A General Welfare Decomposition for CGE Models

Transcription

1 urdue University urdue e-ubs GTA Tecnical apers Agricultural Economics A General Welfare Decomposition for CGE Models Kevin J Hanslow roductivity Commission, Australia Follow tis and additional wors at: ttp://docslibpurdueedu/gtaptp Hanslow, Kevin J, "A General Welfare Decomposition for CGE Models" (2000) GTA Tecnical apers aper 19 ttp://docslibpurdueedu/gtaptp/19 Tis document as been made available troug urdue e-ubs, a service of te urdue University Libraries lease contact epubs@purdueedu for additional information

2 A General Welfare Decomposition for CGE Models Kevin J HANLOW GTA Tecnical aper No 19 January, 2000 Kevin Hanslow, roductivity Commission, GO Box 80 Canberra ACT 2616 Australia anslow@pcgovau

3 A General Welfare Decomposition for CGE Models by Kevin J HANLOW GTA Tecnical aper No 19 Abstract Huff and Hertel (2001) derive a welfare decomposition for te equivalent variation in te GTA model Te derivation appears to be very specific to GTA Neverteless, it contains nearly all te ingredients required for performing welfare decomposition for any CGE model In tis paper, te approac of Huff and Hertel (2001) is generalised to derive a welfare decomposition tat can be applied to most, if not all, CGE models General production and utility functions are accommodated, as are foreign income flows A brief guide to coding te proposed welfare decomposition in GEMACK is also provided Te decomposition is applied to decomposing te equivalent variation in GTA II

4 Table of Contents 1 Introduction 1 2 Te formal Derivation of te Welfare Decomposition 4 21 Motivation 5 22 Notation 5 23 Definitions and Conventions 7 24 Derivation 9 25 ummary of Welfare Decomposition 15 3 Te roperties of te rofits Effects Te rofits Effects are Zero Under tandard CGE Assumptions Te rofits Effects Under Maret ower Only Reductions in Maret ower 21 4 Decomposition of Money Metric and Compensation Measures of Welfare Cange Money Metric Welfare Measures Compensation Welfare Measures Based on te Balance of Trade Function 23 5 Application to te GTA Equivalent ariation Measure of Welfare Cange 24 6 ummary and Outstanding Issues for Future Researc 27 References 29 TABLE Table 1 ummary of te Welfare Decomposition 16 Table 2 Welfare Decomposition Terms wit Guide to GEMACK Implementation 16 Table 3 Calculation of Compensation Based Measures of Welfare 23 III

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6 General Welfare Decomposition for CGE Models by Kevin J HANLOW 1 Introduction In te GTA model, economic welfare is represented as being derived from te allocation of national income between private consumption, government consumption and savings (Hertel 1997) Tis recognises tat ouseolds gain benefits from teir own current ouseold consumption expenditure Tey also benefit from current net national saving, since tis increases teir future ouseold consumption 1 Finally, tey benefit from te government s provision of public goods and services, as proxied by current government expenditure 2 National income is allocated between aggregate private consumption, aggregate government consumption and saving to maximise a top-level Cobb-Douglas utility function Wit tis functional form, successive increases in real ouseold or government expenditure or saving generate equi-proportional increases in economic wellbeing Aggregate private and government consumption are allocated between particular commodities to maximise constant difference elasticity (CDE) and Cobb- Douglas utility functions, respectively As te CDE utility function is non-omotetic, tis recognises tat successive increases in private consumption of particular goods or services need not lead to equi-proportional increases in economic wellbeing Consequently, given suc a definition of economic welfare, ow well off a policy cange actually maes a region depends on wat te cange does to its national income It also depends on te effect of te policy cange on prices, and ence te purcasing power of tat income Finally, it depends on ow ouseolds evaluate te benefits of additional real expenditure Te last item te marginal utility of real income is a consequence of te assumed utility functions National income is nominal net national product (), and is equal to GD less depreciation less net income payments to foreigners One particularly useful feature of GTA tat captures tese dependencies is a welfare decomposition (Huff and Hertel 2001) Tis subdivides te overall measure of welfare into components tat ave a reasonably intuitive interpretation As ust noted, economic well-being depends in part on disposable income, wic can be divided into its components GD, 1 As noted in Hertel (1997), tis derives from te wor of Howe (1975), wo sowed tat te intertemporal, extended linear expenditure system could be derived from an equivalent, atemporal maximisation problem, in wic savings enters te utility function 2 As noted in Hertel (1997), tis derives from te wor of Keller (1980), wo sowed tat if (1) preferences for public goods are separable from preferences for private goods, and (2) te utility function for public goods is identical across ouseolds, ten a public utility function can be derived Te aggregation of tis index wit private utility to provide an overall welfare measure requires te furter assumption tat te level of public goods provided in te initial equilibrium is optimal

