The impact of fiscal policies on agricultural household decisions

Glauben, Thomas; Herzfeld, Thomas; Loy, Jens-Peter; Renner, Swetlana; Hockmann, Heinrich Article — Accepted Manuscript (Postprint) The impact of fiscal policies on agricultural household decisions Economic Modelling Provided in Cooperation with: Leibniz Institute of Agricultural Development in Transition Economies (IAMO), Halle (Saale) Suggested Citation: Glauben, Thomas; Herzfeld, Thomas; Loy, Jens-Peter; Renner, Swetlana; Hockmann, Heinrich (2012) : The impact of fiscal policies on agricultural household decisions, Economic Modelling, ISSN 1873-6122, Elsevier, Amsterdam, Vol. 29, Iss. 2, pp. 166-177, https://doi.org/10.1016/j.econmod.2011.09.010 , https://www.sciencedirect.com/science/article/pii/S0264999311002288 This Version is available at: https://hdl.handle.net/10419/271539 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-nc-nd/4.0/ The Impact of Fiscal Policies on Agricultural Household Decisions Thomas Glauben a, Thomas Herzfeld a b, Jens-Peter Loy c, Swetlana Renner a, Heinrich Hockmann a a Leibniz-Institute of Agricultural Development in Central and Eastern Europe, D- 06120 Halle/Saale, Germany b Wageningen University and Research Centrum, Department of Social Sciences, NL- 6706KN Wageningen, The Netherlands c Department of Agricultural Economics, University of Kiel, D-24098 Kiel, Germany This is an accepted manuscript, which has been published in “Economic Modelling”. Please cite this publication as follows: Glauben, T., Herzfeld, T., Loy, J.-P., Renner, S., Hockmann, H. (2012). The impact of fiscal policies on agricultural household decisions. Economic Modelling 29 (2), 166-177. You can download the published version at: https://doi.org/10.1016/j.econmod.2011.09.010 Abstract This paper provides a comparative static analysis of farm household’s production, consumption, and labor market decisions under alternative tax policies. We explore the implications of non-separable household decisions caused by widespread non-participation in labor, land, financial and/or food markets, as is typical of low income economies. The analytical results indicate that when labor market imperfections occur, most taxinduced responses are ambiguous, mainly due to shadow price effects. This is particularly the case for the labor market and production responses to most tax tools under study, while a decreasing demand for consumption goods appears to be the result in several cases. Furthermore, tax-induced allocation effects may differ between the non-separable and the separable model versions, indicating the potential impact of labor market constraints on farm household responses to tax policies. In particular, standard taxes as well as a land tax may imply production adjustments in the case of non-separability. Keywords: Agricultural household model, non-separability, taxation JEL code: H20, H31, Q12 © <2012>. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/ 1 The Impact of Fiscal Policies on Agricultural Household Decisions 1. Introduction Considering efficiency and redistribution aspects, there is a general consensus in the standard public finance literature that consumption taxes (particularly value added tax) and land tax are superior to agricultural taxes (output and input taxes, market surplus taxes) in developing countries (Newbery 1987; Burgess and Stern 1993; Khan 2001). However, there are at least two good reasons why taxation of household businesses in developing countries deserves special study and cannot simply be treated as a standard taxation problem of standard enterprises. First, in many countries, especially in developing and transition economies, the use of both standard tax tools, value added and income taxes is limited. In contrast to industrialized countries, where income tax is the main source of tax revenues (more than 50%), income taxes constitute only less than one-third of the total tax revenues of developing counties and even less than 25% in transition countries (Gordon and Li 2005; Bahl 2006). Instead, indirect taxes (mostly value added tax, which mainly replaced taxes on foreign trade in last decades) play a major role among developing countries (more than 50% of tax revenues). It is often costly to tax transactions between producers and consumers by a value added tax, especially within the household or on informal