Environmental Policy, Allocation of Resources, Sector Structure and Comparative Price Advantage

Siebert, Horst Article Environmental Policy, Allocation of Resources, Sector Structure and Comparative Price Advantage Zeitschrift für Wirtschaftsund Sozialwissenschaften (ZWS) - Vierteljahresschrift der Gesellschaft für Wirtschaftsund Sozialwissenschaften, Verein für Socialpolitik Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Siebert, Horst (1978) : Environmental Policy, Allocation of Resources, Sector Structure and Comparative Price Advantage, Zeitschrift für Wirtschaftsund Sozialwissenschaften (ZWS) - Vierteljahresschrift der Gesellschaft für Wirtschaftsund Sozialwissenschaften, Verein für Socialpolitik, ISSN 0342-1783, Duncker & Humblot, Berlin, Vol. 98, Iss. 3, pp. 281-293, https://doi.org/10.3790/schm.98.3.281 This Version is available at: https://hdl.handle.net/10419/291410 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Environmental Policy, Allocation of Resources, Sector Structure and Comparative Price Advantage Von Horst Siebert* The paper analyzes how environmental policy affects sector structure, the allocation of resources and comparative price advantage in a two-sector equilibrium model. Environmental quality can be considered as a public good being influenced by emissions from consumption and production processes. Since the assimilative capacity of the environment has been used so far as a free production input, the common-property-resource has been heavily overused. Environmental policy attempts to decide which of the competing uses of the environment should have priority and by which policy instruments environmental scarcity can be internalized into the decisions of the subsystems of the economy. In this paper we analyze to what extent environmental policy will affect sector structure, the allocation of resources and relative price. Since relative price in a closed economy determines comparative advantage (relative to the foreign country), the paper also answers the question to what extent environmental policy will affect the comparative price advantage of a country. In former models (Siebert 1974, 1976) only partial equilibrium models were developed neglecting the demand side or not closing the model with respect to receipts from the emission tax. In this paper, the model is closed with respect to the demand side, and demand conditions are explicitly taken into consideration. The frame of reference is a two-sector-model in which production generates pollutants as a joint product. The government levies an emission tax per unit of pollutant emitted to the environment. We treat the environment as a national public good and ignore international, transnational and regional environmental systems1. Section I presents the assumptions, Section II develops the model, and in Section III the implications of the model are discussed. Section IV points out possible extensions. * Universität Mannheim (WH), D-6800 Mannheim A 5. 1 On these problems compare Walter (1975). OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.98.3.281 | Generated on 2023-04-04 11:54:31 282 Horst Siebert I. Assumptions A 1. In order to keep the model as simple as possible we assume only one type of resource, R, and a production function A 2. The production of commodities i — 1,2 generates pollutants as a joint product. For simplifying purposes there is only one type of pollutants. It is assumed that pollutants emitted rise proportionally or progressively with resources used, i. e. (2) Svi = Hi (Q;) = H{ [F{ (Ri)] = Zi (Ri) with Z; >0, Z'/ ^ 0; H; > 0 The convex emission function Zi is suggested intuitively by engineering production functions2. With the activity level of an engine reaching or exceeding capacity, it is realistic to assume that inputs have to be increased progressively for an additional unit of output. This suggests that emissions rise progressively. A more precise explanation for the convexity of the emission function follows from the application of the mass balance concept to production functions. In terms of weight a mass balance exists between input and output. Since mass cannot be lost in a production process, regular output and emissions must be identical to inputs, in weight terms. Define the production function in weight terms. For a given technology this function must be concave, if the regular production function is concave. Then it follows that the emission function Zi must be convex.3 A3. Resources may also be used for abatement purposes. Let S? indicate the quantity of pollutants reduced in Sector i. The abatement function is given by The abatement function describes a technology that prevents pollutants from entering the environment. Additionally it could be assumed that a technology exists to reduce pollutants ambient in the environment (water treatment). A4. Net emissions or pollutants ambient in the environment are defined as emissions produced minus emissions abated. A diffusion function is not explicitly introduced. (1) Qi = Ft (Ri) with F'i > 0, F'l < 0 (3) sr. = Fj: (rî) with F1.' > 0, Fri < 0 (4) Si = Sf-Sl 2 Gutenberg (1972), S. 326. 