Capter 8 Introduction to Endogenous Policy Teory In tis capter we begin our development of endogenous policy teory: te explicit incorporation of a model of politics in a model of te economy, permitting us to analyze te general political-economic equilibrium. In addition to te requirement of a well-specified model of general economic equilibrium (as developed in te capters 4 troug 6), we now need to develop a model of political interaction consistent (bot pilosopically and matematically) wit te economic model. Te construction of suc a model requires, minimally, explicit caracterization of tree fundamental causal relationsips: te effect of policy outcomes on te welfare of ouseolds (a teory of policy preferences); te effect of policy preferences on political action (a teory of political action); and te effect of political action on policy outcomes (a teory of state action). Wit respect to te teory of political preferences, te endogenous policy approac is quite straigtforward: we use te structure of te economic model to identify te effect of any given set of policies on ouseold welfare; and, via our assumptions of selfisness, materialism, and rationality, along wit our assumptions on te structure of preferences, we generate ouseold evaluations of policies directly from tese effects. Te main topic of tis capter will be te working out of tis logic. Just as caracterizing ouseold preferences over te space of possible consumption bundles does not yield a teory of consumer coice, te teory of political preferences is not sufficient to generate a teory of political action. We need to caracterize te constraints on 1
ouseold political action. However, because te policy, once adopted, applies to te economy as a wole and tus affects all ouseolds, part of tis caracterization must come to grips wit te fact tat te coice is made collectively. In capters 9 and 11 we consider two alternative tecnologies of political action: voting and lobbying. Te most straigtforward mecanism, wit full information, is voting. If we assume tat te tariff can be caracterized as a one-dimensional issue and tat tere are no voting costs, te teory of political preferences immediately yields a teory of political action for te case of a tariff referendum. From tere, we apply a result from formal political teory (Black's median voter teorem) to caracterize te full political-economic equilibrium. From tis simple base, we can incorporate a wide range of extensions including, for example, voting costs; partisan competition; uncertainty; and francise restriction. Lobbying models are somewat more complex because tey necessarily involve expenditure of resources on politics. Furtermore, because lobbying fairly naturally entails collective action among agents wit similar preferences, a fully satisfactory account would incorporate an explicit analysis of Olson-type collective action problems. Tus, capter 10 discusses te problem of organizing for collective action. Te teory of state action is te most underdeveloped part of endogenous policy teory. Altoug existing researc refers often to parties, politicians, bureaucrats, and elections, tere is in fact very little explicit analysis of wat is, in some sense, te supply-side of te political model. Most voting models treat policy determination by simple referendum, wile most lobbying models treat policy determination troug bribery of politicians wit no personal interest in policy outcomes. Te analytical virtue of tese assumptions is tat tey permit solution of te general political-economic equilibrium using only information on effective 2
political demand. In te capters 9 and 11 we will draw on recent researc to illustrate ow politician preferences and institutional structure can be incorporated in endogenous policy models, and ow teir inclusion affects results. Te remainder of tis capter is concerned wit te derivation of ouseold preferences over tariff policy. Houseold Welfare Effects of Commodity-Price Canges We begin wit te general (I-factor J-good) neoclassical production economy of te sort described in Capter 5, in wic eac ouseold ( H) owns some portfolio of factors (z ). Now we want to caracterize te effect of a cange in te commodity-price vector on ouseold welfare. As we saw in capter 2, economic rationality in te neoclassical model is taken to mean tat coice is guided by "well-beaved" preferences as constrained by some budget set. In a description of te ouseold coice problem were prices and income are known, we saw tat suc preferences may be represented by a real-valued indirect utiltiy function relating output prices and income to ouseold welfare, v (p,p,...,p ;ã ), were eac p is te price level in one 1 2 N j of J industries and ã is te income level of te ouseold. Te important properties of tis function for our discussion are tat ouseold welfare is non-increasing in prices, increasing in income, omogeneous of degree zero in prices and income togeter, and quasi-convex in prices. Tese properties combine to insure tat if income increases proportionally more (less) tan all output price levels, ten te individual's welfare unambiguously increases (decreases). Te direction of te effects on te welfare of an individual from a marginal increase in any price level may be seen by signing te derivative of te indirect utility function wit respect 3
