Revenue - neutral tariff reform : theory and an application to Cameroon

DRAFT FOR STAFF USE ONLY REVENUE-NEUTRAL TARIFF REFORM: THEORY AND AN APPLICATION TO CAMEROON Henrik Dah1 (Consultant) S. Devarajan (Consultant) S. van Wijnbergen CPD Discussion Paper No. 1986-25 April 1986 (Rev. May 1986) CPD Discussion Papers report on work in progress and are circulated for Bank staff use to stimulate discussion and comment. The views and interpretations are those of the authors. FIRST DRAFT Comments Welcome IEVENUE-NEUTRAL TARIFF REFORK: THEORY AND AN APPLICATION TO CAMEROON by Henrik Dahl Copenhagen University and Danish Council of Economic Advisers Shantayanan Devarajan World Bank and Harvard University and Sweder van Wijnbergen World Bank and Centre for Economic Policy Research, London April 1986 Revised May 1986 Paper presented at the TIMS/ORSA Joint National Meeting, Los Angeles, April 14-16, 1986. We thank Lans Bovenberg and seminar participants at the Johns Hopkins University for detailed and helpful comments. The views expressed in this paper are our own and do not necessarily reflect those of the institutions with which we are affiliated. ABSTRACT Revenue-Neutral Tariff Reform: Theory and an Application to Cameroon This paper addresses the issue of revenue constrained partial tariff reform. This is an increasingly important issue, as more and more countries are caught between the conflicting demands of restoring price efficiency through reducing tariffs, and preserving government revenues. Where the second best option of using consumer taxes for revenue is not available in the immediate future, tariffs will remain an important "third best" source of revenues. We derive instructive formulae clarifying the optimal structure of revenue raising tariffs. We demonstrate the importance of net import demand elasticities and complementarity with untaxed export goods. We further analyze the empirically important case of revenue raising tariffs in the presence of dictortionary producer taxes. These are shown to modify the optimal tariff structure in an intuitive manner. We then conduct numerical experiments with an eleven sector general equilibrium model of Cameroon. We calculate optimal revenue constrained tariffs and compare them with the uniform rate that generates the same revenue. In addition, we calculate the social cost of changing individual tariff rates. Our major conclusion is that replacing the existing tariff structure with a uniform rate can lead to significant welfare losses as long as the other taxes in the economy remain suboptimal. If, however, the rest of the taxes are set optimally, then a uniform tariff rate is very close to the optimum, even in a revenue-constrained economy. We also find that changes in individual tariff rates can have very different implications for social welfare - in sign as well as in magnitude -- when compared to complete tariff reform. I. ITRODUCTION Tariffs on imported goods protect domestic industries and raise public revenues. Yet, they have consequences which may be un- desirable. By raising input prices and diverting resources out of exportable sectors, tariffs hurt the competitiveness of exports. Domestic industries receive distorted signals and may not be encouraged to adopt the most efficient technologies. Finally, the social costs associated with "rent-seeking" -- private agents attempting to capture the gains from import protection - can be sizeable. For these and other reasons, many governments in developing countries are considering reforming - and in some cases eliminating - their tariff structure. Nevertheless, tariffs are likely to remain an important source of public revenues in many countries. Consumer taxes, which would raise revenue without distorting production incentives, entail very high administrative costs. Even if a switch to a consumer tax is under consideration, putting the necessary administrative machinery in place is likely to take years. There is therefore a legitimate interest in the question of an "efficient" tariff structure, namely, one which generates revenue while minimizing distortions to the rest of the economy. This is the question addressed in this paper. A particular tariff reform that is often proposed is to replace the existing structure with a uniform rate that raises the same revenue. This has several attractive features. First, a uniform tariff rate implies that the relative domestic prices of traded goods covered Disk #17/Tariffs/04-10-86/SDevarajan:gjc -2- by the tariffs equal relative world prices, thereby eliminating one of the distortions created by tariffs. Second, an equal, across-the-board tariff is easy to administer. Third, by committing itself to a single rate, the government reduces the potential benefits from rent-seeking which in turn may lower the level of this socially wasteful activity. However, despite their merits, uniform tariffs have a cost associated with them. If a given amount of revenue has to be raised by tariffs, under certain conditions the tariff structure that maximizes consumer welfare is one where the rates are inversely proportional to the elasticity of net import demand. There is no reason to suspect that demand elasticities are equal across all imports. Moreover, an inefficient domestic tax structure may also call for deviations from uniformity even if the latter would be optimal in a no-tax economy. In short, by departing from optimal tariff rates, uniform tariffs impose a cost on society. The aim of this paper is to assess that cost. We first present a theoretical model that derives optimal tariff rates under various assumptions about the underlying economy. This motivates the experiments with an eleven-sector computable general equilibrium model of Cameroon that follow. We calculate optimal, revenue-constrained tariffs for Cameroon and compare them with the uniform rate that generates the same revenue. In addition, we compute the social costs of changes in individual tariff rates. This paper is based on the theory of revenue-constrained, optimal taxes due to Diamond and Mirrlees (1971), who formalized and extended the ideas of Ramsey (1927) and Pigou (1944) in a general IaLk #17/Triffs/04-10-86/SDevarajan.gj c -3- equilibrium framework. Since then, Heady and Mitra (1984). and Munk (1978, 1980) have relaxed some of the Diamond-Mirrlees assumptions and used computational techniques to derive optimal taxes from stylized models. Our work may be viewed as the next step in that direction, where*we attempt to compute optimal tariffs from an actual model of a particular country. We provide both a theoretical and empirical analysis of the structure of efficient, third-best revenue constrained tariffs. In addition, we derive new numerical techniques to find directions of local welfare improving reforms - an important issue for policymakers. Both the use of actual data and our analysis of partial reform are similar to Ahmad and Stern's (1983) efforts to assess directions of welfare improving tax reform for India, although they focus exclusively on the demand side -- an important restriction. Additionally, our results support, with quantitative evidence, the importance of the interaction between trade policy and the structure of taxation, as stressed by Dixit (1985). Bovenberg (1986) obtains similar results using a simulation model of Thailand. The plan of the paper is as follows. In section II, we develop a theoretical model and derive optimal tariffs under various assumptions about substitution elasticities and the existing indirect tax structure. In section III, we present a model of Cameroon which is used in section IV to compute optimal tariffs and to compare them with a gniform rate. Section V contains our concluding remarks. Dtsk #17/Thriffs/04-10-86/SDLvarajan-gj c -4- II. REVENUE CONSTRAINED TARIFFS: THEORY Consider the simple case of a small open economy exporting M goods, which we aggregate into one commodity for convenience. 