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The efficient tariff: systematically balancing security and welfare concerns.

Imposing a tariff on imports of petroleum has two major effects that encourage conflicting public-policy responses. One effect is the well-documented welfare loss suffered by the domestic economy as a result of the tariff's distortional effects. The other effect is the potentially positive effect that a tariff can have on national security. When tariffs decrease, more domestic demand is supplied by foreign suppliers - which increases the expected value of the economic damage caused by potential future embargoes. The author derives the equation for the "marginal disruption risk cost" and equates this to the marginal welfare cost to find an "efficient" tariff.

The United States was self-sufficient in energy through about 1950, but since that time dependence has been growing rapidly. With oil rig counts (until recently) at modern-day lows and the "oil patch" in a well-documented recession, such a dependence on imports for our energy needs seems unlikely to be reduced or eliminated in the foreseeable future. The recent crisis in the Persian Gulf, which has sent the price of benchmark crude soaring to record nominal levels, emphasizes our nation;s vulnerability to the occasionally stochastic nature of world events or the whims of our petroleum trading partners.

The current surge in energy prices is eerily reminiscent of the 1973-74 and 1979-80 OPEC embargoes on the sale of petroleum to the United States. The impact of the '73-'74 embargo has been estimated as a 10-20 billion dollar drop in U.S. Gross National Product, a recession which at its nadir left 500,000 people cyclically unemployed.[1] the '79-'80 shock had similar results, and the current Iraq-precipitated showdown helped to doom any wistful hopes of a soft landing, to put it mildly. With the United States struggling to tame its gargantuan budget deficit, the loss of foreign petroleum supplies has cast a grave doubt in the minds of many policymakers on the "staying power" of the country's military and economic might. This doubt has led to a fair amount of debate about how we may become more self-sufficient in energy production, culminating recently in the Congressional decision to increase future Strategic Petroleum Reserve purchases. Also, of course, there has been the inevitable discourse about resuscitating the "oil import fee," a proposal which many economists regard as heretical.(2) Tariffs, say these economists, will only exacerbate the problem by increasing even further the domestic price of oil, stunting domestic growth by increasing producers' marginal costs. Proponents of the measure regard it as a means by which to stimulate domestic oil production by artificially increasing the returns to oil exploration and development.

Both of these groups have valid arguments, but while they usually fight tooth-and-nail, it doesn't have to be that way. Tariffs are not an all-or-nothing propositions, and it is possible to balance the magnitude of the economic welfare losses inherent in a tariff of a certain level with the magnitude of the security risk inherent in importing (rather than producing) critical energy resources. Although this may seem intuitive, it is a solution which until now has never been quantified.

A Common Ground

Obviously, we are at a loss to measure "the risk of losing the Iraqi conflict" or other nebulous - though nonetheless important - sense of the words "security risk." The risk that I will be discussing is simply the risk of damage to the economy (as measured by GNP) associated with an oil import shortfall, whatever its nature. Clearly, policymakers must weigh the other dangers which accompany the shortfall. It is my opinion, however, that such fears are admirably addressed by emergency stockpiles such as the Strategic Petroleum Reserve, and should be separated from tariff discussions.

The attractiveness of this approach to risk, as opposed to an approach that considers political concerns, is dual faceted: (1) the economic risk from any sort externally-induced shortfall can be incorporated into the model, and (2) economic risk, like the "damage" done by a tariff to GNP, is denominated in dollars. Since we want to analyze the tradeoff between these two, it is encouraging that we start with a common ground between them.

The Procedure

I shall begin by defining the equations for these two effects in terms of the tariff t. That is. let R(t) be the disruption risk function and W(t) the tariff-induced welfare loss function. While W(t), as we well know, is a positive function of t, R(t) will vary as - t because as tariffs increase (and consequently the domestic price of foreign oil increases) the nation's consumers will substitute to domestic oil and imports less. Therefore, the risk from an abrupt external disruption will decline as well. We want to minimize the sum of these two risks; if L is to entire loss so that L = W(t) + R(t), then the minimum loss is found by setting L*W'(t) - [R.sup.1](t) solving for L* =0. Because W(t) and R(t) are monotonic functions, there is no need for second-order conditions, as we can be assured that the t that makes L* = 0 will, indeed, be at a minimum of L.