7 depreciation, and net income payments to foreigners 3 GD can be furter subdivided into te contributions from primary factors, net indirect taxes and tecnical canges Decomposition along tese lines leads to te following welfare contributions Endowment contributions to welfare arise from canges in te availability of primary factors for example, increases in te stoc of macinery, buildings and agricultural land Tecnical efficiency contributions arise from canges in te use of available inputs in production for example, improvements in labour productivity Allocative efficiency contributions arise wen te allocation of resources canges relative to pre-existing distortions 4 For any small cange in te economy, allocative efficiency contributions are measured as te sum of a number of terms, were eac term is te size of an initial indirect tax distortion, multiplied by te policy-induced cange in te quantity of goods or services affected by tat distortion 5 Te initial indirect tax distortion is te difference between te contribution to output from an additional unit of te good, and te price for wic te good could be obtained in te absence of te tax Te product of te distortion and te cange in te quantity terefore measures te net contribution to output from te cange in te quantity of te good used Te allocative efficiency contribution for a large cange to te economy equals te sum of te contributions for a sequence of small canges tat are equivalent, in total, to te large cange Tere are also contributions to national welfare arising from canges in relative prices (including export relative to import prices, or te terms of trade) as producers and consumers adust teir purcasing and sale patterns in response to policy cange In addition, tere are potentially contributions to welfare arising from te liely flow-on effects of production and terms of trade canges on foreign income flows Te derivation of te welfare decomposition in Huff and Hertel (2001) appears to be very specific to GTA It is even expressed in te TABLO notation of te GEMACK software (Harrison and earson 1996) in wic GTA is implemented Neverteless, it contains nearly all te ingredients required for performing a welfare decomposition for any CGE model Te derivation uses maret clearing conditions for commodities and primary factors, and zero pure profit conditions for industries Tese are relationsips tat would be present in most oter CGE models In tis paper te approac of Huff and Hertel (2001) is generalised to derive a welfare decomposition tat can be applied to most, if not all, CGE models Tere are six main differences between te approac adopted in tis paper and tat in Huff and Hertel (2001) 3 Net income payments to foreigners are zero in GTA 4 Te GTA welfare decomposition was motivated by te wor of Keller (1980), wic sowed ow te aggregate excess burden (te sum across ouseolds of compensating variations) was equal to allocative efficiency effects, in a model formulated for examining tax canges 5 In multi-step model simulations tat correct for linearisation error, tis can give an exact measure of te cange in te welfare loss triangle associated wit a distortion 2

8 First, tis paper decomposes te cange in utility rater tan a money metric measure of te cange in welfare (suc as te equivalent variation used in GTA) Tis decomposition of te cange in utility can be used to decompose bot money metric measures of welfare and compensation measures based on te balance of trade function Tis is important as neiter of tese welfare measures is clearly superior to te oter, and tey differ from eac oter for economies wit existing taxes or subsidies (Martin 1996) econd, tis paper includes welfare contributions from foreign income flows Tird, te decomposition derived in tis paper is general enoug to cope wit multi-product industries wit non-separable inputs and outputs, and non-constant returns to scale in production Fourt, for eac industry, terms measuring te welfare contributions caused by deviations from optimal or price taing beaviour, or from zero pure profits, are derived Tey are linear functions of indices of effective inputs and effective outputs for eac industry Tese terms will be called te profits effects (or effect if te term for a particular industry, or te economy-wide total of all suc terms, is being discussed) 6 Fift, wereas in GTA a nested utility function is assumed income is allocated between total private and government consumption and savings, and ten total consumption is allocated across commodities tere is no requirement for a nested utility function in te current treatment ixt, te welfare decomposition is derived for particular ouseolds Tis empasises ow eac ouseold may ave its own relative price effect, since te composition of expenditure may differ wit income levels, and te composition of income may vary by ouseold type By ten assuming all ouseolds are identical, a welfare decomposition for a representative ouseold, as used in te GTA model, is obtained Anoter difference between te current paper and te original 1996 version of Huff and Hertel is tat te effect of non-omotetic preferences on welfare can be captured in a coefficient by wic all te terms, te sum of wic equals te cange in utility, are multiplied Tis is in contrast to te original 1996 version of Huff and Hertel were te effect of non-omotetic preferences on welfare is one of tese terms te variable described as te contribution to E of marginal utility of income 7 ection 2 describes te conceptual economy for wic te welfare decomposition is derived Te notation to be used and definitions are introduced, and ten te formal derivation is presented Te profits effects are analysed in section 3 First, it is sown tat te profits effects are zero for industries tat are revenue maximising, cost minimising and price taing, and ave zero pure profits econd, it is sown tat, wen te firms in an industry are revenue maximising and cost minimising, te profits effects are sums of terms eac of wic is te product of a measure of 6 Tis name is cosen since tese terms will more usually be non-zero because of non-competitive beaviour, leading to positive pure profits, rater tan because of non-optimising beaviour Te coice of tis terminology trougout tis paper sould not, owever, be allowed to diminis in te reader s mind te possible usefulness of tis term in applications wit non-optimising beaviour 7 Te revised (2001) version of Huff and Hertel eliminates tis term 3

9 maret power in an output (input) maret times te cange in te production (usage) of te output (input) Tird, for a uniform decrease in maret power in all marets, te profits effects are positive ection 4 sows ow bot money metric and compensation based welfare measures can be decomposed using te results of section 2 ection 5 derives a decomposition of te equivalent variation (E) for te GTA model based on te results of sections 2 and 4 ection 6 concludes wit a summary of te current paper and a discussion of issues for future researc 2 Te Formal Derivation of te Welfare Decomposition Consider an economy tat consists of many activities, eac of wic uses various inputs Te inputs are divided into two groups commodities and endowments Te activities are divided into two groups industries, wic produce (possibly multiple) commodities and use bot commodities and endowments as inputs, and final demands, wic do not produce anyting and use only commodities as inputs Eac commodity may be produced by more tan one industry Taxes or subsidies may be levied on all inputs to all activities, and on all outputs from all industries Te assumption tat is fundamental in te derivation of te welfare decomposition is maret clearing te quantity of eac commodity produced in te economy equals te total quantity of tat commodity used in all activities Zero pure profits conditions tat te total cost of all inputs for eac industry equals te total value of all commodities produced by tat industry are used later to eliminate some terms in te welfare decomposition (section 3), but are not essential to te derivation Te maret clearing condition applies to bot domestic and imported commodities Te following convention is adopted to ensure tat te condition applies for imports 8 A final demand activity total imports of eac commodity is included, te inputs to wic are imported commodities wit negative values, equal in magnitude to te total CIF values of imported commodities used by all oter activities Terefore bot te economy-wide production and use of imported commodities is equal to zero; total imports count negatively in final demand; and a maret clearing condition can be considered as applying to imported commodities Oter final demand activities include: total exports of eac commodity; private consumption; and government consumption 8 Tis convention is similar to ow imports are sown in some input-output tables 4

