenever possible to finance installa- tions which they intend to build anyway and which could be eligible for common funding. An example of this can be illustrated by the pipeline example. A gallon of fuel for American aircraft in Germany may travel from a French Atlantic seaport through either the NATO pipeline or an American- owned pipeline. Since thirty-seven percent of the initial costs and oper- ating expenses of the NATO line have been paid by the United States, whereas the American line has cost $57 million and is operated entirely at United States expense, it is cheaper to use the NATO pipeline. B. Operating Accounts Operating accounts known both as "Military Budget" and "Headquarters Accounts" apply to the operating expenses for international headquarters and agencies without a "wartime" mission. The name hardly does justice to the wide variety cf enterprises it supports. 23 The country in which a corporate facility or agency is located has been designated as the "host." The host either donates or leases facil- ities to NATO "but the corporate NATO structure normally pays for the operational activities and such administrative costs as light and heat. Thus the host country in a Military Budget activity carries less of a financial obligation than it does under infrastructure. The reasons impelling nations to support or oppose operating arrange- ments are similar to those in the infrastructure. First, it is the only way that some activities can be carried out. Second, it seems the most equitable since all nations share in the benefits to some degree. Third, some nations particularly favor certain portions of the program and for this reason are induced to accept the overall schedule. C. )onsortium Arrangements In consortium arrangements, the assessments on the members partici- pating are based on the amount of goods or services to be used by each, therefore the problem of cost-sharing can be settled by straight -forward accounting. III. SUMMARY This model shows that in the absence of any cost-sharing arrangements, the tendency for more affluent nations in an alliance to bear a dispropor- tionate share of the common burden is an economic paradox. A sharing arrangement would give each of the members of an alliance an incentive to keep contributing and provide a more adequate level of defense. Whatever disadvantages such arrangements might have, in the absence of one it will normally be impossible for alliances composed of nations acting in their own national interests to avoid a disproportionate and arbitrary sharing of costs. Where a local advantage can be demonstrated infrastructure funds provide a much more satisfactory sharing of costs, particularly where the dollar drain is involved. 2k LIST OF REFERENCES [l] Clower, R. W. and Due, J. F., Intermediate Economic Analysis (Homewood, 111: Richard D. Irwin, Inc. 1966 ) , 5th Edition p. 6l. Olson, M., Jr., and Zeckhauser, R., "On Economic Theory of Alliances," the Rand Corporation, RM-1+297-ISA, 1966. 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