markets. Furthermore, difficulties in observing a household’s annual income restrict the implementation of a well-defined income tax scheme (Ahmad and Stern 1991; Newbery 1987). In many cases, small family farms are not obligated to keep records for quantity of produced and marketed outputs and for the costs of inputs. Furthermore, developing countries have a large informal sector which is excluded from taxation. It becomes apparent in the consumption of a substantial part of self-produced outputs; self-employment and other internal transfers excluded from market transactions. Most prominently, any value added tax (VAT) can be raised only on transactions in the formal sector possibly creating distortions between formal and informal sectors (Emran and Stiglitz, 2005). A major argument in favor of a land tax is a potential increase in land use efficiency and a greater equality. Furthermore, a land tax is seen as not creating production distortions (Newbery, 1987, Skinner, 1991). However, a land tax is difficult to implement due to a strong opposition and lobbying from the part of land owners and due to administrative problems (Khan, 2001; Skinner, 1991). A second difference relates to the implicit dichotomy of consumption and production decisions in conventional household and firm approaches. In particular, when related markets are imperfectly competitive, production organization and consumption choices are jointly determined (Strauss 1986). There is an extensive literature on the identification of feasible taxation tools for peasant households (‘agricultural taxes’). In this context, agricultural taxes are surrogates for standard taxes, in particular for income taxes. Prominent representatives include land taxes, output or input taxes, and poll taxes (Bird 1974; Rao 1989; Burgess and Stern 1993). In addition, some papers investigate the analysis of tax-induced allocation and distribution effects within partial equilibrium frameworks (Atkinson 1987) and dual-economy approaches (Sah and Stiglitz 1987), as well as the application of optimal taxation models to peasant economies (Heady and Mitra 1987; Stiglitz and Dasgupta 1971; Munk 1980). However, very few studies have focused on the rigorous derivation of farm household decisions to tax policies. Ahmad and Stern (1991) examine the farm household effects of several agricultural tax tools (marketed surplus, gross output, and input taxes) within a simplified theoretical farm household approach. Chambers and Lopez (1987) analyze the implications of standard taxes (income, profit, and consumption taxes) on financially constrained farm households within a dynamic approach. Lopez (1994) 2 considers several income tax brackets by the estimation of farm household decisions, but does not explicitly examine their implications on consumption and production decisions. There are several reasons why labor markets may be imperfect, leading to nonseparation of consumption, production and labor-supply decisions (Abdulai and Delgado 1999; de Janvry et al. 1991; Löfgren and Robinson 1999). For example, binding hour constraints in off-farm employment may prevent a complete adjustment in agricultural labor markets (Benjamin 1992). Family and hired labor may be imperfect substitutes in agricultural production (Deolalikar and Vijverberg 1987; Jacoby 1993). Also, farmers may have preferences towards working on or off the farm (Lopez 1994). In addition, costs associated with labor market transactions can explain why households have different relationships to the labor markets (Sadoulet, de Janvry and Benjamin 1996). In this paper, we analyze the comparative statics of farm household decisions under both standard and agricultural taxes, assuming labor markets are imperfect. A non-separable model is developed to allow for imperfections on labor markets. The model implies increasing perunit costs in accessing both the market for hired on-farm labor and the market for off-farm family labor (Carter and Yao 2002). Thus, the relevant wage rate is endogenously determined. The advantage of this approach is twofold. First, the model accounts for several kinds of labor market imperfections, notably institutional restrictions (e.g. binding hour constraints settled by collective agreements), variable transaction costs in accessing labor markets, or heterogeneity between hired and family labor on-farm