joint-product export smuggling and export tax policy

P1: ICA/TKL P2: ICA/ASH P3: ICA/ASH QC: BSA/ICA T1: BSA

Open economies review KL381-06-Fausti January 6, 1997 18:12

Open economies review 8: 61–70 (1997)c© 1997 Kluwer Academic Publishers. Printed in The Netherlands.

Joint-Product Export Smugglingand Export Tax Policy

SCOTT W. FAUSTIDepartment of Economics, South Dakota State University

Key words: smuggling, joint-product effect, revenue-maximizing tax rate, commercial policy

JEL Classification Number: F13, H26, H21

Abstract

The effect of smuggling on tax revenue collection and the revenue-maximizing tax rate is an un-resolved issue in the smuggling literature. Clandestine and joint-product smuggling models arriveat different conclusions concerning smuggling’s effect on tax revenue collection and the revenue-maximizing tax rate. Clandestine (joint-product) smuggling is consistent with the assumption thatlegal and illegal trade are substitutable (complementary) activities for the exporting firm. The effectof smuggling on the tax rate and tax revenue is shown to be dependent on whether smuggling andlegal trade are assumed to be complementary or substitutable activities.

Import and export smuggling continues to be a widespread phenomenon ofinterest to economists. Coffee smuggling in Tanzania and coco smuggling inGhana are examples of agricultural export smuggling. The smuggling of manu-factured imports into Indonesia, India, and Pakistan has been widely discussedin the literature (e.g., Cooper (1974), Deardorff and Stolper (1990)). In the UnitedStates and Canada, high domestic taxes on cigarettes have led to interstate orinter-province smuggling and import smuggling across national borders (e.g.,Bartlett (1994), Thursby et al. (1991)). Since smuggling affects the trade pat-terns of a wide variety of goods subject to trade taxes, commercial policy offi-cials should recognize that smuggling activity will also affect commercial policyoutcomes.

Trade taxes have a long history as revenue raising devices in the third world.The smuggling of imports and exports is a common response in less devel-oped countries to high tariff or export tax rates. The smuggling firm can usefour methods to smuggle exports: a) under-invoicing of exports; b) falsely de-clared exports; c) under-assessment of exports; and d) clandestine smugglingof unreported production.

The first three methods are consistent with “joint-product smuggling’’ de-scribed by Pitt (1981). Joint-product smuggling requires legal trade to act asa cover for illegal trade. This implies that the smuggling firm views legal andillegal trade as complementary activities. Clandestine smuggling is consistent



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with the type of smuggling Bhagwati and Hansen (1973) described in their sem-inal article. In their model, smuggling supplants legal trade. This implies thatthe smuggling firm views legal and illegal trade as substitutable activities.

In the clandestine smuggling literature, Bhagwati and Srinivasan (1973) es-tablish that: 1) smuggling reduces tax revenue collections for a given tax rate;and 2) for a given tax revenue level, the tax rate is higher in the presence ofsmuggling. A comparison of revenue-maximizing tax rates under the clandes-tine smuggling and non-smuggling scenarios is possible under restricted con-ditions. For constant elasticity offer curves, Johnson (1972) demonstrates thatthe ranking of the revenue-maximizing tax rate in the presence of clandestinesmuggling is below the rate for non-smuggling.

In the joint-product smuggling literature, the issue of ranking revenue-maximizing tax rates for the smuggling and non-smuggling scenario has notbeen addressed. Pitt (1981), Deardorff and Stolper (1990), and Fausti (1992)address the “comparison of tax revenue collected’’ issue and they arrive atambiguous results.

The introduction of the concept that legal and illegal trade are either comple-mentary or substitutable activities for the exporting firm provides a resolutionfor the contradictory results found in the clandestine and joint-product smug-gling literature concerning the revenue-maximizing tax rate and tax revenuecollection. When legal and illegal trade are assumed substitutable activities,the implication is that the firm increases its illegal exports at the expense oflegal exports. If it is assumed that legal and illegal trade are complementaryactivities, the implication is that when the firm increases illegal exports, legalexports also increase.

1. Pitt’s smuggling model and the export supply function

The Pitt joint-product smuggling model assumes a small country exporting toworld markets. If domestic firms in the export industry engage in smuggling,then they produce a joint-product export, assumed to be of the type describedby Pitt (1981). Pitt describes a smuggling firm as producing a joint-productexport good composed of a legal export unit combined with an illegal exportunit. Pitt’s smuggling production function embodies a real resource cost andthe confiscation cost associated with joint-product smuggling. The role of legaltrade is to act as a cover for illegal trade.