10 All oter final demand activities will be called investment 9 Nominal national income, or, is equal to te returns to all endowments (inclusive of income taxes), minus te value of depreciation of domestic capital, plus all indirect tax revenue, minus all indirect subsidy payments, plus net foreign income flows generated by a range of net foreign assets Net foreign income flows may be positive or negative Tus nominal is equal to nominal GD, minus depreciation, plus net foreign income flows Nominal is allocated between purcases of private consumption commodities, government consumption commodities, and savings so as to maximise a utility function 21 Motivation Before introducing te notation and conventions required for te formal derivation, a brief overview of te derivation is now provided Te derivation proceeds using linearised equations Real income (tat is, utility) of a ouseold is expressed as a multiple of te difference between nominal ouseold income and an expenditure price index Nominal ouseold income is expressed as a sare of nominal Ten nominal is split into GD minus depreciation plus foreign income Te latter two items are ten decomposed into nominal and real parts Te depreciation terms are written as a sum across industries, but could ust as well ave been left as a macro aggregate Te GD index, any price parts of depreciation and foreign income, and te expenditure price index for te ouseold constitute te relative price contributions to welfare of te ouseold Real GD is ten decomposed, in terms of te industry structure ust outlined, into allocative efficiency, tecnical efficiency and endowment effects It is at tis stage tat te maret clearing conditions are critical Finally, a residual term is obtained, wic is zero if te conventional assumptions of CGE models zero pure profits and optimising and price taing beaviour are satisfied Consequently, quite a bit of notation is required to support te formal derivation bot its macro and micro components and suc notation is now introduced 22 Notation Upper case letters designate levels, lower case percentage canges means cange in uperscripts on a symbol indicate to wat item te symbol is related ubscripts indicate a variety of types of te item indicated by te superscript For example, Π DK designates te asset price of domestic capital of type 9 Tus all te final demands usually represented in an IO table and in te definition of GD are present ince, in some CGE models (for example, te MONAH model described in Dixon and Rimmer (2000)), tere is an investment activity for eac industry, it seemed sensible to allow for te possibility of many investment activities in te current treatment It maes no difference in te formal derivation 5

11 ymbols used are: tax-inclusive price (rental price for assets), but tax-exclusive price wen applied to industry outputs of commodities, tat is, wit superscript O; Π asset price; real quantity; tax-inclusive value (rental value for assets); ˆ tax-exclusive value (rental value for assets); R tax revenue; T ad valorem tax rate; D depreciation rate; R rate of return (lower case is ); U( ) indirect utility function governing te allocation of income; N number of ouseolds; and Λ sare of a ouseold in national income A bar over a symbol indicates effective inputs (outputs) For quantities, tese are te input quantities (output quantities) multiplied (divided) by te corresponding tecnical efficiencies Effective prices are defined so tat: A bold, non-italicised symbol sould be interpreted as a vector For example, C is te vector of tax-inclusive prices of commodities purcased for private consumption Multiplication of two vectors sould be interpreted as te dot (tat is, scalar) product For example, te value of aggregate private consumption equals te sum of consumption prices times consumption quantities, tus: C C C uperscripts used are: net national product; ND net domestic product; GD gross domestic product; DK domestic capital; FY foreign income; FA foreign asset; DE depreciation; C private consumption; G government consumption; I gross investment; 6

12 X exports; M imports; savings; I input into activities; and O output from industries ubscripts used are: to range across types of domestic capital; to range across types of foreign assets; a to range over activities; f to range over final demands (a subset of activities); to range over industries (a subset of activities); i to range over inputs; e to range over endowments (a subset of inputs); c to range over commodities (a subset of inputs); to range over ouseolds; and total over a dimension Were two subscripts occur, te first refers to an element of te set of inputs, wile te second refers to an element of te set of activities 23 Definitions and Conventions Macro Aggregates Te real income of ouseold,, 10 is defined to be te maximised value of utility, tat is: C G (,, ) U, (1) Te percentage canges in aggregates are defined as value-sare-weigted averages across all components For example, national real private consumption is defined by: C q C C C q C c q c C c (2) Again, if tere is a set of investment activities I (a subset of te set of final demands), ten te investment price index is defined by: 10 A superscript is used to empasise tat ouseold income is some sare of national income 7

13 I p I I p I c, f I cf p cf (3) Foreign Income In reality, some foreign income flows for example, foreign aid are not returns to some asset Te convention adopted in suc a case is tat suc foreign income flows are returns on an asset, wit te rate of return constant at one, and te asset price equal to te price index, tus: FA ϕ (4) R FA ϕ 1 (5) and, consequently, te quantity of te asset is defined to be te foreign income flow divided by te price index Tis is a sensible convention, wit te foreign income flow being equal to te real foreign income flow times an expenditure price index Tax-Inclusive and Tax Exclusive rices and alues Te next two equations relate te price received by industry for producing commodity c ( c O ), te economy-wide uniform output tax inclusive price of commodity c ( c O ), and te price paid by industry for commodity c ( c I ) c c ( T ) 1 + (6) c c c ( T ) 1 + (7) c Te next four equations clarify te use of and ˆ to denote tax-inclusive and tax-exclusive values, respectively ˆ (8) c c c ˆ + R (9) c c c c c ˆ (10) c c c ˆ + R (11) i i i i i Note tat equation (11) uses a subscript of i rater tan c, since we wis to accommodate te possibility of industry-specific taxes on primary factor inputs 8