and also between family labor on and off the farm (Low 1982, 1986). In particular, it differs from former approaches, which usually assume either a completely absent labor market or an exogenously fixed rationing of off-farm employment. Second, the approach is applicable to various labor market regimes, including the cases in which farms simultaneously hire on-farm labor and sell off-farm labor. We investigate the comparative statics of the farm household to compare production, consumption, and labor market effects caused by alternative tax policies. In detail, we analyze an income and a value-added tax, the main standard tax tools, as well as an off-farm income tax (‘wage tax’) and several agricultural taxes (market surplus, input and land taxes). To control for tax-induced adjustments related to labor market imperfections, we compare the results to those derived from a separable approach assuming perfect labor markets. These comparisons allow us to examine basic rules regarding the optimality of the tax tools under consideration, at least from the efficiency point of view.1 Since in a world of perfect markets standard taxes are superior to agricultural taxes and land taxes are superior to the other agricultural taxes, it is interesting whether this ranking pertains when labor markets are imperfect. 2. The Model To concentrate on the role of tax policies and labor market constraints, we construct a static model that ignores some aspects of farmers’ decisions, notably (price) risk (Finkelshtain and Chalfant 1991; Fafchamps 1992) and credit constraints (Chambers and Lopez 1987). The model 1 In their seminal work, Diamond and Mirrlees (1971) argue that production efficiency is desirable within an optimal taxation system, even if a full Pareto optimum is not achieved. Thus, tax tools that do not violate production efficiency should to be preferred unless there are administrative limitations or special distributional reasons restricting their use. 3 framework can cover both the case of imperfect and, with few rearrangements, perfect labor markets. We consider a representative household that owns a plot of land and produces market und home-consumed agricultural goods using variable inputs, labor and a land. The farm household is assumed to maximize utility (1) derived from the consumption and leisure subject to a technology constraint (2), time constraint (3), and a ‘tax corrected’ budget constraint. (1) max ( )U c,x c n l m aRC CC + ∈= ) ,, (c subject to (2) 0),( =rxG n l vc a RX X XX + ∈= ), , ,( x and n G RR + ∈= )(r (3) 0 hs l l l ll TX X XC− + − −≥ (4) ( ) () ( ) ( ) ( ) { () () ( ) } 1 11 1 1 vat mm aa y ms c c a a a aa v v v hs l w l GG PC PC PX P X C PC P X gX f X E R τ ττ τ ττ + + ≤− − + − + −+   − +− + − Here U(c) is the farm household’s utility function (1), which assumed to be monotonic, twice differentiable, and concave in each of its arguments. Household maximizes utility defined over a vector of consumption goods { } ,, mal c CG C C C∈= consisting of self-produced agricultural goods (Ca,) a manufactured good (Cm) and leisure (Cl). Production technology (2) is represented by a multi-output, multi-input transformation function (G(x, r) = 0), which is assumed to be well behaved in the usual sense (Lau 1978). Here, { } ,,, cavl PG XXXX∈=x is a vector of production goods, expressed as netputs, and r is a vector of quasi-fixed factors consisting of factor land. The farm household is assumed to produce marketed agricultural goods, i.e. cash crops to be sold on markets, (Xc>0) and homeconsumed agricultural goods (Xa>0) using variable inputs (Xv<0), labor (Xl<0), and the quasifixed factor land (RG>0). The farm household faces a time constraint (3) where Tl denotes the total time available. fh lll XXX= + is the total of on-farm labor time subdivided into family labor )( f l X and hired labor )( h l X . Furthermore, s l X indicates off-farm family labor and Cl the leisure of the family members. In general, four regimes of labor market participation are possible. First, the farm household sells family labor and hires labor at the same time. Second, the household sells labor without hiring. Third, it hires without selling any family labor, or fourth, it neither sells nor hires labor, which can be referred to as autarky. The budget constraint (4) implies that a household’s (‘tax-corrected’) total expenditure (left-hand