Welfare Loss

The equation for the economic welfare loss from the imposition of a tariff is simple and has been previously explored.(4) The GNP loss from a tariff is proportional to the square of the tariff, or

W(t) = h[t.sup.2]

where W(t) is in billions dollars, t is in dollars per barrel, and h is proportionality constant. (The "Project Independence Report" of 1974 suggests a reasonable value of h to be .775 billion.(5) Therefore, the marginal economic welfare loss is the derivative of this equation:

W'(t) = 2ht

Disruption Risk

The more difficult relationship to describe - and a relationship heretofore unexplored - is the one between tariff level and disruption risk. A critical potential problem looms in the measurement of this risk. Because some periods will see supply disruptions while others will not, the best we can do to approximate the current risk is to figure an expected value for the current period's risk. Although the initial equation we derive will assume that that risk is independent of world events, I will later introduce a factor to adjust for subjective assessment of political conditions.

I will begin by determining the new level of imports after the imposition of a tariff. Let [Q.sub.s] and [Q.sub.d] be the initial levels of domestic supply and demand at the international equilibrium price P. Then ([Q.sub.d] - [Q.sub.s]) represents imports under free-market conditions. If [e.sub.s] and [e.sub.d] represents the one-year price elasticities of supply and demand and [Q.sub.s*] and [Q.sub.d*] the new levels of domestic supply and demand at the new price [P.sup.t] = P + tariff,(6) then:

[Mathematical Expression Omitted]

and [e.sub.d], analogously,

[Mathematical Expression Omitted]

For brevity's sake, let Z = [Mathematical Expression Omitted]

We want to find [Q.sub.s*] and [Q.sub.d*], so we solve (for [Q.sub.s*] first):

[Mathematical Expression Omitted]

and, similarly,

[Mathematical Expression Omitted]

Combining (4a) and (4b), we find imports under the new price [P.sup.t] are:

[Mathematical Expression Omitted]

Now let us pause for a moment and consider GNP shortfall as a function of oil supply shortfall. According to the 1973 National Petroleum Council Shortfall Impact Estimate,

Annual [GNP.sub.sf] = k ([S.sub.sf]).sup.2]

where [S.sub.sf] is the oil shortfall in millions of barrels per day (MMB/D) and is k is a proportionality constant estimated at 11 billion by the "Project Independence Report" (p. 365).

We first proceed to find a relevant range for [S.sub.sf]. Clearly, the lower limit is zero, in which case the annual GNP shortfall is zero. The upper limit is (if we consider external supply disruptions only) the total amount of imports, or [Q.sub.d] - [Q.sub.s]. Therefore, if domestic import at the current world price are [Q.sub.s*] - [Q.sub.d*] for any [P.sup.t],

[Mathematical Expression Omitted]

Substituting (5) for the import term,

[Mathematical Expression Omitted]

R(t) and W(t) are graphed in figure 1. The reader will note that Wt) strictly increases and R(t) strictly decreases as t increases.

We now take the derivative of this equation with respect to [P.sup.t] in order to find R'(t).(7)

We begin:

[Mathematical Expression Omitted]

Note that:

[Mathematical Expression Omitted]

Note in turn that, substituting for Z:

[Mathematical Expression Omitted]

Substituting (11) into (10),

[Mathematical Expression Omitted]

which is analogous to:

[Mathematical Expression Omitted]

Substituting (12a) and (12b) into (9) and re-substituting for Z.

[Mathematical Expression Omitted]

Reducing (remembering that [P.sup.t] = P + t).