14 24 Derivation Overview Te derivation proceeds, using linearised equations, as follows Te cange in utility for a particular ouseold is expressed as te difference between nominal ouseold income (wic is some sare of nominal tat accrues to te ouseold) and an expenditure price index (ranging over te prices of private and government consumption goods and saving) for te ouseold Te nominal ouseold income is expressed in terms of te cange in te sare (of te ouseold in ) and te cange in nominal, te latter being equal to canges in nominal GD minus depreciation plus foreign income Te endowment and rate of return contributions to welfare from te latter two items are identified Te price index of GD, te expenditure price index for te ouseold, and any asset price parts of depreciation and foreign income are manipulated to define a relative price contribution to welfare for te ouseold For an economy consisting of identical ouseolds, tis collapses to two welfare contribution terms terms of trade and asset price contributions to welfare Ten it only remains to decompose te percentage cange in real GD Real GD is expressed from te expenditure side as a sare-weigted sum across commodity inputs into all final demand activities Allocative efficiency contributions are derived by splitting off indirect tax revenues from te values of inputs and outputs multiplied by percentage canges in quantities Maret clearing conditions are used to eventually yield an expression tat is a linear function of sare-weigted indices of industries outputs and inputs Tese can be written as a weigted sum of tecnical efficiency terms te tecnical efficiency contribution to welfare and a difference of weigted sums of effective outputs and effective inputs te contribution from non-optimising and/or non-price taing beaviour, or from deviations from zero pure profits Formal Derivation Real income (utility) for ouseold is: C G (,, ) U, (12) Te linearisation of tis is: U U U C C C G G ( ) C + U C C G G ( Λ + Λ ) G G + U + U (13) were Roy s identity as been used to derive te tird line and te fourt line introduces te sare of ouseold in If canges are converted to percentage canges (for example, q/100) ten: 9

15 q U U C C G G ( λ + v p p p ) ( λ + v p ) (14) Nominal can be related to ND and GD as follows: ND FY GD GD GD DE + DE D DK FY + DK FA DK + R FA FA FA (15) Linearisation of tis yields: v + GD GD GD ( p + q ) DE DK DK DK ( d + + q ) FA FA FA FA ( + + q ) (16) Finally, we define te and GD price indices as follows: C C G G p p + p + p (17) and GD p GD C C G G I I X X M M (18) p p p p p We are now in a position to express te percentage cange in real income (utility) for ouseold as a function of te component price and quantity canges using equations (14) and (16)-(18) First, rewrite equation (14) by dividing bot sides by and defining: tus yielding: U Θ (19) q ( + v p ) Θ λ (20) econd, divide bot sides of equation (16) by and substitute te expression for v into equation (20) to yield: 10

16 q λ GD + Θ + p GD GD ( p + q ) DE DK DK DK ( d + + q ) FA FA FA FA ( + + q ) (21) Tird, equation (18) is used to eliminate te expression GD p GD from equation (21) to yield: q λ + GD + q Θ DE FA + p C C G G I I X X M M ( p + p + p + p p ) GD DK DK DK ( d + + q ) FA FA FA ( + + q ) (22) Fourt, te components of te GD price index in equation (22) are collected into tree groups tus: q λ Θ GD + q DE FA + p C C ( p G G + p + p ) I I ( p p ) X X ( p M M p ) GD DK DK DK ( d + + q ) FA FA FA ( + + q ) (23) were te expression p as been added to (subtracted from) te first (second) group Finally, equation (17) is used to replace te first group of prices in equation (23) by te price index A rearrangement of terms ten yields: 11

17 q Θ λ Θ X X M M [ p p ] FA FA p + ( p p ) DE DK DK ( ) d + q FA FA ( q ) FA FA ) GD GD ( q ) DE DK [( ) ( p + )] (24) Note tat Θ is te elasticity of utility wit respect to nominal ouseold income for ouseold It is equal to one for a omotetic direct utility function In te expression for te real income (utility) of ouseold in equation (24), te second line is te impact of canges in te sare of national income accruing to ouseold, and is determined by ow an economic cange affects te particular sources of income of ouseold 11 Te tird to fift lines define te impact of relative prices Te tird line is a terms of trade effect for te wole economy Te fourt line is an effect, again for te wole economy, of prices related to assets eld or to te creation of assets Te fift line is te ouseold specific effect of te price paid by te ouseold for its goods relative to te national average price Te sixt line defines te contribution to real income from losses in te nation s endowment of capital arising from depreciation, wile te sevent line defines contributions from canges in real foreign assets Te eigt line is te impact of canges in rates of return from foreign assets Te final line, involving real GD, needs to be decomposed furter Before proceeding wit te decomposition of real GD, some simplifications for te case were all ouseolds are identical will be derived Tis provides a decomposition of utility for te representative consumer, as would be required in te current implementation of te GTA model Te main simplification is in te relative price contribution ince all ouseolds are now assumed to be identical, te composition of teir expenditure across private and government consumption goods is identical to tat of te nation as a wole Hence te ouseold specific expenditure price index is equal to te price index Formally, designating te number of ouseolds by N, 11 Te furter decomposition of tis term is not pursued in tis paper, wic ultimately as a view to generalising te GTA welfare decomposition, for wic tere is only a single representative ouseold 12

18 p N N C C G G ( p + p + p ) C C p N N p C C C p p p C + + G G p + N p G G G p + + G p + N p p (25) Consequently, te real income (utility) of te representative ouseold can be decomposed tus: q Θ Θ n X X M M [ p p ] ( TOT ) FA FA DE DK [( p + ) ( p + )] ( A_RI) FA FA FA FA DE GD GD q q ( RORF) ( FENDW ) DK DK ( d + q ) ( ENDW ) ( O) (26) Te terms in parenteses on te far rigt-and side sow te correspondence between te algebraic expressions on te rigt-and side of te equation and te contributions in te completed welfare decomposition An equal sign () before te name of te welfare contribution indicates tat te algebraic expression is equal to tis contribution An arrow ( ) indicates tat te algebraic expression is one part of tis contribution Te welfare contributions are: O population cange; TOT terms of trade; A_RI asset price; RORF foreign rate of return; FENDW foreign endowment; and ENDW (domestic) endowment contributions From now on it will be assumed tat we are dealing wit te case in wic all ouseolds are identical, tat is, te case of te representative ouseold It now remains to decompose te real GD component, wic is te final term in equation (26) Real GD can be expressed, from te expenditure side, as: 13