1/ The economy also imports N different goods. Furthermore, we assume sector- specific factors, so the economy is always incompletely specialized. . The production side of the economy is completely described by a revenue function; this revenue function gives the maximum revenue (value added) obtainable from efficient use of the factors of production given producer prices ps: R = Rs (ps;u) (1) where U is the vector of (fixed) factor supplies. The derivative of R with respect to any price yields output supply of the corresponding commodity (Dixit and Norman (1980)): XD 3R (2) i ap s Note that R can incorporate many kinds of production structure. In particular, the input-output structure in the model of section III is a special case. 1/ This can be done without approximation error since we assume world relative prices are fixed. Disk #17/Tariffs/04-10-86/SDevarajan:gjc -5- We describe consumer behaviour through an expenditure function E, yielding the minimum value of expenditure needed to achieve a welfare level U given the vector of consumer prices, pc: E = E(p ;U) (3) The derivative of E with respect to any given price yields the Hicksian demand function for the corresponding commodity: C -- (4) i c api Consumers face the budget constraint R(ps;u) = E(pc;U) (5) Similarly for the government: * * s5 pG = (p - p )R + (p c- p *)E (6) p p * where p is the vector of world prices, and R and E are the vectors of partial derivatives of R and E with respect to p. The RHS of (6) represents government revenue from producer taxes at * s c * rates a = p - p and consumer taxes $ = p - P * If tariffs are the only source of revenue, this can be rapresented by 8 = - a Isk #17/Mhriffs/04-10-86/SDevarajan:gJ c -6- That is, a tariff vector is equivalent to corresponding consumer taxes and producer subsidies. Combining (5) and (6) yields the national budget constraint: R(ps;U) + (p s - p)R = E(pc;U) + (p - pc)E + p G (7) or income equals expenditure, both evaluated at world prices. Equation (5) allows us to rewrite private welfare U, for given world prices p , as a function of a and S: U = U(a,5;p ) (8) Simple differentiation of (8) shows that: aU -1 a- = -E R (8a) Tao U p aU -EU E (8b) 7- U p A tariff vector T implies producer subsidies a= -T and consumer taxes a=T. Hence for tariffs we obtain: --= E (E - R ) (8c) U p where Z is the "net" expenditure function: Z = E - R. DIsk #17/Triffs/04-10-86/SDevarajan*.gj c -7- We will investigate the structure of optimaL revenue- *f constrained taxes. Therefore p G is assumed fixed. It is well known that in the absence of non-distortionary taxes, consumer taxes should be used to raise revenue (Dixit (1985)). This is in many cases not possible for reasons set out in the introduction. We will analyze the "third-best" case where tariffs need to be used for revenue purposes, first at zero producer taxes, and second, for an arbitrary producer tax vector a. The government's problem is to raise revenue T = p G at minimum distortionary cost (maximum private welfare): Max U = U(r; p ) (9) Subject to T'(E - R ) = T p p Consider the empirically important case where only a subset of traded goods can be taxed. In particular, assume that the export good cannot be taxed. 1/ Label this export good "O", and the N import goods from 1 to N. This leads to the constrained optimization problem Min Max U(T;p ) - (T - T"(E - R )) (10) and the associated first order conditions: 1/ Extension to multiple export goods is straightforward but unin- formative. Disk #17/Tariffs/04-10-86/SDevarajan:gjc -8- U = - X(Z' + T'Z + T'ZpUU') (11) -1 -1 Note that Z = (E - R )U = EpuEU 1E and that E EU =CE, a pU pi) pU Ir p UpUT Es vector of income propensities. Hence, (11) can be rearranged to yield: 0 Z T = -(A - XtVC - E 1) Z pp E UI p(1) X = -OZ p Note that Zp is negative definite (there is one untaxed commodity). Therefore, T^Z T = -Z 'T pp p = -GT Thus, G > 0. Since the n x n matrix Z p is of full rank (commodity "0" is not included), (12) can be inverted to yield an expression for the optimal tariff vector T * -OZ Z (13) pp p In general, 6, Z and Z themselves will depend on T ; (13) is therefore a nonlinear expression in T that may or may not have a unique solution. It is instructive to consider some special cases. For example, the case of zero cross pure-substitution effects: Disk #17/Tariffs/04-10-86/SDevarajan:gjc -9- Z a Zp /p for i 7j 0 i *j It follows that p i i- (14) That is, the tariff as a percentage of the market price should b inversely proportional to the net (import) demand elasticity. This is analogous to the Ramsey rule for commodity taxation. There is a second analogy with the Ramsey rule or, more specifically, with the Harberger (1964) interpretation of that rule. Harberger (1964) stresses the importance of the degree of comple- mentarity with leisure. Consider, following Farberger (1964), the simple case of two (import) goods subject to a tariff, and one untaxed (export) good. Also, assume again the special case of zero cross substitution effects between different import goods (Zp = 0 if i0j). Finally, define the net expenditure function Z in s manner similar to the definition of Z, but including the untaxed zero-th commodity (exports). Since Z is homogenous of degree one in prices, Z is homogenous of degree zero. This implies that Z p=0 or, for the special case where Z = 0 for iJ: Disk #17/ITariffs/04-10-86/SDmvarajan:gj c - 10 - pZ + plZ p 0 p Z +p2Z =0 o0 p 2 2 2 Inserting this in the optimal tariff formula yields: Ti G i i 0 az p pO where ei o P, (15) o z ap Pi i the cross-elasticity of import demand with respect to the export price. The interpretation is straightforward. A tariff, through Lerner symmetry (Lerner (1936)), acts as an export tax and causes a socially suboptimal export level. The import that is the closest substitute for i export goods (e large) should therefore be taxed least. Tariffs 0 should be raised most on import goods that are most complementary to the export good, in the sense of having the lower E value. o Consider finally the change in optimal tariffs induced by the existence of suboptimal producer taxes at given rates , apart from the subsidy implied by r>0. We will conduct two experiments, one where the constraint is on the sum of revenues from tariffs and producer taxes (experiment A) and one where we constrain the sum of tariff revenues only (experiment B). A is more straightforward, so we analyse it first. In this case, (10) becomes: Min Max U(a, T) - X(T - T'Z - aiR ) a Tr Disk #17/Tariffs/04-10-86/sD7-m.aJan:gJ c - 11 - Straightforward calculation yields * -1 -1 G= - ZZ - Z R a (16) A pp p pp pp * -1 -1 =-r - (I -R E ) a pp pp The decomposition of (16) is somewhat misleading since in general the * - value of T - EZ1 Z will itself change when a does. pp p The special case of zero cross-elasticities is of interest: -1 then (I - R E ) is diagonal, so that pp pp A i -1 -1 A (1 R E ) >0, (17) La 1ip1 Pipi i.e. higher producer taxes should be offset by higher tariffs. In spite of the intuitive appeal of (17) (after all, a tariff implies a producer subsidy), no such clean cut relation can be ascertained in general. Consider finally the case where tariff revenues themselves are to be constrained, rather than the sum of producer taxes and tariff revenues. A convenient way of modelling this is to assume that producer tax revenues are handed out again to consumers: * * R(p +T-a;v)+aR = E(p +T;U) (18) p dU E -- Z + R a (19) u dr p pp Disk #17/Tariffs/04-10-86/SDevarajan:gjc - 12 - Using (19) yields: Z - T' C Z 1R a TB ppp E pp pp = T + (1 - T' C ) Z1 R a (20) A E pp pp where T'CE < 1 In the special case of diagonal Rpp and E , and ignoring third order derivatives of E and R, we get: 3(T* - T*) 9(T*B - T* (1 ) A(T B -- This is intuitively clear: higher tariffs, through their implied producer subsidy, increase home output and hence revenue from producer taxes. This is more effective, the higher is the corresponding a; so if producer taxes count against revenue requirements, the corresponding tariff rates should be raised more. Thus, it can be seen that the most efficient, revenue- constrained tariff structure depends crucially on the pattern of net demand elasticities and indirect taxation. A practically important question, however, is what the social costs are of adopting a tariff structure that is based on rules-of-thumb like the one advocating DLsk #17/Triff s/04-10-86/SDawarajan:gj c - 13 - uniform tariffs. As a first step towards answering this, we turn in the next section to a description of a CGE model of Cameroon. The model of Cameroon presented here is a special case of the theoretical model of Section II. The production and consumer preference structure are spelled out explicitly, rather than relying on general revenue and expenditure functions. This is done to facilitate calibration on real world data. An explicit input-output structure is introduced, particular separability assumptions are made and so on. III. THE MODEL The structure of the economy analyzed here is shown in Figure 1, giving all commodity and income flows of the economy in the format of a Social Accounting Matrix. The