Pitt’s assumptions are modified by assuming that confiscation revenues col-lected by the government just offset the real resource cost of enforcement in-curred by the government and that domestic firms produce a pure export good.These simplifying assumptions are made so enforcement cost, confiscation rev-enue, and domestic consumption can be ignored in the revenue maximizationmodel developed below.

The analysis begins with the Pitt model of smuggling, the small country casewith the terms of trade fixed. The country produces two traded goods, (X)



JOINT-PRODUCT EXPORT SMUGGLING AND EXPORT TAX POLICY 63

and (M), an exportable and an importable, respectively, with primary factors inperfect competition. Production and trade are carried out by identical exportingfirms. Legal and illegal trade in exports is carried out by the same firm and allexporting firms smuggle.

It is assumed each firm can trade illegally according to Pitt’s “smugglingfunction’’

s∗ = G(l , s) (1)

The term (s∗) is the quantity of good (x) smuggled, (l ) is the quantity of good (x)legally traded, and (s) is the quantity of good (x) input into smuggling activity.The function (G) is strictly concave and a twice differentiable linear homogenousfunction. The function (G) is also assumed to have the following properties:

Gl ≥ 0, (2)

1≥ Gs ≥ 0, (3)

s− s∗ ≥ 0. (4)

Assumption (2) states that the marginal product of legal trade used in smug-gling is non-negative. Assumption (3) states that a unit increase in the smug-gling input (s) results in a positive, but less than or equal to, unit increase inactual ex-post smuggling. Assumption (4) prohibits the cost of smuggling frombeing negative. Pitt states that the difference between ex-ante smuggling (s)and ex-post smuggling (s∗) consists of penalties and confiscation or a mixtureof real resource cost, penalties, and confiscation. Ex-ante smuggling refers tothe amount of (X) allocated to illegal trade. Ex-post refers to the amount of (X)successfully smuggled out of the country.

The ex-post joint-export product is defined as

x = l + s∗. (5)

Joint-product profit for the individual profit maximizing firm is denoted (∏

i ),∏i

= P f ·G(l , s)+ P f · (1− t) · l − Ps · (l + s). (6)

The exogenous variable, P f , denotes the world relative price of exports. Theexogenous variable, t , denotes the ad valorem tax rate. In the non-smugglingcase, the tax distorted domestic relative price of the export good is: Pt =P f (1− t). The variable Ps denotes the domestic cost of producing the exportgood.

The implication of Eq. (6) is that legal and illegal trade in exports is consid-ered a joint-product of the smuggling firm. As in Pitt’s article, firms earn zeroeconomic profit in the long run because the revenue from all foreign trade is



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just equal to the domestic production cost of trade goods. Profit maximizationin production implies producing on the production possibilities curve where themarginal rate of transformation equals domestic relative prices, Ps. SettingEq. (6) to zero, solving for Ps generates an expression for the long-run equilib-rium domestic price ratio as a weighted average of prices received for goodslegally exported in conjunction with goods illegally exported,

Ps = [ P f · s∗/ l + s] + [ P f · (1− t) · l/ l + s]. (7)

In the Pitt paper, Ps > Pt . Pitt calls this result the price disparity effect ofjoint-product smuggling1. Pitt’s model is extended by deriving the aggregatejoint-product export supply function.

For simplicity, let Eq. (8) represent the smuggling firm’s profit function,

yi = yi (Ps, PI ). (8)

Employing Hotelling’s lemma, the firm’s output supply function and input de-mand function are derived from the joint-product profit function,

∂yi (Ps, PI )/∂Ps = xi (P, PI ), x′ > 0, x′′ > 0, ∀ Ps > 0, (9)

∂yi (Ps, PI )/∂PI = i i (P

s, PI ), i ′ < 0, i ′′ < 0, ∀ PI À 0. (10)

The term (xi ) is the ex-post joint-product export supply function for the i thfirm which engages in illegal joint-product export trade. The term (i ) is the inputdemand function for the i th firm which engages in illegal joint-product exporttrade. The input price PI refers to the vector of input prices associated withthe factors of production employed in the production of the export good (X).