19 Θ GD q GD Θ Θ c,f c,f cf qcf ˆ q (27) c,f cf R cf cf q cf ( ALLOC) were equation (11) as been used to split input tax-inclusive values of inputs to final demand into tax-exclusive values and te tax revenue Te sum involving te tax revenues is tat part of te allocative efficiency contribution (ALLOC) attributable to taxes on final demands Te remaining RH term of equation (27) can be expressed as: Θ [ ˆ caqca ˆ cqc ] c,f cf qcf Θ c,a c, ˆ (28) were te sum over all final demands on te LH as been expressed on te RH as te difference of te sum over all activities and te sum over all industries In equation (28), te second sum on te RH, wic ranges over all commodity inputs into industries, can be furter expressed as a difference of te sum over all inputs and te sum over primary factor inputs tus: Θ c, ˆ c q c Θ e, ˆ i q ˆ q i, e i e ( ENDW ) (29) te last sum being part of te contribution of canges in domestic endowments to canges in welfare (ENDW) Te first sum on te RH of equation (29) involves input tax-exclusive values It is now expressed as te difference of a sum involving tax-inclusive values and a sum involving tax revenues, using equation (11), tus: Θ i, ˆ i q i Θ i, i, R i i q q i i ( ALLOC) (30) were te last sum is tat part of te allocative efficiency contribution (ALLOC) attributable to all taxes on inputs to industries Drawing togeter equations (28)-(30) yields: Θ c,f ˆ cf q cf Θ [ ˆ caqca i qi ] c,a i, e, Riq ˆ q e i e i, ( ALLOC) ( ENDW ) Te first term on te RH of equation (31) is dealt wit using te maret clearing conditions, wic are now derived in linearised form In levels, for all commodities c: (31) c a ca (32) Linearisation yields: ca qca cqc a (33) 14

20 and, multiplying by te price, c O, of commodity c: ca qca c qc a ˆ (34) ubstituting equation (34) into te first term on te RH of equation (31) yields: [ caqca i qi ] Θ [ c qc i qi ] Θ ˆ (35) c,a i, c, Te first sum on te RH of equation (35) involves output tax-inclusive values of commodities produced by eac industry Tis sum is expressed as te addition of two sums involving taxexclusive values and tax revenues, using equation (9), tus: i, Θ c, c q c Θ c, ˆ c, c R q c c q c ( ALLOC) (36) te second term on te RH of equation (36) being te final part of te allocative efficiency contribution (ALLOC), tat attributable to output taxes Te final stage in te derivation of te welfare decomposition involves gatering togeter te terms not yet associated wit a particular welfare contribution (te second sum on te RH of equation (31) and te first sum on te RH of equation (36)), and replacing percentage canges in quantities by percentage canges in effective quantities and tecnical efficiencies, tus: Θ [ ˆ q q ] c, c c i, i i Θ [ ˆ q q ] ( ROFIT) c, c c i, i i [ ˆ c ac + iai ] ( TECH ) c, i, Te replacement of quantities by effective quantities and tecnical efficiencies yields te tecnical efficiency contribution (TECH) and te profits effect contribution (ROFIT) (37) 25 ummary of Welfare Decomposition Combining equations (27)-(31) and (35)-(37), and substituting into equation (26), yields te final welfare decomposition for te representative ouseold A tabular summary of te welfare decomposition equations is provided in table 1 Table 2 lists te status, in a GEMACK implementation (Harrison and earson 1996), of eac of te items introduced in te derivation of te welfare decomposition It also provides brief descriptions of eac item 15

21 Table 1 ummary of te Welfare Decomposition q Θ A _ RI Θ RORF Θ FENDW Θ ENDW Θ ALLOC Θ TECH Θ ROFIT Θ O + TOT + A _ RI + RORF + FENDW + ENDW + ALLOC + TECH + ROFIT U O Θn TOT Θ C G (,,, ) X X M M [ p p ] FA FA DE DK [( p + ) ( p + )] DE DK DK [ ( )] e, ˆ eqe d + q [ R q + R q + R q ] c,f [ ] c, ˆ c ac + i,iai [ ˆ q q ] c, FA FA c cf q FA FA c cf i, i, i i i i c, c c Table 2 Welfare Decomposition Terms wit Guide to GEMACK Implementation ymbol Description tatus in GEMACK q ercentage cange in real net national product ercentage cange variable Elasticity of utility wit respect to nominal net Coefficient (non -parameter) Θ national product O opulation cange welfare contribution Cange variable TOT Terms of trade welfare contribution Cange variable A_RI Asset price welfare contribution Cange variable RORF Foreign rate of return welfare contribution Cange variable FENDW Foreign endowment welfare contribution Cange variable ENDW Domestic endowment welfare contribution Cange variable ALLOC Allocative efficiency welfare contribution Cange variable TECH Tecnical efficiency welfare contribution Cange variable ROFIT rofits effect Cange variable 16