corresponding equations are given below. We also comment on the underlying technological and behavioral assumptions. Activities Accounts The eleven sectors of the economy indexed by (i=1,...,11) each D produce one output good, Xi, using a two-level production function that is separable in intermediate inputs and value added VAi. Inter- mediates are used with fixed coefficient technology. Value added is produced through Cobb-Douglas technology with three labor skill categories and a fixed sector-specific capital stock: D alii a2i 3i a41 VAi =A L 1 L2i L3i K (21) where E a =1 Disk #17/Tariffs/04-10-86/SDevarajan:gj c - 14 - Producers maximize profits. Under perfect competition, this implies that the real product wage rates equal the marginal productivity of the skill categories: XD W Xa VA L (22) pi i where pVA is the price of value added (defined below). pi Wage rates are determined by the condition that all labor markets clear: E L = S(23) i Note that we assume a fixed labor supply. A fixed proportion of the value of domestic output is paid as indirect (production) taxes to the government: PD(1-tD) = PVA + ZA p (24) All prices and wages are measured in terms of the numeraire commodity, imported manufactured goods. Domestic output can be used for sale on the domestic market or for exports: XD XXD + Ei, (25) if 1O i DLsk #17/ Tariffs/04-10-86/ SDe-varajan:gj c 二 16 We assume competitive firm behavior. Hence, the w6rld prices of exports p E are given by i E D E Pi PiO+t P (26) where t E is the export tax on good io i In another deviation from Section II, export demand is downward sloping with constant elasticity, n i : Log E n Log p E (27) i 0 Note that since n is f.',nite, there is a justification for an export tax based on optimal tax considerations. Demand by domestic agents (intermediate, consumer, investment and government demand) is determined by two-level utility functions. At the first level, where total demand is generated, the function varies across components of demand. Intermediate demand is determined by fixed coefficients, as mentioned earlier: INT Z A X i ij J The single representative consumer in the economy is assumed to maximize a Cobb-Douglas utility function: 11 U = 11 C i=1 Disk #17/Tariffs/04-10-86/SDevarajan:gjc - 17 - subject to a budget constraint that household income less *savings is available for consumption. This gives the linear expenditure system (28) as a first order condition: P Ci. =i(Y - SH) (28) Note that this system implies own price and income elasticity of unity and cross price elasticities of zero. Both investment li and government demand Gi are fixed exogenously in this exercise. The second level of the utility function determines the allocation of total demand between imports and domestically produced goods. Here, we assume all the different types of consumers (inter- mediate consumers, households, government, investors) have the same CES function over imports and domestic goods. Hence, we can aggregate across all components of demand for domestic goods to XxD and determine the allocation between this and import demand Mi by: D M p 16 a XxD PM 1-6 X Pi i i where ai is the elasticity of substitution between imported and domestic goods. 1/ 1/ The values used for a are given in the Appendix. Disk #17/Tariffs/04-10-86/SDevarajan:gj c - 18 - The domestic price of imports is given by PM = p (1 + tM (29) where pw is the world price and tM the tariff rate and the composite i i goods price, pi, is determined by p = pDXD + pM . (30) Equilibrium Total supply is met by four demand categories: intermediates, private consumption, government consumption, and investment; where the latter includes both fixed investment and inventories (STi) X= INT + C + G + I + ST (31) 1 i. i I i i Government revenue RG is composed of indirect taxes TD = Et pD D (32) Disk #17/Tariffs/04-10-86/SDevarajan:gjc - 19 - tariff revenues TM = Z i tMPf Mi (33) and revenues from export duties: TE it EE . (34) i Thus, RG = TD + TM + TE (35) Tariff and export duty revenues are handed out in a lump-sum fashion to the households (who also receive all value-added): YVArp'XD + m" + TE Y Z PVA D+TM+ (36) This somewhat artificial assumption is made to eliminate income effects that would otherwise arise from changing export duty rates and tariff rates. 1/ The rest of government revenue is either consumed or saved: 1/ Note that without this assumption, free trade (zero tariffs) can sometimes be inferior to positive tariffs. Disk #17/Tariffs/04-10-86/SDevarajan:gjc - 20 - RG TM TE Z PiG + SG (37) We assume an exogenous current account and exogenous investment, since we are interested in static efficiency only. Hence, private savings SH is residually determined: H G S = Ep.I. - S + CA (38) where I is total use of good j for investment purposes and CA the current account. The model described by (20) - (39) is fully determined if all taxes and tariffs are taken as parameters. It is first solved in this manner to obtain the benchmark base case. Next, the tariff rates are allowed to vary (subject to the revenue constraint (35)) so as to maximize the consumer's utility. This is done through the use of a non-linear optimization package. The particular solution algorithm, is MINOS5 and the language GAMS. (Bisschop and Meeraus (1982], Brooke, Drud and Meeraus [1984]). This procedure has the added advantage of yielding shadow prices attached to constraints; these prices can be derived from the dual solution of the optimization problem and will be used extensively in what follows. Disk #17/Thriffs/04-10-86/SDevarajan:gjc - 21 - IV. RESULTS The. model described in the previous section was calibrated to data of the Cameroonian economy for the year 1979-80. The relevant data are given in the Appendix; for details of the calibration procedure, see Benjamin and Devarajan (1984]. The structure of indirect taxes and import tariffs is, therefore, that which existed in Cameroon at that time. We assume very high export demand elasticities, reflecting Cameroon's weak market power in world markets. All export demand elasticities are set equal to -20, a relatively high number but nevertheless one which implies -- in an undistorted economy -- a positive optimal export tax. To assess the importance of the arguments against uniform tariffs, the model is used to determine optimal tariffs that generate the same level of revenue as before. By "optimal" we mean those tariff rates which maximize the utility of the representative consumer in the economy. However, since ours is a static world, we constrain the tariffs on investment goods -- capil-al goods and cement and base metals -- to remain at their actual 1979-80 levels. If the tariffs on investment goods were also allowed to vary, there will be a tendency to shift the entire tariff burden onto these goods as they play no role in the consumer's (single-period) utility function. We compare the outcome under optimal tariffs with that when the tariffs are constrained to be uniform at the rate that generates the same amount of revenue. As before, the tariffs on investment goods are untouched by this experiment. Disk #17/Tariffs/04-10-86/SDevarajan:gj c - 22 - The wlf are implications of any tariff reform depend crucially on the other indirect taxes in the system. We therefore make various assumptions about the underlying structure of taxation. We take the existing domestic indirect taxes as given or we eliminate them entirely; we set export taxes at zero or we assume they are set optimally. When there exist suboptimal taxes in the system (any domestic indirect tax or a zero export tax, for example), the optimal tariff structure will be affected in an attempt to neutralize the effect of this distorting tax. As we show, this effect is empirically significant. We first consider the impact of all these experiments on private welfare, measured here as the value of the objective function which is the utility of consumption (Table 1). Table 1: Welfare Level Zero Export Taxes Optimal Export Taxes Ind Taxes Ind Tax=O Ind Tax=O Base 191.72 191.72 191.72 Uniform 191.23 192.08 192.26 Optimal 192.08 192.09 192.26 Disk #17/ariffs/04-10-86/SDevarajan:gjc - 23 - Consider first the case when domestic indirect taxes are at their 1979- 80 levels and export taxes are zero (column 1). Among all cases considered in this paper, this represents the one where the rest of the economy is in its most distorted state. Notice that the introduction of uniform tariffs leads to a welfare loss (albeit a small one) when compared to the present tariff structure. Not