side of (4)) must not exceed its (‘tax-corrected’) total income (right-hand side). Households may receive income from farming and from off-farm employment. In addition, it receives (E>0) or pays (E<0) transfers, which are determined exogenously. Here, ; ,,, i Pi macv= denotes a vector of exogenous consumer and producer prices before tax, while j τ is a vector of parameters of tax policies to be analyzed including a value-added tax ( τ vat), a market surplus tax ( τ ms), as well as taxes on inputs ( τ v), household’s monetary income ( τ y), offfarm wages ( τ w), and land ( τ G). It is assumed that all designed tax policies are alternative tax 4 instruments, so that the respective tax under consideration is the only tax policy applied to the farm household.2 Monetary expenditures are generally subject to value-added taxes. However, the internal transfers of self-produced agricultural goods are normally not observed by tax authorities. Thus, only the expenditures for market commodities ( mm PC )are subject to the value-added tax ( τ vat). The basis of the income tax ( y τ ) is the household’s monetary income, including profits from farming () ( ) h cc aa v v l PX PX P X g X+− − , where ( ) h l gX denotes hired labor costs (see below), and also off-farm labor income ( () s l fX ), and transfers ( E ). Due to the virtual absence of record keeping, farm income is often not taxable and thus only incomes from off-farm employment can be taxed by a wage tax ( w τ ). Similarly, market surplus, input, or land taxes are applied as surrogates for an income tax. The base of the market surplus tax ( ms τ ) are revenues from sales of agricultural goods ( ( ) cc a a a PX P X C+− ), assuming internal transfers are not taxable. Expenditures for commercial inputs ( vv PX ) such as fertilizer and chemicals are subject to the input tax ( v τ ) and the market value of land ( G R ) is taxed by a land tax ( G τ ). To consider labor market imperfections, revenues from off-farm employment and hired labor costs are conceptualized as functions of supplied ( ) s l Xf and hired ( ) h l Xg labor time. Under perfectly competitive labor markets, the functions are both linear, with ( ) . s ll f PX= or (.) h ll g PX= . Hence, marginal off-farm income or marginal costs of hired labor are equal to the exogenous wage rate (Pl), in which case, the farm household model is said to be separable. In contrast, when labor markets are imperfectly competitive, both supplied and hired labor functions become nonlinear with the following properties: (.) 0 s l fX ∂∂ > ; 2 2(.) 0 s l fX ∂∂ < and (.) 0 h l gX ∂∂ > ; 2 2 (.) 0 h l gX ∂∂ > , respectively. Now, off-farm income is an increasing and strictly concave function of supplied labor time. Analogously, the costs of hired labor are an increasing and strictly convex function of hired labor time. In this case, the price of labor and leisure (Pl) is endogenously determined and thus the farm household model is non-separable. The production and consumption decisions are simultaneously determined by the stationary solution of the equation system (1) to (4). As indicated earlier, this framework is applicable to several kinds of labor market imperfections. In particular, it accounts for labor market imperfections that lead to a decreasing price effectively received for each further unit of off-farm employment and to an increasing price effectively paid for each further unit of hired labor time. Hence, such conditions can be interpreted as increasing per-unit costs of accessing labor markets, or as increasing transaction costs. Increasing transaction costs associated with working off the farm may be caused by increasing heterogeneity between on- and off-farm family labor. With increasing migration, household members are first transferred to the ‘best jobs’, followed by the ‘next best jobs’ and 2 We assume mutually exclusive tax instruments because we a interested mainly in partial effects of certain taxes on household decisions and not in the interaction effects of commonly imposed taxes. Involving such interactions would increase the intricacy of the theoretical model. 