22 3Te roperties of te rofits Effects Te first part of tis section sows tat under te standard assumptions of CGE models optimising and price taing beaviour and zero pure profits te profits effects are zero Because tese assumptions were introduced from te outset in previous welfare decomposition derivations, te residual profits effects terms were not isolated Te advantage of aving suc a term lies in its possible application in economic models tat pus beyond te standard assumptions of GE teory, by incorporating features suc as imperfect competition 12 In te second and subsequent parts of tis section, te properties of te profits effects wen agents are optimising but ave maret power are examined Te second part of tis section sows ow te profits effects can be written in terms of quantity canges and te demand (supply) elasticities facing te agent in te output (input) marets in wic tey wield some power Tis is ten applied in te tird part of tis section to examine te beaviour of te profits effects under uniform reductions in maret power, as represented by uniform relative decreases in te elasticities 31 Te rofits Effects are Zero Under tandard CGE Assumptions Teorem: If industry maximises revenue, minimises costs, is a price taer and as zero pure profits ten c qc i, i qi c, ˆ (38) If tese conditions are satisfied for all industries ten ROFIT0 13 roof: Define revenue and cost functions for industry, tus: (, ) max{ : ( )} (, ) min{ : ( )} (39) were Y( ) and X( ) denote production possibility and inputs requirement sets, respectively Note tat te revenue and cost functions are expressed in terms of effective prices and effective quantities, wic can cange because of canges in prices, quantities or tecnical efficiencies Te derivation to be presented would not be valid if te revenue and cost functions were expressed in terms of actual prices and quantities, as tese functions would implicitly embody an 12 It sould be empasised tat altoug te welfare decomposition derived in te current paper taes into account te maret power aspects of imperfect competition, via te profits effect, it does not tae into account te welfare effects of canging te number of varieties of a commodity Altoug te later derivations in te current section deal wit individual firms and teir maret power, tere is no teory governing te number of firms Hence variety effects cannot be represented uc effects are derived in te welfare decompositions presented in waminatan and Hertel (1996) and Baldwin and enables (1995) 13 Tis teorem is very similar to te result (510) of Keller (1980) Tere it is proved directly from te first order conditions for te maximisation of profit subect to a production function In te current paper it is proved using revenue and cost functions 17

23 18 assumption of constant tecnical efficiency (tat is, constant production tecnology) 14 Te zero pure profits condition can be written in one of four ways: ( ) ( ) ( ) ( ),,,, (40) artial differentiation, wit respect to quantities, of eac of te first two expressions yields: (41) Te assumption of price taing ensures tat partial derivatives of prices wit respect to quantities do not occur in te previous two equations, tat is: 0 0 (42) Te assumptions of revenue maximising and cost minimising beaviour allow us to apply eperd s lemma to te revenue and cost functions, yielding, respectively: (43) Terefore, linearisation of te tird expression for zero pure profits yields: [ ]100 ˆ ˆ p q p q (44) Linearisation of te fourt expression for zero pure profits yields: [ ]100 ˆ ˆ p p q q + + (45) Te difference of te final lines in equations (44) and (45) is equal to: 14 Te current treatment embodies te assumption tat production tecnology only canges via canges in te tecnical efficiencies associated wit industry outputs and inputs

24 [ ˆ ˆ q + p q p ] [ ˆ ˆ q q + p p ] 2 [ ˆ q q ] (46) so, consequently: ˆ q q (47) wic, wen written in summation notation, is: c, c qc i, i qi ED ˆ (48) Te previous teorem maes assumptions about te optimising beaviour of an industry, wereas suc assumptions are more properly related to te firms constituting an industry As can be inferred from te first line of equation (54) in te next subsection, te profits effect for an industry is equal to te sum of profits effects across all firms in an industry provided te firms ave te same effective input and output prices If tis condition does not old ten eiter te industry could conceptually be split into several industries eac wit te desired property, or te tecnical efficiency and profits effect contributions to welfare (TECH and ROFIT, respectively) would need to be rewritten wit a firm dimension For te remainder of tis section firms in a particular industry (indexed by a subscript of ψ) are assumed to: 1 Maximise profits; 2 Have some maret power in all input and output marets; 3 Face negative demand elasticities in all output marets; and 4 Face positive supply elasticities in all input marets Te distinction between effective and actual prices and quantities is dropped for te remainder of tis section To maintain it would cause notational clutter, and would not lead to any extra insigts for te issues of maret power discussed 32 Te rofits Effects Under Maret ower Only Te profit maximisation problem for firm ψ in industry is: Coose a vector of input and output quantities ψ (49) ψ ψ to maximise 19

25 c ψc i i ψ i c ˆ (50) subect to a production frontier defined by F ( ) 0 (51) ψ ψ Te function F ψ ( ) is an increasing (decreasing) function of output (input) quantities Te production tecnology constraint will be satisfied wit equality for a profit maximising firm (a fact tat is used below) Taing into account te firm s maret power, te first order conditions are: ˆ c ˆ dc + d i ψc di d ψi ψc ψi Fψ λψ Fψ λψ ( ) ψ ψc ( ) ψ ψi ˆ c ( ε ) 1 1 i ψc ( + ε ) ψi Fψ λψ ( ) ψc ψ Fψ λψ 0 ( ) were λ ψ is te Lagrange multiplier (wic will be positive a fact used below), and te ε>0 are te magnitudes of inverse demand (supply) elasticities faced by te firm in output (input) marets 15 For any small cange in quantities it must be te case tat: F ψ ( ) 0 ψ Fψ c ( ) ψ F ψ ψ ( ψ ) F ( ) ψ ψ c + ψ i ψc ψ ψi ψi ψi ψ 0 (52) (53) so c ˆ c c i, i i [ ˆ ] 100 c c qc i i qi [ ˆ c ε c c + i ε i i ] ψ ψ c i i [ ε q + ε q ] c ψc ψ ψc ψ ψc ψi ψ ψi ψi ψ 100 (54) Tus te profits effect for industry can be expressed as a sum of measures of te maret power of individual firms and canges in teir input and output quantities Also, te terms in te profits effect resemble very closely allocative efficiency effects, wit te elasticities playing te role of ad-valorem tax rates Tis is not altogeter surprising because, as can be seen from te first order conditions, te elasticities are te rate of mar-up (mardown) of price over (under) marginal cost (benefit) for eac output (input), and mar-ups (mardowns) are distortions ust lie taxes 15 For ease of expression, te ε sall be referred to as elasticities 20