3 Compare Sontheimer (1975). OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.98.3.281 | Generated on 2023-04-04 11:54:31 Environmental Policy, Allocation of Resources 283 A 5. Firms maximize profits and regard commodity prices, factor prices and the emission tax as given. A 6. The resource can be used for production and abatement and is given (5) + H2 + R[ + Rt 2 = R A 7. Commodity demand is given by (6) Q? =Di(p, Y) with p = pi/p2 where pi indicate nominal prices and p is the relative price. A 8. Income Y is defined from the production side. There are no savings. In order to close the model, we assume that the government spends the tax income received in form of transfers to the households. Consequently disposable income of the households is identical to net national income at market prices and is defined as (7) Y = pQi + Q2 Observe that Y includes transfers not explicitly shown and that p is consumers price and not producers price. If Y would be defined with respect to producers price p*, emissions taxes (and transfers) would appear explicitly on the right side of (7). A 9. Commodity markets must be in equilibrium so that (8) Qi = Qf A 10. The government levies an emission tax z (in nominal terms) on net emissions Si, with z being changed parametrically4. II. The model 1. Factor demand by the profit maximizing firm is given by maximizing U = Pi Qi - r (Ri + R]) — zSi s.t. Qi-FilRj)^ 0 4 Additionally, a damage function may be introduced indicating that environmental quality is affected by net emissions U = G (S) with G' < 0, G" < 0. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.98.3.281 | Generated on 2023-04-04 11:54:31 284 Horst Siebert H{ (Qi)-S?< 0 ^ - F\ (Rtr) < 0 - Si + SV - sj < 0 where r denotes the resource price in nominal terms. Assuming that production takes place in both sectors, i. e. that we have a meaningful problem, and defining r = ?/p2 and z = z/p2 the conditions for profit maximizing factor demand are given as R = (PZHJ F[ (Rx) (9) r = (1 - ZH2) F2 (Rg) r = zFl' (Rj) 2. The system of equations (1) - (9) has the 17 variables S?, Si, Sf{, Qi, Ri, Rrif Qf, p, Y and r and 18 equations. The definition of Y in equation 7 states that total demand is equal to income, so that in a twosector model the equilibrium condition for one of the product markets is redundant (Walras Law) and should be omitted. By substitution the system can be simplified to F1 (Ri) = D1 (p, pFi (Ri) + F2 (R2)) (i) r = zFfl (Rj) (ii-iii) r = (p-zH1) F[ (R{) (iv) r = (1 -ZH2) F2 (Rg) (V) R = Rj -jRg Rj R*2 (Vi) Total differentiation and substitution of (10 vi) into (i) - (v) yields al 0 0 1 dR1 — H j Fj dz 0 a2 0 1 0 dR2 -H2F'2dz (11) U 0 1 0 dR[ = Fri dz zFr2 zFr2 zFr2 1 0 dr Fr2dz ~D1YF2 0 0 -b2 dp 0 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.98.3.281 | Generated on 2023-04-04 11:54:31 Environmental Policy, Allocation of Resources 285 The coefficients are defined as follows5 (12) o< = zH'l F? - (Pi - zH\) F'l > 0 (i) b1 = l-DlYv == D2Y (ii) b2 = Dlp + D1Y Fx< 0 (iii) In (12 i) we have Pi = p for i = 1 and p* = 1 for i = 2. III. Implications The problem is to determine how the allocation of resources is affected by environmental policy. We first study how factor demand of firms changes with an emission tax for a given relative price p. We then analyze how relative price changes, and how the allocation of resources and national income are affected in this case. 1. Assuming a given commodity price and considering only the factor market conditions and the resource constraint, i. e. (10 ii - vi), the change in factor use in response to an increase in the emission tax is given by the subsystem of equation 11 not containing the fifth row of the system and not containing the fifth column of the matrix of derivatives. From appendix I we have the following results dRi (13 i) —-i > 0 dz (13 ii) <0: H^F'^H'zF, ZdR; (13 iii) -^<0 HFindicates the marginal tendency to pollute (per unit of resource). Hx Fx > H2 F'2 specifies that Sector 1 is pollution intensive6. For 5 b2 < 0 follows from Slutsky's rule. Let D^ denote the pure substitution effect. We have comp, Di*> = Di*W ^ or Di*w = Di*> + (Rl) = b2 < 0 , since the pure substitution effect is always negative. Sv Sp « If Z1 (Rx) > Z2 (R2) for Rx = Rg, H^ F^ > H'2 F'2 can be specified as~ > ^ for R{ > R2. This transformation also holds for Rt < R2 if either Sector 1 is not "very" small compared to Sector 2 or if Z2 has a sufficiently weaker curvature than Zx. Observe that H'x F^ > H'2 F'2 demands that the Zrfunction should not cross, i. e. emission intensities should not be reversed. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.98.3.281 | Generated on 2023-04-04 11:54:31 286 Horst Siebert given commodity prices, an emission tax will reduce the output of the pollution-intensively produced commodity. Resource use in the pollution abatement activity of the pollution-intensively producing sector will increase. Also we know that resources will be withdrawn from production and will be used in abatement activities. This effect does not depend on differences in the production intensity of the two sectors. 