surprisingly, optimal tariffs lead to a welfare gain. The picture changes somewhat when indirect taxes .are eliminated. The discrepancy between uniform and optimal tariffs narrows considerably. It appears as if the optimal tariffs in the earlier experiment were compensating for the existing domestic taxes. The discrepancy narrows even further when optimal export taxes are introduced. Again, with suboptimal (i.e., zero) export taxes, the optimal tariffs attempt to "simulate" an export tax, thereby achieving a slight welfare gain over the uniform tariffs. Much of this reasoning is confirmed when we examine the tariff rates that actually obtained in each of the experiments (Table 2). Disk #17/Tariffs/04-10-86/SDevarajan:gj c -24- Table 2: Tariff Rates (Indirect Tax Pates in Parentheses) Base Rates OPtfimal Pevenue-onstrained Rates Zero kport Taxes Optimal Icport Taxes Ind Taxes ind Tax=0 Ind Tax=0 (0.02) Food Crops 0.22 -0.06 0.09 0.15 (0.19) Cash Crops 0.23 -0.28 0.13 0.14 (0.06) Forestry 0.28 9.31 0.12 0.14 (0.04) Food Processing 0.35 0.27 0.11 0.15 (0.10) Cbnsumer Goods 0.38 0.28 0.11 0.14 (0.03) Interm. Goods 0.18 0.22 0.15 0.14 (0.00) Services 0.00 0.04 0.19 0.14 UNFORM RATE 0.16 0.15 0.14 Notice that in the presence of indirect taxes and absence of export taxes, the optimal tariff rates vary widely across sectors. Indeed, in the cash crops sec'nr, the optimal tariff is negative. Virtually all the output of this sector is exported so that the sizeable production tax acts like an export tax. The negative optimal tariff, therefore, attempts to dampen the effect of this tax which is clearly excessive in light of an export demand elasticity of -20. The 931 percent tariff on forestry is due to the fact that imports of this commodity are miniscule. As the distortions are progressively removed (reading across Table 2), the optimal tariff structure becomes more uniform. In the Disk #17/Tariffs/04-10-86/SDevarajan:gjc - 25 - least distorted case, it is practically indistinguishable' from the uniform tariff. This also follows from the theory presented in Section II. With fully optimal export taxes, all goods are subject to taxation. However, it is the impossibility to tax all goods that gives rise to non-uniformity; leisure in the standard Ramsey-commodity tax analysis (Ramsey (1927)), Atkinson and Stiglitz (1980)) and exportables in the analysis of Section II. Perhaps more surprising is the fact that the optimal export, tax in these cases is negative (Table 3). This is explained by the fact that the optimal tariffs, through Lerner symmetry, also act as export taxes. However, the level of these tariffs is "too high" (14 percent) for export demand elasticities of -20. Thus, the role of the optimal export tax, in the presence of tariff distortions, is to act as a subsidy in order to achieve the appropriate wedge between world and domestic prices. Table 3: Optimal Export Tax IND TAX=O Base 0.00 Zero Tariffs 0.052 Uniform -0.085 Optimal -0.085 Disk #17/Tariffs/04-10-86/SDevarajan:gjc - 26 - So far, we have been considering cases where the entire tariff structure is changed, either to a uniform or an optimal one. However, it is also useful to consider the social costs of raising or lowering individual tariff rates. We calculate these as follows. We allow the tariff rates to vary along an extremely narrow range (+.001) and calculate their optimal levels (tariffs on investment goods are again again not allowed to vary). Given the revenue constraints, some tariffs will lie on the lower end of the range and others on the upper end. We then report the shadow prices associated with the constraints on tariff rates. These shadow prices are derived from the dual solution of the optimization procedure. They answer the question: what is the social cost of, say, decreasing the tariff on good i, taking into account the fact that some other tariffs will have to rise in order to preserve government revenue? Clearly, such answers are useful in guiding partial tariff reform. In particular, it is often alleged that even if uniform tariffs are not desirable, raising the lowest tariff and lowering the highest leads to a welfare improvement. We can test this assertion in the context of our revenue-constrained economy. Disk #17/Thriffs/04-10-86/SIevarajan:gjc - 27 - As Table 4 shows, the desirable pattern of partial tariff reform. is generally synchronous with the existing tariff structure, although there are exceptions. For example, in all four cases, a decrease in the highest tariff -- that on consumer goods -- is welfare- improving, as is an increase in the lowest (services). However, note that in the presence of indirect taxes, an increase in the tariff on cash crops is called for -- even though the optimal tariff for this commodity (i.e. when all other tariffs are allowed to attain their optimal levels) is negative. Thus, not just the magnitude but the direction of change is altered when going from partial to global tariff reform. This is, of course, consistent with the fact that the objective function is not concave with respect to the set of policy instruments. That the presence of other distortionary taxes alters rules-of-thumb based on first-best principles is reinforced by reading across Table 4. As the economy becomes increasingly less distorted (going from left to right) the pattern of partial reform more closely approximates the rule of "lower the highest and raise the lowest" tariff. Disk #17/Tariffs/04-10-86/SDevarajan:gjc - 28 - Table 4: Shadow Prices: Evaluated at Existing Tariff Levels Zero Export Taxes Optimal Export Taxes Ind Taxes Ind Tax=0 Ind Tax Ind Tax=0 Food Crops -0.01 0.02 -0.02 -0.01 Cash Crops 0.46 -0.02 .03 -0.02 Forestry 0.00 0.00 0.00 0.00 Food Processing -0.85 -0.23 -.35 -.34 Consumer Goods -1.85 -0.62 -.83 -.85 Interm. Goods 0.00 0.00 0.00 .21 Services 2.23 0.94 0.94 1.12 In Table 5, the shadow prices corresponding to uniform tariffs are presented. These confirm the point made earlier, namely, that uniform tariffs are nearly optimal when the rest of the tax system is optimal. However, when this condition does not hold (column 1), there are significant welfare gains from deviating, even partially, from a uniform structure. Disk #17/Tariffs/04-10-86/SDevarajan:gjc - 29 - Table 5: Shadow Prices: Evaluated at Uniform Tariffs Zero Export Taxes Optimal Export Taxes Ind Taxes Ind Tax=O Ind Tax Ind Tax=O Food Crops -0.63 0.03 -0.01 -0.00 Cash Crops -4.20 -0.01 0.06 0.00 Forestry 0.02 0.00 0.00 0.00 Food Processing 3.40 -0.13 0.02 0.01 Consumer Goods 7.50 -0.26 0.11 0.02 Interm. Goods 1.90 0.17 0.00 -0.02 Services -8.00 0.25 -0.02 -0.01 Disk #17/Thriffs/04-10-86/SDevarajan:gjc - 30 - V. CONCLUSIONS In this paper, we addressed the issue of revenue constrained partial tariff reform. This is an increasingly important issue, as more and more countries are caught between the conflicting demands of restoring price efficiency through reducing tariffs, and preserving government revenues. Where the second best option of using consumer taxes for revenue is not available in the immediate future, tariffs will remain an important "third best" source of revenues. In the theoretical part of the paper, we derived instructive formulae clarifying the optimal structure of revenue raising tariffs. We demonstrated the importance of net import demand elasticities and complementarity with untaxed export goods, in an analogy with the Ramsey rule for commodity taxation. We further analyzed the empirically important case of revenue raising tariffs in the presence of distortionary producer taxes. These were shown to modify the optimal tariff structure in an intuitive manner. We then conducted numerical experiments with an eleven sector general equilibrium model of Cameroon. We calculated optimal revenue constrained tariffs and compared them with the uniform rate that generates the same revenue. In addition, we calculated the social cost of changing individual tariff rates. Our major conclusion was that replacing the existing tariff structure with a uniform rate can lead to significant welfare losses as long as the other taxes in the economy remain suboptimal. For example, Disk #17/Tariffs/04-10-86/SDevarajan:gj c - 31 - in the case of Cameroon, if existing domestic indirect taxes are untouched by the reform, then the optimal tariffs are by no means uniform. If, however, the rest of the taxes are set optimally, then a uniform tariff rate is very close to the optimum, even in a revenue- constrained economy. We also found that changes in individual tariff rates can have very