26 Consistent wit tese insigts, an increase in any input or output quantity for a firm maes a positive contribution to te profits effect, and ence to welfare, ceteris paribus 33 Reductions in Maret ower Te value of te profits effect for an industry corresponding to canges in firms maret power is examined in te remainder of tis section Decreases in maret power will be represented as decreases in one or more of te inverse demand and supply elasticities Under a small perturbation in te elasticities, te first order conditions yield: 0 ˆ c ( 1 ε ) ψc 0 1 i ψi κ ψc ψc ( + ε ) κ ψi ( 1 ε ) ψi Fψ λψ ψc ( + ε ) 1 ψi 2 ( ) F ( ) ψc Fψ λψ ψ Fψ λψ 2 ( ) F ( ) 2 ( ) F ( ) ψi ψ ˆ Fψ λψ ψc 2 ( ) F ( ) ψi c ψ i ψ ε ψc ˆ ε c ψi ε i λψ ε ψc ψi ψ ψc λψ ψ ψi ψ ψ λψ ψ ψ λψ ψc ψ ψi ψ ψ ψ ψ ψ ψ ψ ψ ψ (55) were te κ are te absolute values of te derivatives of prices wit respect to quantities If eac of tese equations is multiplied by te associated canges in quantities, and ten summed over all inputs and outputs, [ ˆ ε + ε ] c c c 2 ( ) κ 1 ( ε ) + ( ) κ ( 1+ ε ) ψc ψc ψc ψc i ψc i i ψi ψi ψi 2 ψi ψi + λ ψ ψ 2 F ψ ψ ( ) ψ ψ Te first term on te rigt and side is positive if all demands faced by te firm are elastic (so te ε O are all less tan one) Te second term is positive Te tird term is positive if F ψ ( ) represents a non-increasing returns to scale production tecnology However, tis may not sit comfortably wit te assumption of maret power, wic migt be associated wit some economies of scale If, owever, tose economies of scale arise from te existence of a fixed cost, ten te first order conditions are identical to tose derived above wit F ψ ( ) determining te variable inputs In tis case F ψ ( ) could quite reasonably be non-irt Tis discussion of fixed costs ignores te possibility tat tese are actually a fixed amount of some aggregate of inputs For example, te fixed costs in waminatan and Hertel (1996) are CE composites of primary factors In tese cases te composition of fixed costs, and ence teir actual cost to te industry, will vary wit prices and will be determined as part of te profit maximisation decision But provided tat te production function used to produce te fixed costs from its component inputs is non-irt, te inferences to be drawn below will remain valid Terefore, we sall persist wit te simpler specification of fixed costs assumed in te previous paragrap, to minimise notational clutter ψ (56) 21

27 o for te final teorem of tis section we introduce te assumptions: 5 All firms face elastic demands for all outputs; and 6 Te production tecnology implied by te function F ψ ( ) is non-irt Teorem: Under assumptions 1-6, a uniform reduction in maret power across all inputs and outputs for all firms in industry : ε ε ψc ψc ε ε ψi ψi δ < 0 ψ, c, i (57) leads to a reduction in mar-ups (mardowns) and excess profits, and ence an increase in regional welfare, ceteris paribus roof: By combining equation (57) for te uniform relative canges in elasticities, equation (56) for te impact of canges in maret power, and te equation (54) for relating te profits effects to te elasticities and quantity canges, we obtain δ > 0 ψ ψ [ ˆ + ] [ ˆ c ψ c εψc i ψ i εψi δ c c i i ] c i 2 2 ( ψ ) κ ψ 1 ( εψ ) + ( ψ ) κ ψ 1 ( + εψ ) c c c c i i i i c + λ ψ i ψ 2 F ψ ψ ( ) ψ ψ ψ (58) under assumptions 1-6 ED 4 Decomposition of Money Metric and Compensation Measures of Welfare Cange Martin (1996) discusses te properties of money metric measures of welfare cange, based on te expenditure function, and compensation measures, based on te balance of trade function Te two measures of welfare are not equal in an economy wit existing distortions, and neiter one is clearly superior to te oter Terefore it is desirable to be able to use bot types of welfare measures, and to be able to decompose eiter one into a sum of components, as as been done for te equivalent variation in GTA Fane and Aammad (2000) decompose a compensation measure of welfare in a very general context Tey represent te welfare measure as a sum of allocative efficiency and terms of trade effects 16 Because conventional assumptions of CGE models are introduced at an early stage of te derivation (for example, by describing te beaviour of agents in terms of expenditure functions, tus implying optimising beaviour), no residual profits effects are identified 16 Endowment and tecnical efficiency canges could probably be readily accommodated, but were not of primary interest in te context of te paper 22

28 Te decomposition of te cange in utility presented in tis paper will now be applied to bot money metric or compensation measures of welfare 41 Money Metric Welfare Measures Te equivalent variation is te income tat must be given to an agent, at some fixed set of prices, to mae tem as well-off as tey would be under some policy cange It can be expressed in terms of te expenditure function tus: E E U1 U0 ( 0, U1) E( 0, U 0 ) (, U ) E 0 U du (59) In a numerical simulation, te small increments in utility calculated at eac step of te solution procedure correspond to te du in te integral, and can be decomposed as sown above (table 1) Tus, all tat is required to convert to a decomposition of te equivalent variation is multiplication by te derivative of te expenditure function, wit respect to utility, evaluated at te initial prices Compensation Welfare Measures Based on te Balance of Trade Function A compensation measure of te welfare cange attributable to a policy is te value of an income transfer from abroad tat must be given to a nation so tat its level of welfare remains constant as te policy is reversed Fane and Aammad (2000) describe te calculation of tis welfare measure by postulating tree states of te economy base (B), uncompensated (U) and equivalent (E) In table 3, U represents utility, T represents all policy variables, and A represents an exogenous transfer of income from abroad (as distinct from foreign income flows tat may be affected by te policy cange troug effects suc as canges in foreign investment) A cange in A can be included in te decomposition of utility as an extra foreign income flow not decomposed into its Table 3 Calculation of Compensation Based Measures of Welfare ariable type Base Uncompensated Equivalent Utility U B U U U E U U olicy variables T B T U T E T B Income transfer from abroad A B A U A B A E ource: Adapted from table 1 of Fane and Aammad (2000) 17 Tis derivative for te GTA model will be derived in section 5 23