5 so on (Low 1982, 1986). Furthermore, increasing search and transportation costs may lead to a decreasing net wage rate. Increasing per-unit costs of hired labor may result from increasing search, supervision, and monitoring activities. These increases may stem from the growing difficulty in finding the ‘right’ staff for the different and often farm-specific areas of production, or the rising supervision and monitoring costs per-unit of hired labor, as the staff and hired labor time increases. Similarly, the existence of land-specific experience may lead to a decreasing substitutability between family and hired labor. Hired labor becomes less productive and the costs for a standardized hired labor unit increase. Taking fixed costs3 of accessing labor markets into account might mainly contribute to the explanation of the different labor market participation regimes. The present paper does not analyze the different market participation regimes and thus does not explicitly model fixed transaction costs within the theoretical framework. It is assumed that the farm household hires on-farm and supplies off-farm labor simultaneously. The model presented here is applicable to all other market participation schemes. The stationary solutions to the maximization problem (1)-(4) determine the optimal quantities of consumption and production goods, as well as the allocation of time, assuming there exists an interior solution (positive Lagrange multipliers for the constraints 0,, > µφλ and positive optimal choice variables c*, x* > 0). (5) ( ) * .0 i Ci UP λ −= {} ,,i CG m a l∈= (6) ( ) * .0 i Pi GP φλ += {} ,,,i PG c a v l∈= (7) * ** (.) (.) l ll f Pg = = (8) { } ( ) ( ) { } * * * ** * ,, , 0 hs Pi i l l G Ci i i cav i ma PX g X f X R E PC ∈∈ − + −+− = ∑∑ (9) 0)( =rx,G (10) 0=−−++ l s l h lll CXXXT where 0, > φλ denote the Lagrangian multipliers associated with the budget and the technology constraints, respectively; lii fGU ,, and l g represent the first derivatives of the corresponding utility, production, and labor market functions. * l P µλ = denotes the unobservable internal wage in the case of non-separability, with µ as the Lagrangian multiplier associated with the time constraint. In the separable version, * l P indicates the exogenous ‘tax corrected’ wage rate. Furthermore, * Ci P and * Pi P represent the ‘tax corrected’ decision prices for consumption and production goods, respectively. Thus, the ‘tax corrected’ consumption price for manufactured goods is ( ) *1 Cm vat m PP τ = + . Considering market surplus tax, the decision price for consumption 3 Note that the approach could additionally incorporate fixed costs of transactions that are invariant to the traded quantity, but also could affect the farm household’s decision to participate in markets (Sadoulet et al., 1996) for the labor markets; Goetz (1992) as well as Key et al. (2000) for food markets; Skoufias (1993), and Carter and Yao (2002) for the land market). Fixed transaction costs may include bargaining and negotiation efforts and transportation costs, often taking place once per transaction, and are invariant to the level of transaction. 6 of self-produced agricultural goods is ( ) * 1 Ca ms a PP τ = − , however, it is equal to the market price before taxes * Ca a PP = if only the income tax has been imposed.4 Notably, the ‘tax corrected’ production price for home-consumed agricultural goods is ( ) ( ) * 11 Pa y ms a PP ττ =−− . Obviously, this price coincides with the consumption price in the case of market surplus tax ( ) *1 Pa ms a PP τ = − . However, given the existence of an income tax only, the ‘tax corrected’ production price * Pa P will be different from the consumption price * Ca P . Furthermore, the ‘tax corrected’ prices for marketed agricultural goods and variable inputs are indicated by ( ) ( ) *11 Pc y ms c PP ττ =−− and ( ) () * 11 Pv y v v PP ττ =−+ , respectively. In addition, we define * G GG RR τ = , ( ) * 1 y EE τ = − , ( ) ( ) ( ) ( ) *.1 1 . yw ff ττ =−− , and ( ) ( ) ( ) *.1 . y gg τ = − . 