[Mathematical Expression Omitted]

This is the equation for the upper limit of the marginal disruption risk. A graph of this function is shown in Figure 2. Note that R'(t) varies as - t, as predicted.

By plotting R'(t) and W'(t) on the same graph, we can identify visually the most efficient tariffs as the tariff that causes R'(t) = W'(t) in absolute value (See Figure 3). The visual method or iterative calculation may be used to find the intersection point. Figure 4 shows a sample calculation for k = 11 billion, [e.sub.s] = 2, [e.sub.d] = -.5, h = .775 billion, [Q.sub.s] = 9 mmb/d, [Q.sub.d] = 14 mmb/d, and P = $40/bbl.


The Large Country Case

I have repeatedly noted that equation (13) applies only to the "small country case" in which the importing nation has no power to affect the world price of the commodity in question, so [P.sup.t] does indeed equal P (the pre-tariff price) plus the tariff. If a country is large, however, with regard to a particular imported commodity, then [P.sup.t] = P + st, where

[Mathematical Expression Omitted]

Here [e.sub.ES] is the support elasticity and [e.sub.ID] is the import-demand elasticity for petroleum in large country. Because s is a constant, we can follow steps similar to the ones we took above the derive a new equation analogous to equation (13) but adjusting to the large country case. The only net difference in the final result is that everywhere "t" appears in equation (13) it must be replaced by st, thus R'(t):

[Mathematical Expression Omitted]

See Figure 5 and Figure 6 for the large-country analogs to Figures 3 and 4. Remember that these are maximum values of R'(t) and, consequently, the figures show the maximum efficient tariff.

Incorporating the Likelihood of Disruption

I have defined, in (13) and (15), the marginal cost function of the maximum disruption risk. We have therefore explored the boundaries of R'(t). A more useful function to generate, however, would be one which estimates the expected value of R'(t) and W'(t), the marginal disruption risk cost and marginal welfare cost. This would clearly be a more accurate indicator of the true tradeoff between these two effects.

The expected value of an event is simply the value of the event given that it occurs times its probability of occurrence. Equations (1) and (8) give the value for W(t) and R(t), respectively and we can, therefore, say that

E(W(t)) = g W(t) (16) and

E(R(t)) = f R(t), (17) where g and f are the probabilities of W(t) and R(t) occurring, respectively. Notice that g=1, because we assume that the welfare cost occurs without fail for any given tariff (thought the size of W(t), obviously, varies with the tariff itself). Thus, E(W(t)) = W(t). On the other hand, the probability that a petroleum disruption occurs in a given year is assured not 1, so expected value of the disruption risk cost is less than the maximum called for in equation (8), and the expected marginal value of the disruption is E(R(t))' = f(R'(t)) since f is a constant.

Recall that we defined R(t) to be the GNP shortfall that would occur if all petroleum imports were interrupted, as in equation (8). Suppose we expect such an event to have a probability of occurrence of .1: about one year in ten, all imports will be suspended. Such a case is illustrated in Figure 7, which is identical to Figure 5 expect that f = .1. For comparison, Figure 5' curve is superimposed on the graph as f = 1. Note that the equilibrium tariff is much lower with f = .1, at about $2.12 compared to 413.09.

Differential Tariff Rates Across

Trading Partners

We have so far assumed that all countries face a tariff imposed uniformly by the large country. With the flexibility accorded by f, the "likelihood of disruption factor," it is possible (and desirable) to treat each trading partner separately - to assign each partner its own "efficient tariff." some partners are extremely unlikely to be party to a supply disruption; accordingly, since the risk of disruption is low, we would expect to be able to offer these partners a lower tariff barrier. Consider two countries, Canada and Iraq, in trade of petroleum with the United States. Assume econometricians estimate [f.sub.c] = .01 and [f.sub.I] = .3, and assume for simplicity that the countries have similar export supply point elasticities with respect to the United States. To figure the most efficient tariffs for each, we suppose first that Canada supplies all of [Q.sub.s], then we suppose that Iraq supplies all of [Q.sub.s]. If all other conditions are the same as in Figure 5, we obtain the results illustrated in Figure 8. We should assign to Canada a tariff of $0.23 and to Iraq a tariff of $5.48.