29 rate of return, asset price and real parts It is included as a cange rater tan a percentage cange, since its value may pass troug zero Consequently, considering a small cange of te type UE, q 0 O + TOT + A _ RI + RORF + FENDW + ENDW + ALLOC + TECH + ROFIT Θ A (60) so O + TOT + A _ RI + RORF + FENDW + ENDW + ALLOC + TECH + ROFIT - A ( 100 Θ ) (61) In contrast to te money metric measure of welfare, te compensation measure does not involve te elasticity of utility wit respect to income Table 1 sows ow all te terms in parenteses in te numerator are multiplied by Θ, so consequently it cancels out between te numerator and denominator 5 Application to te GTA Equivalent ariation Measure of Welfare Cange To obtain a decomposition of te GTA equivalent variation it is necessary to derive expressions for te elasticity of utility wit respect to income (te coefficient Θ ) and te derivative of te expenditure function wit respect to utility (evaluated at initial prices) for te GTA representative ouseold In GTA, te representative ouseold as a nested utility function wit two levels First, at te upper level, total ouseold income is allocated between private and government consumption goods in total, and saving Ten, at te lower level, te income allocated to eac of total private and government consumption is allocated across individual commodities so as to maximise subutility functions, of CDE and Cobb-Douglas forms for private and government consumption, respectively Te upper level decision of allocating income between expenditure categories maximises a Cobb-Douglas utility function of te lower level sub-utilities and real saving Tus, te indirect utility function for te representative ouseold in GTA is, using an obvious parallel to te notation already establised, ln C G f f f f [ (,,, )] ln[ U ( )] f { C G } U,,, α (62) were f is interpreted as a vector of prices or a scalar for f {C,G} or f, respectively, and α f are te Cobb-Douglas parameters at te upper level Te aggregate expenditures f are functions of total income and all prices, and are determined by te optimisation problem: Coose C, G and to maximise 24

30 subect to f { C G, } f f f [ U ( )] f ln,, α (63) f { C, G }, Te first order conditions from tis problem are: f f f f [ U ( )] ln, f α λ f (64) (65) were λ is te Lagrange multiplier But ln C G f f f [ U (,,, )] f ln[ U (, )] α f C, G, f λ λ { } f { C, G, } f f (66) using te first order conditions and te constraint tat total expenditure equals total income Tis is te familiar result tat te Lagrange multiplier in a utility maximisation problem is te marginal utility of income But a simple expression for λ can be found by considering te first order condition for saving, tus: ln λ α ln α α [ U (, )] [ ] (67) o Θ ln α C G [ U (,,, )] ln (68) 25

31 Te derivative of te expenditure function wit respect to utility (required for te calculation of te E) can be derived simply by differentiating te identity: 18 [, U (, Y) ] Y E (69) to yield: so [, U (, Y) ] U (, Y) E 1 (70) U Y E [, U (, Y) ] U (, Y) U Y 1 (71) To apply tis expression in calculating te E, te prices sould be eld constant at teir initial values, and Y sould be defined so tat: C G (, Y) U (,,, ) U (72) Tis can be implemented by incorporating in GTA a sadow ouseold demand system, in wic prices are eld constant at teir initial values but utility is equal to te value determined in te policy simulation, as described in McDougall (2001) It sould be noted tat te derivative of te expenditure function used in converting canges in utility to an E does not cancel out wit Θ, since tese expressions are evaluated at different values of te prices and nominal income Tey are, owever, equal at te initial point of a policy simulation Furter, te Cobb-Douglas parameter α, wic can be arbitrarily cosen to be any positive number, does cancel between te two expressions Formally expressed, te contribution to te E for eac small step of te policy simulation is: 18 Te price vector and te nominal income Y introduced at tis point designate te values to be used in te calculation of te E Tey are not te same as te prices ( C, G, ) and income ( ) arising in te policy simulation 26

32 E [, U (, Y )] E [, U (, Y )] U U E U [, U (, Y )] (, Y ) (, Y ) ( ξ ) U ξ Y Y Y U U 1 U q lnu lny α Y (, Y ) Θ U ξ Θ U ξ Θ U ξ α Y Y (73) were Y is te value of nominal savings implied by te sadow ouseold demand system, and ξ is a value-weigted linear combination of percentage canges in quantities and relative prices, defined from te welfare decomposition terms listed in table 1 tus: ξ X X M M FA FA DE DK [ p p ] + [( p + ) ( p + )] n + FA FA FA FA + q DE DK DK [ ˆ ( + )] + [ + + ] e, eqe d q R c,f cf qcf R i, iqi R c, cqc [ ˆ + ] + [ ] c, c ac i, i ai ˆ c, c qc i, i qi It will be observed tat te E is invariant to monotonic transformations of te utility function, as expected 6 ummary and Outstanding Issues for Future Researc (74) Tis paper as presented a very general derivation of a welfare decomposition It is valid for any CGE model in wic economic welfare is represented as being derived from te allocation of national income between private consumption, government consumption and savings according to utility maximisation by a representative ouseold Te derivation rests only on te assumption of maret clearing in all commodities and, implicitly, watever differentiability assumptions are required to ensure tat relationsips can be linearised Even te assumption of maret clearing could probably be relaxed wit te explicit representation of canges in stocs One of te most innovative aspects of te resulting decomposition is te profits effect It is a type of residual term tat arises because of te absence, in te derivation of te welfare decomposition, of any assumptions about optimising beaviour by firms or zero-pure-profits Te profits effect captures te welfare effects of any maret power wielded by some firms, and can be related to te demand and supply elasticities faced by suc firms Te latter are related to mar-ups, wic lead to extra terms in welfare decompositions derived for models wit imperfect competition, suc as waminatan and Hertel (1996) and Baldwin and enables (1995) In contrast to tese papers it sould be noted, owever, tat wile te profits effect captures te welfare contributions of 27