3. Comparative static analysis To facilitate the comparative static analysis, we transform the primal decision problem (1)-(4) into a dual representation (Diewert 1982). First we define a dual restricted profit function { } ** ( ,) max | (,) 0 PP x p r px GxrΠ≡ = , where * P p is the (decision) price vector of the production goods and * ( ,) P prΠ is the maximal profit. Following Hotelling’s lemma, the optimal quantities of production goods are obtained by taking the first derivative of the profit function with respect to prices. Thus, {} ** (.) ( , ); , , , Pi i P P X p r i cavl∂Π ∂ = ∀ ∈ . We can also define a dual expenditure function as { } ** ( , ) min | ( ) CC c ep U pcUc U≡≥  , where * C p is the (decision) price vector of the consumption goods and  U is the obtainable utility level. According to Shepard’s lemma, the derived Hicksian compensated demand function can be given as { } * (.) ( , ); , , H Ci i C e P C p U i mal ∂∂ = ∀∈  . Substituting the indirect utility function * ( ,) C Vp Y for  U , it holds that ** * (,(,)) (,) H i C C iC C pVpY CpY≡ . Thus, the Hicksian demand at utility * ( ,) C Vp Y is the same as the Marshallian demand at income Y. For the non-separable model version, condition (7) defines the off-farm labor supply * (,) ss l ll j X XP τ = and the demand for hired labor * (,) hh l ll j X XP τ = as implicit functions of the endogenous labor price ( * l P ) and of those tax parameters ( , yw ττ ) that (directly) affect the general wage level and hence the position of the labor market functions5. Substituting the dual objective and the associated demand and supply functions into the time constraint (10) results in: (11) ( ) ( ) ( ) ( ) * * ** , , , ,0 hs l lP llj llj lC T X pr X P X P CpY ττ ++ − −= , 4 Considering both regimes, decision price is ( ) ( ) ( ) * 11 Ca ms y y a PP τ ττ =− −+ . 5 Here, the income tax affects the position of both functions, with ( ) * (.) 1 (.) y ff τ = − and ( ) *(.) 1 (.) y gg τ = − , while the wage tax affects only the position of the first, with ( ) * (.) 1 (.) w ff τ = − . 7 where () ( ) ( )( ) () * * * ** * . . . .. h s hs l l l l l l G Ci i i CG Y g X f X P T X X R E PC ∈     =Π− + + + − − + =     ∑ . Equation (11) implicitly defines the shadow wage ( * l P ) around the optimal solution of the non-separable model. Hence, ( ) * * * ** , ,, , , , l PC l Gj P p p rT E R χτ = is an implicit function of exogenous decision prices for consumption and production goods ( * P p and * C p ), fixed resources (r), total time available (Tl), land tax payments (RG*), and those tax parameters ( |, j j yw τ = ), which directly affect the wage level. Note that the impact of the other tax policies on the shadow price is already reflected by ‘tax-corrected’ exogenous prices. Based on the above defined functions, we can derive farm household’s consumption, production and labor market responses ( , ,, sh ll Z PG CG X X= ) to changes in any of the desired tax parameters ( | , , ,,, jj y w ms v r vat τ = ). In the case of non-separability, we can decompose the tax-induced farm household reaction for any arbitrary tax policy into the following two components (de Janvry et al. 1991; Sonoda and Maruyama 1999): (12) * * * . l l j j lj P const P ZZ Z P ττ τ = ∂ ∂∂ ∂ = + ∂ ∂ ∂∂ . The first term (direct component) on the right-hand side represents the supply or demand reactions to changes in the tax parameters assuming a constant endogenous labor price (Pl*). The second term (indirect component) represents the adjustments to the changes in the internal wage rate caused by changes in the same tax parameter. In order to determine the indirect component of the non-separable model, we have to derive the tax-induced shadow price adjustment from equation (11), applying the implicit function theorem (de Janvry et al. 1991): (13) ( ) ( ) ( ) * * j j jj j hsH l l l l lY l lh sH jll ll ll ll XXXC C P P XX XC τ τ ττ τ ∂ ∂τ + − − −Ψ = = − +−− . The numerator on the right-hand side represents the change in the time allocation due to increasing tax rates. Here, {} * * ,, j l Pi l i cav Pi j XP XP τ ∂∂ ∂ ∂τ ∈ = ∑ denotes tax-induced on-farm labor adjustment, and ( ) *. jl hh l lj P const XX ττ = =∂∂ and ( ) *. jl ss l lj P const XX τ τ = =∂∂ , respectively, are the direct labor market reactions to increasing income or wage taxes6. Furthermore, { } * * , j H Hl Ci l i ma Ci j CP CP τ ∂∂ ∂ ∂τ ∈ =∑ and ( ) lY l C CYΨ= ∂ ∂ Ψ are the tax-induced substitution and income 6 As noted before, direct labor market reactions result only for an income and a wage tax, since only these taxes directly affect the general wage level. Thus, the following direct tax-induced labor market reactions result: ( ) ( ) ( ) * 2* * 2 . .0; | , 1 l s ll j s j jP const l Xf Pj yw X ∂∂τ τ ∂τ ∂ = =− <= − , and () () * 2* * 2 . . 10 l h ll h y yP const l Xg P X ∂∂ τ ∂τ ∂ = =−> − . 14 5. References Abdulai, A., Delgado, C.L. (1999). Determinants of Nonfarm Earnings of Farm-Based Husbands and Wives in Northern Ghana. American Journal of Agricultural Economics, 81, 117-130. 