different implications for social welfare -- in sign as well as in magnitude -- when compared to complete tariff reform. As for the implications of our results for policy, this paper should not be viewed as either supporting or opposing uniform tariff rates in developing countries. Rather, it is an attempt to calibrate one of the costs of this policy, against which the other benefits must be measured before making a recommendation. As we show in the paper, the use of rules-of-thumb such as advocacy of a uniform tariff structure can be seriously misleading in a distorted economy. Unfortunately, robust rules-of-thumb for "second-best" economies are hard to come by. Nevertheless, our results indicate that knowledge of the existing tax system and estimates of some key elasticities, all tempered with the judgement of the policymaker, can be a useful guide to tariff reform in a revenue-constrained economy. isk #17/Tariffs/04-10-86/SDevarajan:gjc - 32 - REFERENCES Atkinson, A.B. and J.E. Stiglitz, (1980). Lectures on Public Economics, McGraw-Hill. Ahmad, S.E. and N.H. Stern, (1981). "On the Evaluation of Indirect Tax System: An Application to India". DERC Discussion Paper No. 1. University of Warwick. Benjamin, N. and S. Devarajan, (1985). "Final Report on a Social Accounting Matrix and Computable General Equilibrium Model of Cameroon," West Africa Country Programs Department, World Bank. Bisschop, J. and A. Meeraus, "On the Developmeit of a General Algebraic Modeling System in a Strategic Planning EnvAronment", Mathematical Programming Study, Vol. 20 (1982), pp. 1-29. Bovenberg, L. (1986) "Indirect Taxation in Developing Countries: A General Equilibr4um Approach." Fiscal Affairs Department, International Monecary Fund Brooke, A., A. Drud and A. Meeraus, "High Level Modeling Systems and Nonlinear Programming", DRD Discussion Paper Report No. Revised DRD113, Appeared in Nonlinear Optimization, 1984, P.T. Boggs, R.H. Byrd, and R.E. Schnabell (eds.), p. 178-198, SIAM, Philadelphia, 1985. Diamond, P.A. and J.A. Mirrlees, (1971). "Optimal Taxation and Public Production: I and II". American Economic Review 61: 8-27 and 261-278. Dixit, A. (1985). "Tax Policy in Open Economies," in Auerbach, A.J.and Feldstein, M. eds., Handbook of Public Economics, Amsterdam, North Holland. Dixit, A. and V. Norman, (1980). Theory of International Trade, Welwyn: Nisbets. Harberger, A. (1964). "Taxation, Resource Allocation and Welfare," in Due, J. ed., The Role of Direct and Indirect Taxes in the Federal Reserve System, Princeton: Princeton University Press. Heady, C.J. and P.K. Mitra, (1984). "Distributional and Revenue Raising Arguments for Tariffs". Mimeo. Lerner, A.P. (1936). "The Symmetry between Import and Export Taxes," Economica, Vol. III, August. Disk #17/Thriffs/04-10-86/SDevarajan:gjc - 33 - Munk, K.J. (1980). "Optimal Taxation with Some Non-taxable Comaodities," Review of Economic Studies, Vol. 47, 755-765. Ramsey, F.P. (1927). "A Contribution to the Theory of Taxation," Economic Journal, Vol. 37, pp. 47-61. Disk #17/Tariffs/04-10-86/SDevarajan:gj c OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE GAMS 2.00 IBM CMS 2 SET I SECTORS /AG-SUBSIST FOOD CROPS 3 AG-EXP+IND CASH CROPS 4 SYLVICULT FORESTRY 5 IND-ALIM FOOD PROCESSING 6 BIENS-CONS CONSUMER GOODS 7 BIENS-INT INTERMEDIATE GOODS 8 CIM-INT CONSTRUCTION MATERIALS 9 BIENS-CAP CAPITAL GOODS 10 CONSTRUCT CONSTRUCTION 11 SERVICES PRIVATE SERVICES 12 PUBLIQUES PUBLIC SERVICES / 13 14 ICll) SECTORS WITH CONSTANT TARIFF RATES 15 IT(l) TRADED SECTORS 16 IN(I) NONTRADED SECTORS 17 LC LABOR CATEGORIES / RURAL , URBAN-UNSK URBAN-SKIL / 1B ALIAS (1,J) 19 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 2 PARAMETERS GAMS 2.00 IBM CMS 21 22 PARAMETER DELTAU) ARMINGTON FUNCTION SHARE PARAMETER (UNITY) 23 ACMI ARMINGTON FUNCTION SHIFT PARAMETER (UNITY) 24 RHOC(I) ARMINGTON FUNCTION EXPONENT (UNITY) 25 ETAMI EXPORT DEMAND ELASTICITY (UNITY) 26 AD(l) PRODUCTION FUNCTION SHIFT PARAMETER (UNITY) 27 CLESMI PRIVATE CONSUMPTION SHARES (UNITY) 28 GLES(I) GOVERNMENT CONSUMPTION SHARES (UNITY) 29 TMOMI TARIFF RATES (UNITY) 30 ITAX(I) INDIRECT TAX RATES (UNITY) 31 ALPHL(LC,I) LABOR SHARE PARAMETER IN PRODUCTION FUNCTION (UNITY) 32 33 *DUMMIES TO HOLD INITIAL DATA 34 35 MOOI) VOLUME OF IMPORTS ('79-80 BILL CFAF) 36 EOMI VOLUME OF EXPORTS ('79-80 BILL CFAF) 37 XDOMI VOLUME OF DOMESTIC OUTPUT BY SECTOR ('79-80 BILL CFAF) 38 KOMI VOLUME OF CAPITAL STOCKS BY SECTOR ('79-80 BILL CFAF) 39 (I) M VOLUME OF INVESTMENT BY SECTOR OF ORIGIN ('79-80 BILL CFAF) 40 DSTO(I) VOLUME OF INVENTORY INVESTMENT BY SECTOR ('79-80 BILL CFAF) 41 INTOMI VOLUME OF INTERMEDIATE INPUT DEMANDS ('79-80 BILL CFAF) 42 XXDO(I) VOLUME OF DOMESTIC SALES BY SECTOR ('79-80 BILL CFAF) 43 XOMI VOLUME OF COMPOSITE GOOD SUPPLY ('79-80 BILL CFAF) 44 PWEO(I) WORLD MARKET PRICE OF EXPORTS (UNITY) 45 PWMO(I) WORLD MARKET PRICE OF IMPORTS (UNITY) 46 PD0(M DOMESTIC GOOD PRICE (UNITY) 47 PEO(I) DOMESTIC PRICE OF EXPORTS (UNITY) 48 PMOMI DOMESTIC PRICE OF IMPORTS (UNITY) 49 PVAO(I) VALUE ADDED PRICE BY SECTOR (UNITY) 50 QD(I) DUMMY VARIABLE FOR COMPUTING AD(I) (UNITY) 51 XLLB(I.LC) DUMMY VARIABLE (L MATRIX WITH NO ZEROS) (UNITY) 52 WAO(LC) AVERAGE WAGE RATE BY LABOR CATEGORY ('79-80 MILL CFAF PR WORKER) 53 LD(LC) EMPLOYMENT (1000 PERSONS) 54 LSO(LC) LABOR SUPPLIES BY CATEGORY (1000 PERSONS) 55 26v 274 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 3 BASE DATA GAMS 2.00 IBM CMS 57 WAO("RURAL") = .11 58 WAO("URBAN-UNSK") = .15678 59 WAO("URBAN-SKIL") = 1.8657 60 61 SCALAR 62 ERO EXCHANGE RATE / 1 / 63 GRO GOVERNMENT REVENUE / 76.54692 / 64 GDTOTO INITIAL GOVERNMENT CONSUMPTION / 135.03 / 65 CDTOTO INITIAL PRIVATE CONSUMPTON / 947.98 / 66 FSAVO FOREIGN SAVING (FOREIGN CURRENCY) / 7.71825 / 67 68 69 TABLE IO(I.J) INPUT-OUTPUT COEFFICIENTS 70 71 AG-SUBSIST AG-EXP+IND SYLVICULT IND-ALIM BIENS-CONS BIENS-INT CIM-INT BIENS-CAP CONSTRUCT SERVICES PUBLIQUES 72 73 AG-SUBSIST .03046 .30266 .00206 .04120 74 AG-EXP+IND .01518 .02043 .01123 .00669 75 SYLVICULT .00243 .02106 76 IND-ALIM .00341 .00629 .03241 .01234 .00503 .00092 .01532 77 BIENS-CONS .00105 .05385 .00435 .00103 .00338 78 BIENS-INT .00676 .12385 .02095 .03794 .08309 .23461 .18289 .01567 .14665 .00929 .08466 79 CIM-INT .00002 .00025 .00017 .11238 .05095 .05593 .27608 .11722 .18643 .00018 80 BIENS-CAP .00041 .00971 .02427 .00931 .01229 .05259 .02053 .05013 .02622 .00389 81 CONSTRUCT .00472 .00113 .00318 .10456 .01831 .05302 .00172 .00031 .01457 .00385 .00394 82 SERVICES .00375 .30649 .26666 .10100 .26072 .23006 .11793 .09922 .13692 .13728 .24145 83 PUBLIQUES .00022 .00293 .00327 .00536 .00539 .00957 .00486 .00081 .00447 .00219 84 85 PARAMETER EMPL(I,LC) EMPLOYMENT MAPPING 86 EMPL(I.LC) = 1 ; EMPL("AG-SUBSIST","URBAN-SKIL") = 0 ; EMPL("PUBLIQUES","RURAL") = 0 87 88 TABLE XLE(I,LC) LABOR BY SECTOR AND CATEGORY 89 90 RURAL URBAN-UNSK URBAN-SKIL 91 92 AG-SUBSIST 1654.43 162.89 93 AG-EXP+IND 399.93 45.50800 5.05700 94 SYLVICULT 7.66200 1.78900 .59700 95 IND-ALIM 12.98900 9.43400 2.35800 96 BIENS-CONS 28.34400 37.46200 12.48800 97 BIENS-INT 18.33100 16.55300 8.30000 98 CIM-INT 1.45800 1.31700 .66000 99 BIENS-CAP 3.11200 2.82000 1.20800 100 CONSTRUCT 22.58400 28.46200 7.11600 101 SERVICES 121.20 125.80 61.96000 102 PUBLIQUES 83.02900 32.77100 103 104 TABLE ZZ(*,I) PARAMETERS AND INITIAL CONDITIONS 105 106 AG-SUBSIST AG-EXP+IND SYLVICULT IND-ALIM BIENS-CONS BIENS-INT CIM-INT BIENS-CAP CONSTRUCT SERVICES PUBLIQUES 107 108 MO 2.46100 8.03900 .02300 17.96100 37.06200 138.57 49.61600 134.72 74.43900 109 EO 4.59400 125.07 22.33700 23.45100 5.86400 101.33 10.50100 3.83800 81.62600 110 XDO 330.48 131.45 29.50300 72.02400 118.43 284.38 34.16900 10.29800 174.12 615.7900 163.98 111 K 495.73 170.89 73.76000 .14E+03 236.87 853.13 102.5100 20.60000 435.29 769.7300 180.36 112 RHOC 1.50000 .90000 .40000 1.25000 1.25000 .50000 .75000 .40000 .40000 .40000 .40000 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 4 BASE DATA GAMS 2.00 IBM CMS 113 ETA 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 114 TM .22050 .23300 .27800 .35340 .38260 .17680 .26330 .26800 115 ITAX .002 .191 .057 .038 .096 .026 .014 .029 .034 .076 116 CLES .27440 .00445 .05599 .14099 .17738 .00400 .31921 .02358 117 GLES 1.00000 118 DST 4.03300 3.50900 1.02500 3.19000 7.10100 3.49400 .43300 119 ID 6.71000 113.360 138.130 120 121 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 5 COMPUTATION OF PARAMETERS AND COEFFICIENTS FOR CALIBRATION GAMS 2,0 IBM CMS 123 124 RHOC(I) = (1/ZZ("RH0C",I)) - 1 125 ETA(I) = ZZ("ETA",I); 126 TMO(I) = zz("TM",J). 