Notice the positive incentives provided by this method of tariff assignment! The trading partner has a very strong interest in maintaining good ties with the large country to take steps to diminish that country's assessment of f, for when f falls, so do the tariff barriers. The large country also has an incentive to seek ways to lower the true f, for as tariffs fall so does W(t), the welfare loss associated with the tariff. It should be encouraging to free-marketeers that a system of tariff assignment has built-in incentives for tariff reduction!

Policy Implications

Energy policy, in the past, has usually been guided by the theory that some current welfare should be traded for future security interests, but this sense has never been aided by a tool to estimate what the security risks are. Clearly, there are some times when preserving domestic capacity and encouraging domestic conservation is worth the pain which accompanies a tariff, but tariffs (when they have been assigned) generally have suffered from two problems. First, it has not been easy to gauge how large a tariff should be to provide the measure of protection required. Second, it has been the case that "tariffs in motion tend to remain in motion" - tariffs seem to be politically more difficult to remove than to apply.

The efficient tariff model solves these two problems in ways that I have already discussed. It provides a measured, calculated policy response to a legitimate concern, while simultaneously providing incentives for adjusting the response as the concern is allayed. It can furthermore react quickly to marketplace changes: e.g., as the international equilibrium price changes the efficient tariff can be periodically adjusted as often as is necessary.(9)

I should clarify one final point. lest these words seem too militant. I am not arguing that tariffs based on this model be instituted on the morrow. On the contrary, because the welfare losses would begin to mount immediately while the gains from risk reduction would accrue over a long period of time in the future, it would be prudent to install this mechanism in an environment of stability and general economic growth, so as not to exacerbate current woes for the sake of some seemingly nebulous future gain. It is this author's opinion that the present economic climate does not meet these criteria; nonetheless, I believe that such a model should be instituted as soon as conditions do permit. Finally, I encourage and anticipate debate on this topic, and I welcome criticisms of as well as refinements to this model.


(1.) U.S. Federal Energy Administration, "project Independence Report," (Washington, D.C., US-GPO, Nov. 1974), p.2. (2.) At least in the small-country case where the importing nation cannot affect the world price of the commodity and therefore has no positive "optimum" tariff. I will discuss the large-country case late. (3.) Remember that R(t) is an inverse function of t! (4.) See, for example, the "Project Independence Report,' op, cit., p. 397. (5.) This number may be smaller today than in '74 due to increased fuel efficiency, but there's also the opposing effect of a higher level of imports. The actual number will remain an issue for econometricians to decide. (6.) Once again, this assumes for the time being that the country is a "small country." (7.) Because [P.sup.t] = P+t with P given, differentiating with respect to [P.sup.t] is equivalent to differentiating with respect to t. (8.) This equation is derived by using definitions of the elasticities of the import-demand and export-supply curves. For a discussion, see Mordechai e. Kreinin, International economics: A Policy Approach (fifth ed.), Harcourt Brace Jovanovich, 1987, pp. 442-444. (9.) I have often been asked whether this model is applicable to other commodity markets. I certainly can see no reason why it would not be, provided the disruption risk and welfare risks can be quantified. Few commodities, however, have been researched so thoroughly and publicly in there areas as has petroleum, for obvious reasons.


Kreinin, Mordechai E., International Economics: A Policy Approach (fifth ed.), (Harcourt Brace Jovanovich, 1987). U.S. Federal Energy Administration, "Project Independence Report," (Washington, D.C., USGPO, Nov. 1974).
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Author:Ashton, Michael
Publication:American Economist
Date:Mar 22, 1992
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