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Baltimore: John Hopkins University Press. 1 Table 1: Comparative statics for income tax in non-separable model jy ττ = Direct tax-induced labor market reactions Direct effect from tax-induced price changes of PG Indirect effect on PG Direct income effect Direct substitution effect from price changes of CG Indirect effect on CG h l X s l X * Pc p * Pa p * Pv p * Cm p * Ca p i j Z τ ∂ ∂ * l h l jP const X τ = ∂ ∂ * l s l jP const X τ = ∂ ∂ * * i j Pc Pc p X p τ ∂ ∂ ∂∂ * * i j Pa Pa p X p τ ∂ ∂ ∂∂ * * i j Pv Pv p X p τ ∂ ∂ ∂∂ * * il lj Xp p τ ∂∂ ∂∂ i C Y ∂ ∂ Ψ * * i Cm Cm j Cp p τ ∂∂ ∂∂ * * i Ca Ca j Cp p τ ∂∂ ∂∂ * * il lj Cp p τ ∂∂ ∂∂ Shadow price * 0 l j P τ ∂< ∂ > 0 1 < 0 2 < 0 3 < 0 3 (> 0 4) 3 - < 0 2, 6 = 0 = 0 - Labor market responses ? h l j X τ ∂= ∂ > 0 1 - - - - < 0 1 - - - - ? s l j X τ ∂= ∂ - < 0 2 - - - > 0 2 - - - - Production responses , ? ca j X τ ∂ ∂= - - < 0 3 < 0 3 > 0 3 > 0 3 - - - - ? v j X τ ∂ ∂ = - - < 0 3 < 0 3 > 0 3 (> 0 4) 3 - - - - ? l j X τ ∂ ∂ = - - < 0 3 < 0 3 (> 0 4) 3 > 0 3 - - - - Consumption responses ( ) ?0 m j C τ ∂< ∂= - - - - - - < 0 6 = 0 = 0 (< 0 7) 5 () ?0 a j C τ ∂< ∂ = - - - - - - < 0 6 = 0 = 0 (< 0 7) 5 ? l j C τ ∂ ∂ = - - - - - - < 0 6 = 0 = 0 > 0 5 2 Table 1a: Comparative statics for income tax in separable model Notes: Following assumptions were considered by deriving the comparative statics: 1 convexity of *(.)g in h l X ; 2 concavity of * (.)f in s l X ; 3 concavity of (.) Π in ( ) i p i PG∈ ; 4 v X and l X are complements; 5 convexity of (.)e in ( ) i p i CG∈ ; 6 a C , m C and l C are normal goods; 7 a C are substitutes for l C . jy ττ = Direct tax-induced labor market reactions Direct effect from tax-induced price changes of PG Direct income effect Direct substitution effect from price changes of CG h l X s l X * Pc p * Pa p * Pv p * l p * Cm p * Ca p * l p i j Z τ ∂ ∂ * l h l jP const X τ = ∂ ∂ * l s l jP const X τ = ∂ ∂ * * i j Pc Pc p X p τ ∂ ∂ ∂∂ * * i j Pa Pa p X p τ ∂ ∂ ∂∂ * * i j Pv Pv p X p τ ∂ ∂ ∂∂ * * il lj Xp p τ ∂∂ ∂∂ i C Y ∂ ∂ Ψ * * i Cm Cm j Cp p τ ∂∂ ∂∂ * * i Ca Ca j Cp p τ ∂∂ ∂∂ * * il lj Cp p τ ∂∂ ∂∂ Labor market ( ) ? sh ll j XX τ ∂− = ∂ - - < 0 3 < 0 3 > 0 3 > 0 3 < 0 6 - - > 0 5 Production responses , 0 ca j X τ ∂ ∂= 8 - - < 0 3 < 0 3 > 0 3 > 0 3 - - - - 0 v j X τ ∂ ∂ = 8 - - < 0 3 < 0 3 > 0 3 (> 0 4) 3 - - - - 0 l j X τ ∂ ∂ = 8 - - < 0 3 < 0 3 (> 0 4) 3 > 0 3 - - - - Consumption responses () ?0 m j C τ ∂< ∂= - - - - - - < 0 6 = 0 = 0 < 0 5, 7 ( ) ?0 a j C τ ∂< ∂ = - - - - - - < 0 6 = 0 = 0 < 0 5, 7 ? l j C τ ∂ ∂ = - - - - - - < 0 6 = 0 = 0 > 0 5 3 Table 2: Comparative statics for wage tax in non-separable model jw ττ = Direct tax-induced labor market reactions Direct effect from tax-induced price changes of PG Indirect effect on PG Direct income effect Direct substitution effect from price changes of CG Indirect effect on CG h l X s l X * Pc p * Pa p * Pv p * Cm p * Ca p i j Z τ ∂ ∂ * l h l jP const X τ = ∂ ∂ * l s l jP const X τ = ∂ ∂ * * i j Pc Pc p X p τ ∂ ∂ ∂∂ * * i j Pa Pa p X p τ ∂ ∂ ∂∂ * * i j Pv Pv p X p τ ∂ ∂ ∂∂ * * il lj Xp p τ ∂∂ ∂∂ i C Y ∂ ∂Ψ * * i Cm Cm j Cp p τ ∂∂ ∂∂ * * i Ca Ca j Cp p τ ∂∂ ∂∂ * * il lj Cp p τ ∂∂ ∂∂ Shadow price * 0 l j P τ ∂< ∂ = 0 < 0 2 = 0 = 0 = 0 - < 0 2, 6 = 0 = 0 - Labor market responses 0 h l j X τ ∂< ∂ = 0 - - - - < 0 1 - - - - ? s l j X τ ∂= ∂ - < 0 2 - - - > 0 2 - - - - Production responses , 0 ca j X τ ∂ ∂> - - =0 = 0 = 0 > 0 3 - - - - ( ) 4 ?0 v j X τ ∂ ∂ = > - - = 0 = 0 = 0 (> 0 4) 3 - - - - 0 l j X τ ∂ ∂ > - - = 0 = 0 = 0 > 0 3 - - - - Consumption responses ( ) 5 ?0 m j C τ ∂< ∂ = - - - - - - < 0 6 = 0 = 0 (< 0 7) 5 ( ) 5 ?0 a j C τ ∂< ∂ = - - - - - - < 0 6 = 0 = 0 (< 0 7) 5 ? l j C τ ∂ ∂ = - - - - - - < 0 6 = 0 = 0 > 0 5 4 Table 2a: Comparative statics for wage tax in separable model Notes: Following assumptions were considered by deriving the comparative statics: 1 convexity of *(.)g in h l X ; 2 concavity of * (.)f in s l X ; 3 concavity of (.) Π in ( ) i p i PG∈ ; 4 v X and l X are complements; 5 convexity of (.)e in ( ) i p i CG∈ ; 6 a C , m C and l C are normal goods; 7 a C are substitutes for l C . jw ττ = Direct tax-induced labor market reactions Direct effect from tax-induced price changes of PG Direct income effect Direct substitution effect from price changes of CG h l X s l X * Pc p * Pa p * Pv p * l p * Cm p * Ca p * l p i j Z τ ∂ ∂ * l h l jP const X τ = ∂ ∂ * l s l jP const X τ = ∂ ∂ * * i j Pc Pc p X p τ ∂ ∂ ∂∂ * * i j Pa Pa p X p τ ∂ ∂ ∂∂ * * i j Pv Pv p X p τ ∂ ∂ ∂∂ * * il lj Xp p τ ∂∂ ∂∂ i C Y ∂ ∂ Ψ * * i Cm Cm j Cp p τ ∂∂ ∂∂ * * i Ca Ca j Cp p τ ∂∂ ∂∂ * * il lj Cp p τ ∂∂ ∂∂ Labor market ( ) ? sh ll j XX τ ∂− = ∂ - - = 0 3 = 0 3 = 0 3 > 0 3 < 0 6 - - > 0 5 Production responses , 0 ca j X τ ∂ ∂> - - = 0 3 = 0 3 = 0 3 > 0 3 - - - - () 4 ?0 v j X τ ∂ ∂= > - - = 0 3 = 0 3 = 0 3 (> 0 4) 3 - - - - 0 l j X τ ∂ ∂ > - - = 0 3 = 0 3 = 0 3 > 0 3 - - - - Consumption responses ( ) 5 ?0 m j C τ ∂< ∂ = - - - - - - < 0 6 = 0 = 0 (< 0 7) 5 ( ) 5 ?0 a j C τ ∂< ∂ = - - - - - - < 0 6 = 0 = 0 (< 0 7) 5 ? l j C τ ∂ ∂ = - - - - - - < 0 6 = 0 = 0 > 0 5 5 Table 3: Comparative statics for market surplus tax in non-separable model j ms ττ = Direct tax-induced labor market reactions Direct effect from tax-induced price changes of PG Indirect effect on PG Direct income effect Direct substitution effect from price changes of CG Indirect effect on CG h l X s l X * Pc p * Pa p * Pv p * Cm p * Ca p i j Z τ ∂ ∂ * l h l jP const X τ = ∂ ∂ * l s l jP const X τ = ∂ ∂ * * i j Pc Pc p X p τ ∂ ∂ ∂∂ * * i j Pa Pa p X p τ ∂ ∂ ∂∂ * * i j Pv Pv p X p τ ∂ ∂ ∂∂ * * il lj Xp p τ ∂∂ ∂∂ i C Y ∂ ∂Ψ * * i Cm Cm j Cp p τ ∂∂ ∂∂ * * i Ca Ca j Cp p τ ∂∂ ∂∂ * * il lj Cp p τ ∂∂ ∂∂ Shadow price * ? l j P τ ∂= ∂ (<0 7) = 0 = 0 < 0 3 < 0 3 = 0 - < 0 2, 6 = 0 < 0 5, 7 - Labor market responses ? h l j X τ ∂= ∂ = 0 - - - - ? (< 0) 1 - - - - ? s l j X τ ∂= ∂ - = 0 - - - ? (> 0) 2 - - - - Production responses , ? ca j X τ ∂ ∂= - - < 0 3 < 0 3 = 0 (> 0) 3 - - - - ? v j X τ ∂ ∂ = - - < 0 3 < 0 3 = 0 (> 0 4) 3 - - - - ? l j X τ ∂ ∂ = - - < 0 3 < 0 3 = 0 (> 0 4) 3 - - - - Consumption responses ( ) 7 ?0 m j C τ < ∂= ∂ - - - - - - < 0 6 = 0 (< 0 7) 5 (< 0 7) 5 ? a j C τ ∂ ∂ = - - - - - - < 0 6 = 0 > 0 (< 0 7) 5 ? l j C τ ∂ ∂= - - - - - - < 0 6 = 0 (< 0 7) 5 (> 0) 5 6 Table 3a: Comparative statics for market surplus tax in separable model Notes: Following assumptions were considered by deriving the comparative statics: 1 convexity of *(.)g in h l X ; 2 concavity of * (.)f in s l X ; 3 concavity of (.)Π in ( ) i p i PG∈ ; 4 v X and l X are complements; 5 convexity of (.)e in ( ) i p i CG∈ ; 6 a C , m C and l C are normal goods; 7 a C are substitutes for l C . j ms ττ = Direct tax-induced labor market reactions Direct effect from tax-induced price changes of PG Direct income effect Direct substitution effect from price changes of CG h l X s l X * Pc p * Pa p * Pv p * l p * Cm p * Ca p * l p i j Z τ ∂ ∂ * l h l jP const X τ = ∂ ∂ * l s l jP const X τ = ∂ ∂ * * i j Pc Pc p X p τ ∂ ∂ ∂∂ * * i j Pa Pa p X p τ ∂ ∂ ∂∂ * * i j Pv Pv p X p τ ∂ ∂ ∂∂ * * il lj Xp p τ ∂∂ ∂∂ i C Y ∂ ∂ Ψ * * i Cm Cm j Cp p τ ∂∂ ∂∂ * * i Ca Ca j Cp p τ ∂∂ ∂∂ * * il lj Cp p τ ∂∂ ∂∂ Labor market ( ) ( ) 0 sh ll j XX τ ∂− ∂ > - - < 0 3 < 0 3 = 0 = 0 < 0 6 - < 0 5, 7 = 0 Production Responses , 0 ca j X τ ∂ ∂< - - < 0 3 < 0 3 = 0 = 0 - - - - 0 v j X τ ∂ ∂ < - - < 0 3 < 0 3 = 0 = 0 - - - - 0 l j X τ ∂ ∂< - - < 0 3 < 0 3 = 0 = 0 - - - - Consumption responses ( ) ?0 m j C τ ∂< ∂ = 7 - - - - - - < 0 6 = 0 < 0 5, 7 = 0 ? a j C τ ∂ ∂ = - - - - - - < 0 6 = 0 > 0 = 0 ?( 0) l j C τ ∂< ∂= 7 - - - - - - < 0 6 = 0 < 0 5, 7 = 0 7 Table 4: Comparative statics for input tax in non-separable model j vat ττ = Direct tax-induced labor market reactions Direct effect from tax-induced price changes of PG Indirect effect on PG Direct income effect Direct substitution effect from price changes of CG Indirect effect on CG h l X s l X * Pc p * Pa p * Pv p * Cm p * Ca p i j Z τ ∂ ∂ * l h l jP const X τ = ∂ ∂ * l s l jP const X τ = ∂ ∂ * * i j Pc Pc p X p τ ∂ ∂ ∂∂ * * i j Pa Pa p X p τ ∂ ∂ ∂∂ * * i j Pv Pv p X p τ ∂ ∂ ∂∂ * * il lj Xp p τ ∂∂ ∂∂ i C Y ∂ ∂ Ψ * * i Cm Cm j Cp p τ ∂∂ ∂∂ * * i Ca Ca j Cp p τ ∂∂ ∂∂ * * il lj Cp p τ ∂∂ ∂∂ Shadow price * ? l j P τ ∂ ∂= = 0 = 0 = 0 = 0 (> 0 4) 3 - < 0 5, 6 (> 0 7) 5 = 0 - Labor market responses ? h l j X τ ∂= ∂ = 0 - - - - ? - - - - ? s l j X τ ∂= ∂ - = 0 - - - ? - - - - Production responses , ? ca j X τ ∂ ∂= - - = 0 = 0 < 0 3 ? - - - - ? v j X τ ∂ ∂ = - - = 0 = 0 < 0 3 ? - - - - ? l j X τ ∂ ∂ = - - = 0 = 0 (> 0 4) 3 ? - - - - Consumption responses ? m j C τ ∂ ∂ = - - - - - - < 0 6 = 0 = 0 ? ? a j C τ ∂ ∂ = - - - - - - < 0 6 = 0 = 0 ? ? l j C τ ∂ ∂ = - - - - - - < 0 6 = 0 = 0 ?