127 ITAX(I) = ZZ("ITAX",I) 128 CLES(I) = ZZ("CLES",I); 129 GLES(I) = ZZ("GLES",I); 130 XLLB(I,LC) = XLE(I,LC) + (1 - SIGN(XLE(I,LC))); 131 132 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 6 INITIALIZATION OF VARIABLES FOR CALIBRATION GAMS 2.00 IBM CMS 134 135 MO(I) = ZZ("MO",I); 136 IT(') = YES$MO(I); 137 IN(I) = NOT IT(M); 138 IC(I) = NO ; 139 IC(I)SIT(I) = YES 140 EO(I) = ZZ("EO",I); 141 XDO(I) = ZZ("XDO",I); 142 KO(I) = ZZ("K",1); 143 PDO(I) = 1 144 PMO(I) = 1 145 PEO(I) = 1 146 PWMO(I) = PMO(I)/((1+TMO(I))*ERO) 147 PWEO(I) = PEO(I)/ERO 148 PVAO(I) = PDO(I) - SUM(J, IO(J.I)*PDO(J) ) - ITAX(I) 149 XXDO(I) = XDO(M) - EOI); 150 OSTO(I) = ZZ("OST",I); 151 IDD(I) = ZZ("ID",I); 152 LSO(LC) = SUM(1, XLE(I,LC) ); 153 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH UOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 7 CALIBRATION OF ALL SHIFT AND SHARE PARAMETERS GAMS 2.00 IBM CASS 155 156 * GET DELTA FROM COSTMIN, XO FROM ABSORPTION, AC FROM ARMINGTON 157 DELTA(IT)$MD(IT) = PMD(IT)/PDD(IT)*(MO(IT)/XXDO(IT))**(1+RHOC(IT)) 158 DELTA(IT) = DELTA(IT)/(l+DELTA(IT)) ; 159 XO(I) = PDO(I)*XXDO(I) + (PMO(I)*'MO(I))SIT(I) 160 AC(IT) = XO(IT)/(DELTA(IT)*MDCIT)**(-RHOC(IT)) + (1-DELTA(IT))*XXDO(IT)**(-RHOC(IT)))**(-1/RHOC(IT)) 161 162 * GET INTO FROM INTEQ, GAMMA FROM ESUPPLY, ALPHL FROM PROFITMAX 163 INTO(I) = SUM(J, IO(I,J)*XDO(J) ); 164 ALPHL(LC.I) = (EMPL(I.LC) * WAO(LC) * XLE(I,LC)) /(PVAO(I)*XDO(I)); 165 166 * GET AD FROM OUTPUT, LD FROM PROFITMAX, AT FROM CET 167 QD(I) = (XLLB(I,"RURAL")**ALPHL("RURAL",I))*(XLLB(I."URBAN-UNSK")**ALPHL("URBAN-UNSK".I)) 168 *(XLLB(I,"',RBAN-SKIL")**ALPHL("URBAN-SKIL",I))*(KO(I)**(1 - SUM(LC, ALPHL(LC,I))) ) 169 AD(I) = XDO(I)/QD(I); 170 LP(LC) = SUM(I, (XDO(I)*PVAO(I)*ALPHL(LC,I)/(EMPL(I,LC)*WAO(LC)))$EMPL(I,LC)); 171 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 8 MODEL DEFINITION - VARIABLES GAMS 2.00 IBM CMS 173 VARIABLES 174 PD(I) DOMESTIC PRICES (UNITY) 175 PM(I) DOMESTIC PRICE OF IMPORTS (UNITY) 176 PE(I) DOMESTIC PRICE OF EXPORTS (UNITY) 177 PK(I) RATE OF CAPITAL RENT BY SECTOR (UNITY) 178 PX(I) AVERAGE OUTPUT PRICE BY SECTOR (UNITY) 179 PCI) PRICE OF COMPOSITE GOODS (UNITY) 180 PVACI) VALUE ADDED PRICE BY SECTOR (UNITY) 181 PWMCI) WORLD MARKET PRICE OF IMPORTS (UNITY) 182 PWE(I) WORLD MARKET PRICE OF EXPORTS (UNITY) 183 TM(I) TARIFF RATES (UNITY) 184 ER EXCHANGE RATE (UNITY) 185 TEM EXPORT TAX RATES (UNITY) 186 TMAVG AVERAGE TARIFF RATE (UNITY) 187 XCI) COMPOSITE GOODS SUPPLY ('79-80 BILL CFAF) 188 XD(I) DOMESTIC OUTPUT BY SECTOR ('79-80 BILL CFAF) 189 XXD(I) DOMESTIC SALES ('79-80 BILL CFAF) 190 E(I) EXPORTS BY SECTOR ('79-80 BILL CFAF) 191 M(I) IMPORTS ('79-80 BILL CFAF) 192 K(I) CAPITAL STOCK BY SECTOR ('79-80 BILL CFAF) 193 WA(LC) AVERAGE WAGE RATE BY LABOR CATEGORY (CURR MILL. CFAF PR PERSON) 194 LS(LC) LABOR SUPPLY BY LABOR CATEGORY (1000 PERSONS) 195 L(I.LC) EMPLOYMENT BY SECTOR AND LABOR CATEGORY (1000 PERSONS) 196 INTMI INTERMEDIATES USES ('79-80 BILL CFAF) 197 CDCI) FINAL DEMAND FOR PRIVATE CONSUMPTION ('79-80 BILL CFAF) 198 GD(I) FINAL DEMAND FOR GOVERNMENT CONSUMPTION ('79-80 BILL CFAF) 199 ID(I) FINAL DEMAND FOR PRODUCTIVE INVESTMENT ('79-80 BILL CFAF) 200 DSTMI INVENTORY INVESTMENT BY SECTOR ('79-80 BILL CFAF) 201 V PRIVATE GOP (CURR BILL CFAF) 202 GR GOVERNMENT REVENUE (CURR BILL CFAF) 203 TARIFF TARIFF REVENUE (CURR BILL CFAF) 204* INDTAX INDIRECT TAX REVENUE (CURR BILL CFAF) 205 DUTY EXPORT DUTY REVENUE CCURR BILL CFAF) 206 GDTOT TOTAL VOLUME OF GOVERNMENT CONSUMPTION ('79-80 BILL CFAF) 207 MPS MARGINAL PROPENSITY TO SAVE (UNITY) 20Q HHSAV TOTAL HOUSEHOLD SAVINGS (CURR BILL CFAF) 209 GOVSAV GOVERNMENT SAVINGS (CURR BILL CFAF) 210 DEPRECIA TOTAL DEPRECIATION EXPENDITURE (CURR BILL CFAF) 211 SAVINGS TOTAL SAVINGS (CURR BILL CFAF) 212 FSAV FOREIGN SAVINGS (CURR BILL DOLLARS) 213 DK(I) VOLUME OF INVESTMENT BY SECTOR OF DESTINATION ('79-80 BILL CFAF) 214 *WELFARE INDICATOR FOR OBJECTIVE FUNCTION 215 UTILITY OBJECTIVE FUNCTION VARIABLE ('79-80 BILL CFAF) 216 217 218 P.LO(I) =.1 ;PD.LOCI) = .1 ;PM.LO(IT) =.I; PWE.LOCIT) = .1 X.LO(I) = .1 219 XD.LO(I) =.1 M.LO(IT) =.01 ;XXD.LO(IT) = .01 ; WA.LO(LC) .01 ; INT.LO(I) =.1 Y.LO .1 220 E.LO(IT) =.1 L.LO(I,LC) .01 ;CD.LO(I)$CLES(I) = .1 221 222 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 9 MODEL DEFINITION - EQUATIONS GAMS 2.00 IBM CMS 224 EQUATIONS 225 PMDEF(I) DEFINITION OF DOMESTIC IMPORT PRICES (UNITY) 226 PEDEF(I) DEFINITION OF DOMESTIC EXPORT PRICES (UNITY) 227 PDPEEQUAL(I) PRICE EQUALIZATION (UNITY) 228 ABSORPTION(I) VALUE OF DOMESTIC SALES (CURR BILL CFAF) 229 SALES(I) VALUE OF DOMESTIC OUTPUT (CURR BILL CFAF) 230 ACTP(I) DEFINITION OF ACTIVITY PRICES (UNITY) 231 TMEQ(I) TARIFF RATE EQUALIZATION (UNITY) 232 TMSH1 FIXED TARIFF RATES (UNITY) 233 TMSH2 FIXED TARIFF RATES (UNITY) 234 ACTIVITY(I) PRODUCTION FUNCTION ('79-80 BILL CFAF) 235 PROFITMAX(I,LC) FIRST ORDER CONDITION FOR PROFIT MAXIMUM (1000 PERSONS) 236 LMEQUIL(LC) LABOR MARKET EQUILIBRIUM (1000 PERSONS) 237 EDEMAND(I) EXPORT DEMAND (UNITY) 238 ESUPPLYI) EXPORT SUPPLY (UNITY) 239 ARMINGTON(I) COMPOSITE GOOD AGGREGATION FUNCTION ('79-80 BILL CFAF) 240 COSTMIN(I) FIRST ORDER CONDITION FOR COST MINIMIZATION OF COMPOSITE GOOD (UNITY) 241 XXDSN(I) DOMESTIC SALES FOR NONTRADED SECTORS ('79-80 BILL CFAF) 242 XSN(I) COMPOSITE GOOD AGGREGATION FOR NONTRADED SECTORS ('79-80 BILL CFAF) 243 INTEQ(J) TOTAL INTERMEDIATE USES ('79-80 BILL CFAF) 244 CDEQ(I) PRIVATE CONSUMPTION BEHAVIOR (CURR BILL CFAF) 245 DSTEQ(I) INVENTORY INVESTMENT ('79-80 BILL CFAF) 246 GDP PRIVATE GDP (CURR BILL CFAF) 247 GDEQ GOVERNMENT CONSUMPTION BEHAVIOR ('79-80 BILL CFAF) 248 GREQ GOVERNMENT REVENUE (CURR BILL CFAF) 249 TARIFFDEF TARIFF REVENUE (CURR BILL CFAF) 250 INDTAXDEF INDIRECT TAXES ON DOMESTIC PRODUCTION (CURR BILL CFAF) 251 DUTYDEF EXPORT DUTIES (CURR BILL CFAF) 252 HHSAVEQ HOUSEHOLD SAVINGS (CURR BILL CFAF) 253 GRUSE GOVERNMENT SAVINGS (CURR BILL CFAF) 254 DEPREQ DEPRECIATION EXPENDITURE (CURR BILL CFAF) 255 TOTSAV TOTAL SAVINGS (CURR BILL CFAF) 256 CAEQ CURRENT ACCOUNT BALANCE (CURR BILL DOLLAR) 257 ISBAL SAVINGS INVESTMENT BALANCE (CURR BILL CFAF) 258 EQUIL(I) GOODS MARKET EQUILIBRIUM ('79-80 BILL CFAF) 259 OBJ OBJECTIVE FUNCTION ('79-80 BILL CFAF) 260 261 6U~ LLZ UJAVWI =3= (31)wlJ g3)b1i 9 SU ((r)d*ø'r)OI 'r~)nns + (I)VAd =3= «(I)XVlI - )()d*(t)d13V trLz -()LSI)*I3)+ (I)OXX*(I)Od =g= (I)o1X*(I)Xd *(I)sSs Z (11%Ifi()l)+ WG)XX*WQ)d =3= (I)X*WId -Ø)NOIJWUOS9¥ OLI 69z L9Z t13*(II)aMd =R= UlIx):U + OU ORJx)d *(.L)4a0d 99z 99 (UI)WIl + 0).82*(11)WMd =3= (-LI)Wd (1 0)32(lfd tr9 siAlI O100' SW4VD >3019 33lUd, NOIIINIA90 IRCOW 01 9Vd 91:0ZLl 99/Ol/t70 SgX¥1. 133HIGNI 31152WOa H-LIM NOISU3A - -19C0IW 3UnlJntf-15 AI8V-L -1YVII-d0 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 11 OUTPUT AND FACTORS OF PRODUCTION BLOCK GAMS 2.00 IBM CMS 283 284 ACTIVITY(I).. XD(I) E AD(I) * PROD(LC$EMPL(I,LC), L(I,LC)**ALPHL(LC.1) )*K(I)**(- SUM(LC. ALPHL(LC,I)) 285 286 EDEMAND(IT).. E(IT)/EO(IT) E ( PWEO(IT)/PWE(IT) )**ETA(IT) 287 288 ESUPPLY%IT).. XD(IT) E XXD(IT) + E(IT) 289 290 ARMINGTON(IT).. X(IT) E AC(IT)*(DELTA(IT)*M(IT)**(-RHOC(IT)) + (I-DELTA(IT))*XXD(IT)**(-RHOCCIT)))**(-I/RHOC(IT)) 291 292 COSTMIN(IT).. M(IT)/XXD(IT) E= PD(IT)/PM(IT)*DELTA(IT)/(I-DELTA(IT)) )**(]/(I RHOC(IT))) 293 294 XXDSN(IN).. XXD(IN) E XD(IN) 295 296 XSN(IN).. X(IN) E XXD(IN) 297 298 PROFITMAX(I,LC)$EMPL(I,LC).. WA(LC)*EMPL(I,LC)*L(I,LC) LE XD(I)*PVA(I)*ALPHL(LCI)); 299 300 LMEQUIL(LC).. SUM(I L(ILC) =E LS(LC); 301 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 12 DEMAND BLOCK GAMS 2.00 IBM CMS 303 304 INTEQ(J).. INT(J) =E= SUM(I, IO(J,I)#XD(I) ); 305 306 CDEQ(I).. P(I)*CD(I) =E= CLES(I)*(V - HHSAV) 307 308 GDP.. V =E= SUM(l, PVA(I)*XD(I) ) + TARIFF + DUTY 309 310 GDEQ(I).. GD(I) =E= GLES(I)*GDTOT 311 312 TARIFFDEF.. TARIFF =E= SUM(IT, TM(IT)*M(IT)*PWM(IT) )*ER 313 314 DUTYDEF.. DUTY =E= SUM(IT, TE(IT)*PE(IT)*E(IT)) 315 316 INDTAXDEF.. INDTAX =E= SUM(I, ITAX(I)OPX(I)*XD(I) ) 317 318 GREQ.. GR =E= TARIFF + DUTY + INDTAX 319 긔 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 14 MARKET CLEARING GAMS 2.00 IBM CM$ 331 332 EQUIL(T).. X(I) =E= INT(I) + CD(I) + GD(I) + ID(I) + DST(I) 333 334 OBJ..' UTILITY =E= PROD(I$CLES(I). CD(I)**CLES(I)) 335 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 15 MODEL SETUP - INITIALIZATION GAMS 2.00 IBM CMS 337 338 Y.L(I) = XO(I) 339 XD.L(I) = XDO(I); 340 XXD.L(I) = XXDO(I); 341 CD.L(I) = CLES(I) * CDTOTO; 342 M.L(I) = MO(I); 343 E.L(I) = EO(I); 344 ID.L(I) = IDO(I); 345 DST.L(I) = DSTO(I)4 346 INT.L(IM) = INTO(I); 347 PD.L(I) = PDO(I); 348 PM.L(I) = PMO(I); 349 PE.L(I) = PEO(I); 350 