Equation (9) provides the general form of the i th firm’s joint-product ex-postexport supply function. Summing horizontally across all firms in the exportindustry allows the industry joint-product ex-post export supply function to bederived,

X∗(Ps, PI ) =n∑

i=1

xi . (11)

Joint-product aggregate output price, Ps, is a weighted average determinedby the following variables and parameters: P f , Pt , L, S, and S∗. The decisionto smuggle requires the firm to transfer a portion of (X) from legal trade (L)to illegal trade (S). This decision makes (S) a substitute activity for (L). Thesmuggling decision determines the ex-ante and ex-post amount of legal tradethe firm engages in.

The nature of a joint-product opens the door for the assumption that the ex-ante joint-product supply function has two components: 1) an ex-ante supplyfunction for illegal goods, and 2) an ex-ante supply function for legal goods. It is




assumed that, if input prices are constant, the ex-ante aggregate joint-productexport supply function has the following specific form,

X(Ps, PI ) = L(t, S)+ S(t). (12)

The tax represents a proxy for the relative price differential between legal andillegal goods and provides the relative price link between legal and illegal trade2.The decision to smuggle requires that (S) by substituted for (L). Therefore, thesupply of legal exports is dependent on the amount of the export good the firmdecides to smuggle. The smuggling decision provides the joint-product linkbetween legal and illegal trade3.

However, the increase in the price of exports for the firm, i.e., Ps > Pt , has anoutput effect, increasing the amount of (X) produced for export. If the outputeffect is greater (less) than the substitution effect, (L) and (S) can be consid-ered complementary (substitutable) activities for the exporting firm. If legaland illegal trade are substitutable (complementary) activities for the firm, thenthe firm’s decision to smuggling generates a negative (positive) joint-producteffect and legal trade declines (increases).

The country’s supply of exports to the world market is assumed to havetwo possible states of nature: 1) all firms engage in legal trade only; and 2)all firms engage in joint-product smuggling. For simplicity, under State 1, thelegal-trade-only export supply function is assumed to be a function of the taxdistorted world price of exports, Pt . Holding the world price P f constant, theexport supply function is defined as L(t), dL/dt = L ′ < 0.4

Under State 2, the legal export supply function, L(t, S), is defined as a functionof the export tax rate and the ex-ante illegal export supply function. The partialderivatives are assumed to have the following signs: 1) Lt = ∂L/∂t < 0, and 2)Ls = ∂L/∂S≤> 0. The sign of Ls is dependent on whether legal exports (L) andillegal exports (S) are substitutes or complements, i.e., the joint-product effect.The smuggling decision is dependent on the tax rate, therefore the smugglingsupply function is defined as S(t). The derivative is assumed to have the fol-lowing sign: S′ = dS/dt > 0. Finally, it is assumed that all other factors affectingthe legal export supply function under both states of nature are held constant.

2. The effect of joint-product smuggling on total exports and trade taxrevenues

The first proposition addresses the issues concerning the effect of joint-productsmuggling on total domestic export production, legal exports, and tax revenuecollection:

Proposition 1. The introduction of joint-product smuggling will: 1) increasetotal export production; and 2) increase tax revenues if Ls > 0, or 3) decreasetax revenues if Ls < 0.



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The small country assumption made earlier implies that the demand for exportsis perfectly elastic. Assume State 1, the level of total domestic production ofexports (X), after the export tax is levied but before smuggling is introduced,is equal to L1,

X1 = L1. (13)

After smuggling is introduced, State 2, the level of total domestic production ofexports, is equal to the ex-ante sum of legal and illegal exports,

X2 = L2+ S2. (14)

Assume the ex-ante supply of total exports has a positive relationship with theex-post price of joint-product exports. The introduction of joint-product smug-gling generates price disparity, Ps ≥ Pt . This implies the domestic productionof exports increases, X2 ≥ X1. Substituting for X2, we have L2 + S2 ≥ X1, orits equivalent, S2 ≥ X1 − L2. The presence of smuggling implies that S2 ≥ 0.Substituting for X1 produces inequality (15),

S2 ≥ (L1− L2). (15)

Inequality (15) demonstrates that the domestic production of exports destinedto be marketed via illegal channels is greater than the possible decline in theproduction of exports destined to be marketed via legal channels, so total ex-ports increase. However, in the joint-product smuggling literature, the effect ofsmuggling on legal trade is ambiguous, i.e., (L1− L2)

≤> 0.5

The preceding analysis is an alternative way of presenting Pitt’s discussionof tax revenue maximization in the presence of joint-product smuggling6. How-ever, an interesting implication of the joint-product relationship has been over-looked. Pitt demonstrates that a positive level of smuggling may be necessaryto maximize tax revenue. For smuggling to increase legal trade and tax rev-enues, i.e., L2> L1, legal and illegal trade must be complementary activities forthe exporting firm.