2. Allowing the commodity price to vary we have the following results from appendix II (as sufficient conditions): f d' y > 0 (14i) A>0: { ?F T , , I D^ + D^F^O dRr (14 ii) --1 > 0: D1YF2 + D^yFj > 0 Assuming (14 i) is given we have 2 dR{ ^ (14 iii) ——1 < 0 (14 iv) dz dRL<0. J D1Y> 0 dz ' \ H; F[ > H2 F2 dp ^ ( h\f\> H' F' (14v) -r->0: \ > >22 < ' dz y a2 D2Y FJ p > ax DlY F2 dY ^ (14 vi) -r-<0: a z H1F1> H2F2 F2 1 - —2- — r)lp > <x > 1 with a = - 1 - PFi In (14 vi) rjip denotes the direct price elasticity of demand. Diagram 1 summerizes the sufficient conditions of equation 14. We have the following results: 3. Assume both commodities are not inferior, so that their marginal propensities to consume (DiY>0) are nonnegative. Then the determinant A > 0. Assume Sector 1 is the pollution-intensively producing sector. Then we have: Resource use in the pollution-intensively producing sector will decline. Resource use in each abatement activity will increase; resource in production (2 Ri) will be reduced. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.98.3.281 | Generated on 2023-04-04 11:54:31 Environmental Policy, Allocation of Resources 287 Diagram 1 : Sufficient conditions Environmental policy will shift the sector structure of the economy in favor of the abatement activities with production being affected negatively. We can establish that production in the pollution-intensively producing sector will decline7. In the less pollution-intensively producing Sector 2, resource use may increase or decrease. The model allows both cases. Thus, in one case Sector 1 and Sector 2 lose resources to the abatement activity, whereas in the other case, Sector 1 loses resources to Sector 2 and the abatement activity. Under the assumptions made, emissions will be reduced and environmental quality will improve. This follows from 2 dRi/dz < 0 and 2 dRr{/dz > 0. 4. Condition (14 v) for a rise in the relative price can be split into two sufficient conditions8. i) D'2Y > pDlY. Under the conditions specified below, national income will decline as a consequence of environmental policy. Then D2Y> pD'lY guaranties that demand for the pollution-intensively produced commodity 1 is reduced less than demand for the commodity 2. This difference in the income effect of the two commodities makes sure that 7 This also holds if Sector 2 were the pollution-intensively producing sector. 8 Note hat F1P>F2 follows from H[ FX > H'2F2. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.98.3.281 | Generated on 2023-04-04 11:54:31 288 Horst Siebert the relative price of the pollution-intensively produced commodity must rise. dR* . dR2 ii) a2 > ai: |—— | > | | specifies9 that (for given p and z), Sector 1 is more sensitive to changes in resource price than Sector 2; we may also say that Sector 1 is more dependent on the resource R. This condition can be interpreted as a rudimentary form of a factor-intensity condition in a one-factor model. We can expect that this condition unfolds into a set of factor intensity conditions in a multi-factor model. As a result we have: The relative price of the pollution-intensively produced commodity will rise if the marginal propensity to consume for this commodity is lower than the less pollution-intensively produced commodity and if the pollution-intensively producing sector depends heavily on the resource R. Sufficient conditions for a rise in the relative price can partly substitute each other. Assume Sector 1 is "very" pollution-intensive10. Then the relative price of commodity 1 may rise even if it has a high income elasticity of demand and loses demand quantities with a decline in income. Or for identical pollution-intensities of both sectors, the relative price will rise, if Sector 1 has a sufficiently smaller propensity to consume and thus loses a smaller quantity in demand requiring a higher adjustment in relative price. Finally, assume Sector 2 heavily depends on resource R. Then p can rise nevertheless, if Sector 1 is sufficiently more pollution-intensive or if Sector 1 has a sufficiently lower income elasticity. dp/dz > 0 indicates that environmental policy will under the conditions indicated affect the comparative price advantage of a country. Assume a country exports the pollution-intensively produced commodity 1. Then environmental policy will reduce the comparative price advantage of that country11. Consider two countries with a different abundance of environmental services and assume that z > z* reflects the difference in endowment with z* indicating the emission tax of the » Differentiate the factor demand conditions (9) for given p and z with respect to r 10 Assume for instance Sector 2 does not pollute at all with H2 = 0. 11 If a country exports the less pollution-intensive commodity and if it undertakes environmental policy, its comparative price advantage will be improved. dRt 1 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.98.3.281 | Generated on 2023-04-04 11:54:31