P.L(I) = PDO(I); 351 PVA.L(I) = PVAO(I); 352 PWE.L(I) = PWEO(I); 353 WA.L(LC) = WAO(LC); 354 L.L(I,LC)= XLE(I,LC); 355 GR.L = GRO; 356 GOVSAV.L = -32.58585 357 TARIFF.L = 76.54692 358 Y.L = SUM(I, PVAO(I)*XDO(I) ) + TARIFF.L 359 GD.L("PUBLIQUES") = 135.03; 360 INDTAX.L = 102.45 361 SAVINGS.L= 280.97 362 FSAV.L = FSAVO 363 TM.L(I) = TMO(I) 364 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 36 CLOSURE GAMS 2.00 IBM CMS 366 367 K.FX(I) = KO(I); 368 PWM.FX(I) = PWMO(I); 369 LS.FX(LC) = LSO(LC); 370 ER.FX = ERO; 371 FSAV.FX = FSAVO 372 DST.FX(I) = DSTO(I) 373 ID.FX(I) = IDO(I) 374 GDTOT.FX = GDTOTO; 375 M.FX(IN) = 0; 376 L.FX("PUBLIQUES","RURAL") = 0; 377 L.FX("AG-SUBSIST","URBAN-SKIL") = 0; 378 E.FX(IN) 0; 379 * TARIFF.FX = 76.54692 380 * TM.FX("SERVICES") = 0 381 TM.FX(IT) = TM0(IT) 382 * TM.FX("BIENS-CAP") = TMO("BIENS-CAP") 383 * TM.FX(IT) = 0 384 * TE.FX(IT) = 0 385 * TM.LO(IT) = .999*TMO(IT) 386 * TM.UP(IT) = 1.001*TMO(IT) 387 * TM.LO("SERVICES") = -.001 388 * TM.UP("SERVICES") = .001 389 TE.LO(IT) = -INF; 390 TE.UP(IT) = INF; 391 392 MODEL CAMCGE2 MODIFIED SQUARE CAMCGE / 393 PMDEF, PEDEF, POPEEQUAL, ABSORPTION, SALES, ACTP, ACTIVITY, EDEMAND. ESUPPLY, ARMINGTON, COSTMIN 394 XXDSN, XSN, PROFITMAX, LMEQUIL, INTEQ, CDEQ, GDP, GDEQ. TARIFFDEF, DUTVDEF, I"DTAXDEF, GREQ, GRUSE 395 TOTSAV, CAEQ, EQUIL, OBJ / 396 397 MODEL SHADOW MODIFIED CAMCGE TO GIVE SHADOW PRICES AND FIND OPTIMAL EXPORT TAX / 398 PMDEF, PEDEF, PDPEEQUAL, ABSORPTION, SALES, ACTP, ACTIVITY, EDEMAND, ESUPPLY, ARMINGTON, COSTMIN, TMSHI, TMSH2 399 XXDSN, XSN, PROFITMAX, LMEQUIL, INTEQ, CDEQ. GDP, GDEQ. TARIFFDEF, DUTYDEF, INDTAXDEF, GREQ, GRUSE 400 TOTSAV, CAEQ, EQUIL, 08J / 401 402 MODEL OPTIMALTE MODIFIED CAMCGE TO GIVE SHADOW PRICES AND FIND OPTIMAL EXPORT TAX / 403 PMDEF, PEDEF, PDPEEQUAL, ABSORPTION. SALES, ACTP, ACTIVITY, EDEMAND, ESUPPLY, ARMINGTON, COSTMIN 404 XXDSN, XSN, PROFITMAX, LMEQUIL, INTEQ, CDEQ, GDP, GDEQ, TARIFFDEF, DUTVDEF, INDTAXDEF, GREQ, GRUSE 405 TOTSAV, CAEQ, EQUIL, OBJ / 406 407 MODEL FLAT FLAT TARIFF STRUCTURE / 408 PMDEF, PEDEF, PDPEEQUAL, ABSORPTION, SALES, ACTP, TMEQ, ACTIVITY, EDEMAND, ESUPPLY, ARMINGTON, COSTMIN, TMSHI.TMSH2 409 XXDSN, XSN, PROFITMAX, LMEQUIL. INTEQ, CDEQ, GDP, GDEQ, TARIFFDEF, DUTYDEF, INDTAXDEF, GREQ, GRUSE 410 TOTSAV, CAEQ, EQUIL, OBJ / 411 412 MODEL OPTIMAL OPTIMAL TARIFF STRUCTURE / 413 PMDEF, PEDEF, PDPEEQUAL, ABSORPTION, SALES, ACTP, ACTIVITY, EDEMAND, ESUPPLY, ARMINGTON, COSTMIN 414 XXDSN, XSN. PROFITMAX, LMEQUIL, INTEQ, LDEQ, GDP, GDEQ, TARIFFDEF, DUTYDEF, INOTAXDEF, GREQ. GRUSE 41$ TOTSAV, CAEQ, EQUIL, OBJ / 416 417 OPTIONS LIMROW=O,LIMCOL=O,ITERLIM=1000,RESLIM=200 418 419 SOLVE SHADOW MAXIMIZING UTILITY USING NLP; OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 17 SYMBOL LISTING GAMS 2.00 IBM CMS SYMBOL TYPE REFERENCES ABSORPTION EQU DECLARED 228 DEFINED 270 IMPL-ASN 419 REF 393 398 403 408 413 AC PARAM DECLARED 23 ASSIGNED 160 REF 290 ACTIVITY EQU DECLARED 234 DEFINED 284 IMPL-ASN 419 REF 393 398 403 408 413 ACTP EQU DECLARED 230 DEFINED 274 IMPL-ASN 419 REF 393 398 403 408 413 AD PARAM DECLARED 26 ASSIGNED 169 REF 284 ALPHL PARAM DECLARED 31 ASSIGNED 164 REF 2*167 2*168 170 2*284 298 ARMINGTON EQU DECLARED 239 DEFINED 290 IMPL-ASN 419 REF 393 398 403 408 413 CAEQ EQU DECLARED 256 DEFINED 328 IMPL-ASN 419 REF 395 400 405 410 415 CAMCGE2 MODEL DECLARED 392 DEFINED 392 CD VAR DECLARED 197 IMPL-ASN 419 ASSIGNED 220 341 REF 306 332 334 CDEQ EQU DECLARED 244 DEFINED 306 IMPL-ASN 419 REF 394 399 404 409 414 CDTOTO PARAM DECLARED 65 DEFINED 65 REF 341 CLES PARAM DECLARED 27 ASSIGNED 128 REF 220 306 2*334 341 COSTMIN EQU DECLARED 240 DEFINED 292 IMPL-ASN 419 REF 393 398 403 408 413 DELTA PARAM DECLARED 22 ASSIGNED 157 158 REF 2*158 2*160 2*290 2*292 DEPRECIA VAR DECLARED 210 DEPREQ EQU DECLARED 254 DK VAR DECLARED 213 DST VAR DECLARED 200 IMPL-ASN 419 ASSIGNED 345 372 REF 326 332 DSTEQ EQU DECLARED 245 DSTO PARAM DECLARED 40 ASSIGNED 150 REF 345 372 DUTY VAR DECLARED 205 IMPL-ASN 419 REF 308 314 318 322 DUTYDEF EQU DECLARED 251 DEFINED 314 IMPL-ASN 419 REF 394 399 404 409 414 E VAR DECLARED 190 IMPL-ASN 419 ASSIGNED 220 343 378 REF 272 286 288 314 328 EDEMAND EQU DECLARED 237 DEFINED 286 IMPL-ASN 419 REF 393 398 403 408 413 EMPL PARAM DECLARED 85 ASSIGNED 3*86 REF 164 2*170 284 2*298 EQUIL EQU DECLARED 258 DEFINED 332 IMPL-ASN 419 REF 395 400 405 410 415 ER VAR DECLARED 184 IMPL-ASN 419 ASSIGNED 370 REF 264 266 312 324 - ERO PARAM DECLARED 62 DEFINED 62 REF 146 147 370 ESUPPLY EQU DECLARED 238 DEFINED 288 IMPL-ASN 419 REF 393 398 403 408 413 ETA PARAM DECLARED 25 ASSIGNED 125 REF 286 ED PARAM DECLARED 36 ASSIGNED 140 REF 149 286 343 FLAY MODEL DECLARED 407 DEFINED 407 FSAV VAR DECLARED 212 IMPL-ASN 419 ASSIGNED 362 371 REF 324 328 FSAVO PARAM DECLARED 66 DEFINED 66 REF 362 371 GD VAR DECLARED 198 IMPL-ASN 419 ASSIGNED 359 REF 310 322 332 GDEQ EQU DECLARED 247 DEFINED 310 IMPL-ASN 419 REF 394 399 404 409 414 GOP EQU DECLARED 246 DEFINED 308 IMPL-ASN 419 REF 394 399 404 409 414 GDTOT VAR DECLARED 206 IMPL-ASN 419 ASSIGNED 374 REF 310 GDTOTO PARAM DECLARED 64 DEFINED 64 REF 374 GLES PARAM DECLARED 28 ASSIGNED 129 REF 310 GOVSAV VAR DECLARED 209 IMPL-ASN 419 ASSIGNED 356 REF 322 324 GR VAR DECLARED 202 IMPL-ASN 419 ASSIGNED 355 REF 318 322 GREQ EQU DECLARED 248 DEFINED 318 IMPL-ASN 419 REF 394 399 404 409 414 GRUSE EQU DECLARED 253 DEFINED 322 IMPL-ASN 419 REF 394 399 404 409 414 GRO PARAM DECLARED 63 DEFINED 63 REF 355 HHSAV VAR DECLARED 208 IMPL-ASN 419 REF 306 324 HHSAVEQ EQU DECLARED 252 I SET DECLARED 2 DEFINED 2 REF 18 124 125 126 127 128 129 2*130 135 136 137 139 140 141 142 2*146 147 3*148 2*149 150 151 152 5*159 163 4*164 4*167 4*168 2*169 5*170 220 7*270 7*272 4*274 7*284 6*298 300 2*304 3*306 2*308 2*310 3*316 2*322 3*326 6*332 3*334 338 339 340 341 342 343 344 345 346 347 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 18 SYMBOL LISTING GAMS 2.00 IBM CMS SYMBOL TYPE REFERENCES 348 349 350 351 352 354 2*358 363 367 368 372 373 CONTROL 86 124 125 126 127 128 129 130 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 159 163 164 167 169 170 3*218 2*219 2*220 270 272 274 284 298 300 304 306 308 310 316 322 326 332 334 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 354 358 363 367 368 372 373 IC SET DECLARED 14 ASSIGNED 138 139 REF 276 L)NTROL 276 ID VAR DECLARED 199 IMPL-ASN 419 ASSIGNED 344 373 REF 326 332 100 PARAM DECLARED 39 ASSIGNED 151 REF 344 373 IN SET DECLARED 16 ASSIGNED 137 REF 2*294 2*296 CONTROL 294 296 375 378 INDTAX VAR DECLARED 204 IMPL-ASN 419 ASSIGNED 360 REF 316 318 INDTAXDEF EQU DECLARED 250 DEFINED 316 IMPL-ASN 419 REF 394 399 404 409 414 INT VAR DECLARED 196 IMPL-ASN 419 ASSIGNED 219 346 REF 304 332 INTEQ EQU DECLARED 243 DEFINED 304 IMPL-ASN 419 REF 394 399 404 409 414 INTO PARAM DECLARED 41 ASSIGNED 163 REF 346 10 PARAM DECLARED 69 DEFINED 69 REF 148 163 274 304 ISBAL EQU DECLARED 257 DEFINED 326 IT SET DECLARED 15 ASSIGNED 136 REF 137 139 6*157 2*158 159 8*160 3*264 3*266 2*268 270 272 5*286 3*288 9*290 7*292 3*312 3*314 4*328 381 CONTROL 157 158 160 2*218 2*219 220 264 266 268 286 288 290 292 312 314 2*328 381 389 390 ITAX PARAM DECLARED 30 ASSIGNED 127 REF 148 274 316 J SET DECLARED 18 REF 2*148 2*163 2*274 2*304 CONTROL 148 163 274 304 K VAR DECLARED 192 IMPL-ASN 419 ASSIGNED 367 REF 284 KO PARAM DECLARED 38 ASSIGNED 142 REF 168 367 L VAR DECLARED 195 IMPL-ASN 419 ASSIGNED 220 354 376 377 REF 284 298 300 LC SET DECLARED 17 DEFINED 17 REF 2*130 152 3*164 168 4*170 4*284 5*298 2*300 353 354 369 CONTROL 86 130 152 164 168 170 219 220 2*284 298 300 353 354 369 LD PARAM DECLARED 53 ASSIGNED 170 LMEQUIL EQU DECLARED 236 DEFINED 300 IMPL-ASN 419 REF 394 399 404 409 414 LS VAR DECLARED 194 IMPL-ASN 419 ASSIGNED 369 REF 300 LSO PARAM DECLARED 54 ASSIGNED 152 REF 369 M VAR DECLARED 191 IMPL-ASN 419 ASSIGNED 219 342 375 REF 270 290 292 312 328 MPS VAR DECLARED 207 MO PARAM DECLARED 35 ASSIGNED 135 REF 136 2*157 159 160 342 OBJ EQU DECLARED 259 DEFINED 334 IMPL-ASN 419 REF 395 400 405 410 415 OPTIMAL MODEL DECLARED 412 DEFINED 412 OPTIMALTE MODEL DECLARED 402 DEFINED 402 P VAR DECLARED 179 IMPL-ASN 419 ASSIGNED 218 350 REF 270 274 306 322 326 PD VAR DECLARED 174 IMPL-ASN 419 ASSIGNED 218 347 REF 268 270 272 292 PDPEEQUAL EQU DECLARED 227 DEFINED 268 IMPL-ASN 419 REF 393 398 403 408 413 PDO PARAM DECLARED 46 ASSIGNED 143 REF 2*148 157 159 347 350 PE VAR DECLARED 176 IMPL-ASN 419 ASSIGNED 349 REF 266 268 272 314 PEDEF EQU DECLARED 226 DEFINED 266 IMPL-ASN 419 REF 393 398 403 408 413 PEG PARAM DECLARED 47 ASSIGNED 145 REF 147 349 PK VAR DECLARED 177 PM VAR DECLARED 175 