However, for the Bhagwati and Hansen (1973) type of clandestine smuggling,one would expect legal and illegal goods to be substitutes. If legal and illegaltrade are assumed to be substitutable activities in a joint-product smugglingmodel, then the introduction of smuggling will reduce legal exports and taxrevenue, L1> L2, as predicted in the clandestine smuggling literature. Thisdiscussion establishes Proposition 1.

3. The effect of joint-product smuggling on the revenue-maximizingexport tax rate

It is assumed that the government’s goal is to maximize revenues. Under State1, the export tax rate is set to maximize revenues collected before joint-product




smuggling begins. Domestic production and thus export supply are solely de-pendent on the exogenous world price for the exported good. Any tax leviedon exports must be fully absorbed by domestic producers. Given this set ofcircumstances, the legal export supply function is defined as L(t). The govern-ment’s total revenue function is defined as,

TR= t · P f · L(t).7 (16)

Total tax revenue is defined as tax revenue collected on exports evaluated atworld prices. To determine the revenue-maximizing tax rate, the first derivative(dTR/dt) is set to zero in Eq. (17) and the revenue-maximizing tax rate is derivedin Eq. (18),

dTR/dt = P f · L + P f · t · L ′ = 0, (17)

t0 = −(L/L ′) > 0. (18)

When joint-product smuggling is introduced, the government’s total revenuefunction is altered by replacing the legal export supply function L(t) in Eq. (16)with L(t, S). The supply of legal exports is now a function of t and S (State 2).The revenue-maximizing tax rate in the presence of smuggling is derived,

TR = t1 · P f · L(t, S), (19)

dTR/dt = P f · L + P f · t1 · [Lt + Ls · S′] = 0, (20)

t1 = −L/[Lt + Ls · S′] > 0. (21)

In Eqs. (20) and (21), the term Ls · S′ captures the indirect (joint-product) ef-fect of a marginal change in the tax rate on the supply of illegal goods. Itssign is dependent on whether legal and illegal export trade are substitutable orcomplementary activities for the exporting firm, LS < 0 or LS > 0 respectively.The partial derivative ∂L/∂t = Lt < 0 represents the direct effect of a marginalchange in the tax rate on the supply of legal exports. Under the assumptionthat the direct effect dominates the indirect effect, t1 > 0.

Proposition 2. The introduction of joint-product smuggling will reduce therevenue-maximizing tax rate if ∂L/∂S< 0.

To establish Proposition 2, the ratio

t1/t0 = (−L ′/L) · (−L/[Lt + LS · S′]) = L ′/[Lt + LS · S′] (22)

is examined under the following assumption, ∂L/∂S< 0.When it is assumed that LS< 0, the substitution effect outweighs the output

effect producing a negative joint-product effect. This implies that once theexporting firm decides to engage in smuggling, the amount of legal trade it



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engages in declines, reducing total tax revenues collected at the current taxrate. Under the assumption LS < 0, the ratio t1/t0 < 1, indicating the tax ratemust be reduced in order to maximize tax revenue8. These results are consistentwith the clandestine smuggling literature.

Proposition 3. The introduction of joint-product smuggling will increase therevenue-maximizing tax rate if ∂L/∂S> 0.

If LS > 0, then the output effect outweighs the substitution effect producing apositive joint-product effect. This implies that once the exporting firm decidesto engage in smuggling, the amount of legal trade the firm engages in willincrease and total tax revenues collected by the government will rise at thecurrent tax rate. Under the assumption LS > 0, the ratio t1/t0 > 1, indicatingthe tax rate must be increased to maximize tax revenue. The tax revenue resultis consistent with the joint-product literature. The revenue-maximizing tax rateresult contributes to the discussion of smuggling’s effect on tax policy in theliterature.

Proposition 4. The introduction of joint-product smuggling will have no effecton the revenue-maximizing tax rate if ∂L/∂S= 0.

When LS = 0, it indicates that the exporting of legal and illegal goods areunrelated activities. This implies that once the exporting firm decides to en-gage in smuggling, the amount the firm decides to smuggle is independent ofthe amount it decides to export via legal channels, i.e., the joint-product ef-fect is zero. While this assumption is intuitively unappealing, it implies thatthe ratio in Eq. (22) reduces to L ′/Lt (see endnote 8). To simplify the anal-ysis it is now assumed that the legal trade supply response to a change inthe export tax rate is the same under both states of nature, L ′ = Lt . Un-der this assumption t1/t0 = 1, indicating that the introduction of joint-productsmuggling has no effect on the revenue-maximizing tax rate or tax revenuescollected.