IMPL-ASN 419 ASSIGNED 218 348 REF 264 270 292 PMCEF EQU DECLARED 225 DEFINED 264 IMPL-ASN 419 REF 393 398 403 408 413 OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 19 SYMBOL LISTING GAMS 2.00 IBM CMS SYMBOL TYPE REFERENCES PMO PARAM DECLARED 48 ASSIGNED 144 REF 146 157 159 348 PROFITMAX EQU DECLARED 235 DEFINED 298 IMPL-ASN 419 REF 394 399 404 409 414 PVA VAR DECLARED 180 IMPL-ASN 419 ASSIGNED 351 REF 274 29B 308 PVAO PARAM DECLARED 49 ASSIGNED 148 REF 164 170 351 358 PWE VAR DECLARED 182 IMPL-ASN 419 ASSIGNED 218 352 REF 266 286 328 PWEO PARAM DECLARED 44 ASSIGNED 147 REF 286 352 PWM VAR DECLARED 181 IMPL-ASN 419 ASSIGNED 368 REF 264 312 328 PWMO PARAM DECLARED 45 ASSIGNED 146 \REF 368 PX VAR DECLARED 178 IMPL-ASN 419 REF 272 274 316 QD PARAM DECLARED 50 ASSIGNED 167 REF 169 RHOC PARAM DECLARED 24 ASSIGNED 124 REF 157 3*160 3*290 292 SALES EQU DECLARED 229 DEFINED 272 IMPL-ASN 419 REF 393 398 403 408 413 SAVINGS VAR DECLARED 211 IMPL-ASN 419 ASSIGNED 361 REF 324 326 SHADOW MODEL DECLARED 397 DEFINED 397 REF 419 SIGN FUNCT REF 130 TARIFF VAR DECLARED 203 IMPL-ASN 419 ASSIGNED 357 REF 308 312 318 322 358 TARIFFDEF EQU DECLARED 249 DEFINED 312 IMPL-ASN 419 REF 394 399 404 409 414 TE VAR DECLARED 185 IMPL-ASN 419 ASSIGNED 389 390 REF 266 314 TM VAR DECLARED 183 IMPL-ASN 419 ASSIGNED 363 381 REF 264 276 278 280 312 TMAVG VAR DECLARED 186 REF 276 TMEQ EQU DECLARED 231 DEFINED 276 REF 408 TMSH1 EQU DECLARED 232 DEFINED 278 IMPL-ASN 419 REF 398 408 TMSH2 EQU DECLARED 233 DEFINED 280 IMPL-ASN 419 REF 398 408 TMO PARAM DECLARED 29 ASSIGNED 126 REF 146 278 280 363 381 TOTSAV EQU DECLARED 255 DEFINED 324 IMPL-ASN 419 REF 395 400 405 410 415 UTILITY VAR DECLARED 215 IMPL-ASN 419 REF 334 419 WA VAR DECLARED 193 IMPL-ASN 419 ASSIGNED 219 353 REF 298 WAO PARAM DECLARED 52 ASSIGNED 57 58 59 REF 164 170 353 X VAR DECLARED 187 IMPL-ASN 419 ASSIGNED 218 338 REF 270 290 296 332 XD VAR DECLARED 188 IMPL-ASN 419 ASSIGNED 219 339 REF 272 284 288 294 298 304 308 316 XDO PARAM DECLARED 37 ASSIGNED 141 REF 149 163 164 169 170 339 358 XLE PARAM DECLARED 88 DEFINED 88 REF 2*130 152 164 354 XLLB PARAM DECLARED 51 ASSIGNED 130 REF 2*167 168 XSN EQU DECLARED 242 DEFINED 296 IMPL-ASN 419 REF 394 399 404 409 414 XXD VAR DECLARED 189 IMPL-ASN 419 ASSIGNED 219 340 REF 270 272 288 290 292 294 296 xXDSN EQU DECLARED 241 DEFINED 294 IMPL-ASN 419 REF 394 399 404 409 414 XXDO PARAM DECLARED 42 ASSIGNED 149 REF 157 159 160 340 XO PARAM DECLARED 43 ASSIGNED 159 REF 160 338 Y VAR DECLARED 201 IMPL-ASN 419 ASSIGNED 219 358 REF 306 308 ZZ PARAM DECLARED 104 DFFINED 104 REF 124 125 126 127 128 129 135 140 141 142 150 151 SETS I SECTORS IC SECTORS WITH CONSTANT TARIFF RATES IN NONTRADED SECTORS IT TRADED SECTORS J ALIASED WITH I LC LABOR CATEGORIES OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 20 SYMBOL LISTING GAMS 2.00 IBM CMS PARAMETrERS AC ARMINGTON FUNCTION SHIFT PARAMETER (UNITY) AD PRODUCTION FUNCTION SHIFT PARAMETER (UNITY) ALPHL LABOR SHARE PARAMETER IN PRODUCTION FUNCTION (UNITY) CDTOTO INIIIAL PRIVATE CONSUMPTON CLES PRIVATE CONSUMPTION SHARES (UNITY) DELTA ARMINGTON FUNCTION SHARE PARAMETER (UNITY) DSTO VOLUME OF INVENTORY INVESTMENT BY SECTOR ('79-80 BILL CFAF) EMPL EMPLOYMENT MAPPING ERO EXCHANGE RATE ETA EXPORT DEMAND ELASTICITY (UNITY) ED VOLUME OF EXPORTS ('79-80 BILL CFAF) FSAVO FOREIGN SAVING (FORCIGN CURRENCY) GOTOTO INITIAL GOVERNMENT CONSUMPTION GLES GOVERNMENT CONSUMPTION SHARES (UNITY) GRO GOVERNMENT REVENUE IDO VOLUME OF INVESTMENT BY SECTOR OF ORIGIN ('79-80 BILL CFAF) INTO VOLUME OF INTERMEDIATE INPUT DEMANDS ('79-80 BILL CFAF) Io INPUT-OUTPUT COEFFICIENTS ITAX INDIRECT TAX RATES (UNITY) KO VOLUME OF CAPITAL STOCKS BY SECTOR ('79-80 BILL CFAF) LD EMPLOYMENT (1000 PERSONS) LSO LABOR SUPPLIES BY CATEGORY (1000 PERSONS) MO VOLUME OF IMPORTS ('79-80 BILL CFAF) PDO DOMESTIC GOOD PRICE (UNITY) PEO DOMESTIC PRICE OF EXPORTS (UNITY) PMO DOMESTIC PRICE OF IMPORTS (UNITY) PVAO VALUE ADDED PRICE BY SECTOR (UNITY) PWEO WORLD MARKET PRICE OF EXPORTS (UNITY) PWMO WORLD MARKET PRICE OF IMPORTS (UNITY) QD DUMMY VARIABLE FOR COMPUTING AD(I) (UNITY) RHOC ARMINGTON FUNCTION EXPONENT (UNITY) TMO TARIFF RATES (UNITY) WAO AVERAGE WAGE RATE BY LABOR CATEGORY ('79-80 MILL CFAF PR WORKER) XDO VOLUME OF DOMESTIC OUTPUT BY SECTOR ('79-80 BILL CFAF) XLE LABOR BY SECTOR AND CATEGORY XLLB DUMMY VARIABLE (L MATRIX WITH NO ZEROS) (UNITY) XXDO VOLUML OF DOMESTIC SALES BY SECTOR ('79-80 BILL CFAF) XO VOLUME OF COMPOSITE GOOD SUPPLY ('79-80 BILL CFAF) ZZ PARAMETERS AND INITIAL CONDITIONS VARIABLES CD FINAL DEMAND FOR PRIVATE CONSUMPTION ('79-80 BILL CFAF) DEPRECIA TOTAL DEPRECIATION EXPENDITURE (CURR BILL CFAF) DK kVJOLUME OF INVESTMENT BY SECTOR OF DESTINATION ('79-80 BILL CFAF) DST INVENTORY INVESTMENT BY SECTOR ('79-80 BILL CFAF) DUTY EXPORT DUTY REVENUE (CURR BILL CFAF) E EXPORTS BY SECTOR ('79-80 BILL CFAF) ER EXCHANGE RATE (UNITY) FSAV FOREIGN SAVINGS (CURR BILL DOLLARS) GD FINAL DEMAND FOR GOVERNMENT CONSUMPTION ('79-80 BILL CFAF) GDTOT TOTAL VOLUME OF GOVERNMENT CONSUMPTION ('79-80 BILL CFAF) GOVSAV GOVERNMENT SAVINGS (CURR BILL CFAF) OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DQMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 21 SYMBOL LISTING GAMS 2.00 IBM CMS VARIABLES GR GOVERNMENT REVENUE (CURR BILL CFAF) HHSAV TOTAL HOUSEHOLD SAVINGS (CURR BILL CFAF) ID FINAL DEMAND FOR PRODUCTIVE INVESTMENT ('79-80 BILL CFAF) INDTAX INDIRECT TAX REVENUE (CURR BILL CFAF) INT INTERMEDIATES USES ('79-80 BILL CFAF) K CAPITAL STOCK BY SECTOR ('79-80 BILL CFAF) L EMPLOYMENT BY SECTOR AND LABOR CATEGORY (1000 PERSONS) LS LABOR SUPPLY BY LABOR CATEGORY (1000 PERSONS) M IMPORTS ('79-80 BILL CFAF) MPS MARGINAL PROPENSITY TO SAVE (UNITY) P PRICE OF COMPOSITE GOODS (UNITY) PD DOMESTIC PRICES (UNITY) PE DOMESTIC PRICE OF EXPORTS (UNITY) PK RATE OF CAPITAL RENT BY SECTOR (UNITY) PM DOMESTIC PRICE OF IMPORTS (UNITY) PVA VALUE ADDED PRICE BY SECTOR (UNITY) PWE WORLD MARKET PRICE OF EXPORTS (UNITY) PWM WORLD MARKET PRICE OF IMPORTS (UNITY) PX AVERAGE OUTPUT PRICE BY SECTOR (UNITY) SAVINGS TOTAL SAVINGS (CURR BILL CFAF) TARIFF TARIFF REVENUE (CURR BILL CFAF) TE EXPORT TAX RATES (UNITY) TM TARIFF RATES (UNITY) TMAVG AVERAGE TARIFF RATE (UNITY) UTILITY OBJECTIVE FUNCTION VARIABLE ('79-80 BILL CFAF) WA AVERAGE WAGE RATE BY LABOR CATEGORY (CURR MILL. CFAF PR PERSON) X COMPOSITE GOODS SUPPLY ('79-80 BILL CFAF) XD DOMESTIC OUTPUT BY SECTOR ('79-80 BILL CFAF) XXD DOMESTIC SALES ('79-80 BILL CFAF) Y PRIVATE GDP (CURR BILL CFAF) EQUATIONS ABSORPTION VALUE OF DOMESTIC SALES (CURR BILL CFAF) ACTIVITY PRODUCTION FUNCTION ('79-80 BILL CFAF) ACTP DEFINITION OF ACTIVITY PRICES (UNITY) ARMINGTON COMPOSITE GOOD AGGREGATION FUNCTION ('79-80 BILL CFAF) CAEQ CURRENT ACCOUNT BALANCE (CURR BILL DOLLAR) CDEQ PRIVATE CONSUMPTION BEHAVIOR (CURR BILL CFAF) COSTMIN FIRST ORDER CONDITION FOR COST MINIMIZATION OF COMPOSITE GOOD (UNITY) DEPREQ DEPRECIATION EXPENDITURE (CURR BILL CFAF) DSTEQ INVENTORY INVESTMENT ('79-80 BILL CFAF) DUTYDEF EXPORT DUTIES (CURR BILL CFAF) EDEMAND EXPORT DEMAND (UNITY) EQUIL GOODS MARKET EQUILIBRIUM ('79-80 BILL CFAF) ESUPPLY EXPORT SUPPLY (UNITY) GDEQ GOVERNMENT CONSUMPTION BEHAVIOR ('79-80 BILL CFAF) GDP PRIVATE GDP (CURR BILL CFAF) GREQ GOVERNMENT REVENUE (CURR BILL CFAF) GRUSE GOVERNMENT SAVINGS (CURR BI! CFAF) HHSAVEQ HOUSEHOLD SAVINGS (CURR BILL CFAF) INDTAXDEF INDIRECT TAXES ON DOMESTIC PRODUCTION (CURR BILL CFAF) INTEQ TOTAL INTERMEDIATE USES ('79-80 BILL CFAF) OPTIMAL TARIFF STRUCTURE MODEL - VERSION WITH DOMESTIC INDIRECT TAXES 04/10/86 17:20:18 PAGE 22 SYMBOL LISTING GAMS 2.00 IBM CMS EQUATIONS ISSAL SAVINGS INVESTMENT BALANCE (CURR BILL CFAF) LMEQUIL LABOR MARKET EQUILIBRIUM (1000 PERSONS) OBJ OBJECTIVE FUNCTION ('79-80 BILL CFAF) PDPEEQUAL PRICE EQUALIZATION (UNITY) PEDEF DEFINITION OF DOMESTIC EXPORT PRICES (UNITY) PMDEF DEFINITION OF DOMESTIC IMPORT PRICES (UNITY) PROFITMAX FIRST ORDER CONDITION FOR PROFIT MAXIMUM (1000 PERSONS) SALES VALUE OF DOMESTIC OUTPUT (CURR BILL CFAF) TARIFFDEF TARIFF REVENUE (CURR BILL CFAF) TMEQ TARIFF RATE EQUALIZATION (UNITY) TMSH1 FIXED TARIFF RATES (UNITY) TMSH2 FIXED TARIFF RATES (UNITY) TOTSAV TOTAL SAVINGS (CURR BILL CFAF) XSN COMPOSITE GOOD AGGREGATION FOR NONTRADED SECTORS ('79-80 BILL CFAF) XXDSN DOMESTIC SALES FOR NONTRADED SECTORS ('79-80 BILL CFAF) MODELS CAMCGE2 MODIFIED SQUARE CAMCGE FLAT FLAT TARIFF STRUCTURE OPTIMAL OPTIMAL TARIFF STRUCTURE OPTIMALTE MODIFIED CAMCGE TO GIVE SHADOW PRICES AND FIND OPTIMAL EXPORT TAX SHADOW MODIFIED CAMCGE TO GIVE SHADOW PRICES AND FIND OPTIMAL EXPORT TAX COMPILATION TIME = 1.369 SECONDS