4. Summary and policy conclusions

The conclusions found in the smuggling literature concerning the effect ofsmuggling on tax revenue and the revenue-maximizing tax rate are ambigu-ous. It has been demonstrated here that the relationship between legal andillegal trade determines the effect of smuggling on tax revenue and the revenue-maximizing tax rate (see Table 1). The paper’s policy conclusion, with respectto tax revenue flows from traded goods prone to smuggling activity, is thata government needs to adjust tax policy according to the type of smugglingoccurring.




Table 1. Summary of results.

Joint-product effect Ls < 0 Ls > 0 Ls = 0

Revenue-maximizing tax ratea ts < tns ts > tns ts = tns

Total tax revenues collected TRs < TRns TRs > TRns TRs = TRns

at a specific tax rate

aThe subscript s denotes the smuggling scenario and ns the non-smugglingcase.

Acknowledgments

The author is appreciative of the useful comments provided by the anonymousreferee and the editorial assistance of Mary Brashier. Any remaining errorsare my responsibility. Funding for this research was provided in part by SDSUExperiment Station Project No. 281024.

Notes

1. Price disparity refers to a differential existing between the actual domestic price of the tradedgood and the tax inclusive world price of the traded good.

2. The actual relative price differential is t · (S∗/S) because of the real resource and confiscationcost associated with smuggling.

3. The decision to smuggle and the amount to smuggle (ex-ante), ceteris paribus, is based on thetax rate. Therefore, it is assumed that the legal trade decision (ex-ante) is dependent on thesmuggling decision.

4. If one assumes that legal trade is a function of the domestic price of exports, L(P), and P =P f · (1− t), the results remain unaltered. The decision to make legal trade a function of the taxwas done to simplify the mathematics presented in the paper.

5. Fausti (1992) used this approach to discuss the impact of smuggling on total exports.6. See Pitt (1981, p. 453) for his discussion of tax revenue maximization in the presence of joint-

product smuggling.7. It is assumed that in the absence of smuggling, tax revenue collection is a cost-less activity for

the government. The tax revenue generated by the export tax is assumed to increase, attain amaximum and then decline as the tax rate rises.

8. It is assumed that L ′ = Lt . However, it is possible that the presence of smuggling strengthensor weakens the direct effect of a marginal increase in the tax on legal exports, i.e., L

′ ≤> Lt . If

legal and illegal trade are substitutes, then smuggling strengthens the direct effect, i.e., the firmallocates a greater proportion of X to illegal trade (S). If legal and illegal trade are complements,then smuggling weakens the direct effect. Weakening the assumption of L ′ = Lt strengthensPropositions 2 and 3.

References

Bhagwati, J. and B. Hansen (1973) “A Theoretical Analysis of Smuggling.’’ Quarterly Journal ofEconomics 87, 172–187.

Bhagwati, J. and T.N. Srinivasan (1973) “Smuggling and Trade Policy.’’ Journal of Public Economics2, 377–389.



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Bartlett, B. (1994) “Cigarette Taxes, Smuggling, and Revenues.’’ Tax Notes (June), 1493–1500.Cooper, R. (1974) “Tariffs and Smuggling in Indonesia.’’ In J. Bhagwati (ed.), Illegal Transactions in

International Trade. Amsterdam: North-Holland, pp. 183–192.Deardorff, A. and W.F. Stolper (1990) “Effects of Smuggling under African Conditions: A Factual,

Institutional and Analytic Discussion.’’ Weltwirtschftliches Archive: Review of World Economics126(1), 116–141.

Fausti, S. (1992) “Smuggling and Parallel Markets for Exports.’’ The International Trade Journal 6(4),443–470.

Johnson, H.G. (1972) “Notes on the Economic Theory of Smuggling.’’ Malayan Economic Review17, 1–7.

Pitt, M. (1981) “Smuggling and Price Disparity.’’ Journal of International Economics 11, 447–458.Thursby, M., R. Jensen, and J. Thursby (1991) “Smuggling, Camouflaging, and Market Structure.’’

Quarterly Journal of Economics 105, 789–814.

joint-product export smuggling and export tax policy

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