to te price level: We may divide troug by te marginal utility of income to remove utility units and use Roy s identity 1 Now multiply by p j /ã to get an expression in elasticity form: (1) were we ave substituted (te price j elasticity of nominal income), and (te proportion of ouseold income spent on j). Tus, if te expression in parenteses is positive, an increase in p j increases ouseold real income and good j is an unambiguous friend to te ouseold. Alternatively, te expression in (1) gives te percentage cange in te income of ouseold tat as te same welfare impact as a one percent increase in te price of good j. Since te á j > 0, price increases reduce welfare troug te consumption effect for all ouseolds, so te key to a welfare increase and differential welfare effects among ouseolds must come troug te wealt effect. 1 Ruffin and Jones (1977) develop an expression like tis in teir analysis of te effect of a tariff-induced price cange on te real wage in a specific-factor model. 4
To understand te wealt effect better, we now express te effect of a price cange on ouseold income (ù ) in terms of its basic components. Houseolds derive teir income from renting teir factor-endowment to firms. Since we assume tat tere is no saving or leisure, ouseold income is (2) Wit ouseold endowment eld constant, if we differentiate income wit respect to p j we get (3) Now multiply bot sides by p /ã and manipulate te rigt-and side to get an expression for ù j in terms of Stolper-Samuelson (partial) elasticities and sares of ouseold income derived from factors j j (4) Te â are non-negative, so te sign of ù will depend on te signs of te Stolper-Samuelson ij 2 elasticities (n ji) and te relative magnitudes of te non-zero terms. j If we suppose tat every ouseold owns only one factor of production, we can use tis 2-1 Recall from Capter 5 tat te n ji can be found as elements of te N = È matrix. 5
3 framework to demonstrate tat every ouseold as at least one unambiguous friend. From equation (3) we can see tat, for a ouseold tat owns only factor, te effect of a cange in te price of good j on ouseold income is ù = n ji (since â = 1 and â m = 0 m ). Tus, we can use equation (1) to write te effect of a cange in te price of good k on te real income of ouseold as: (5) Te real position of ouseold improves if te term in parenteses is positive. We know, from te analysis in capter 5, tat all factors ave (locally) unambiguous enemies, so tis term must be negative for some k. So every ouseold as at least one unambiguous enemy. But since N as unit row sums (see footnote 15 in capter 5), and since all income is spent (so tat á k = 1), te sum of tese coefficients over all k is zero. Tat is 4 But since te summation as at least one negative term, it must ave a positive term as well. Tus, te real position of any single-factor ouseold can be raised by an appropriate commodity price rise: every single-factor ouseold as at least one unambiguous friend. If tere were no 3 Tis analysis is drawn from Cassing (1981). 4 Note te difference between tis result and te result from Jones and Scienkman (1977) presented in Capter 5. In Capter 5 it was sown tat we cannot prove tat every column of N contains an element greater tan unity (i.e. tat every factor as at least one unambiguous friend). Wat we sow ere, following Cassing, is tat for every ouseold tere must be a good k suc tat n kj > á k, wic obviously does not require tat n kj > 1. Tus, every single-factor ouseold does ave at least one unambiguous friend. 6
costs of acquiring suc a price cange, ouseold would coose to ave price k raised. A satisfactorily general model sould permit multiple price canges and ouseolds wit multi-factor portfolios. At te level of formal representation, tere is no particular problem wit eiter of tese. Te expression for ù j in (3) accommodates multi-factor portfolios, and wit multiple price canges, te income equivalent welfare cange for ouseold is just te sum of te individual net welfare effects for eac sector experiencing a price cange given in (1), weigted by te proportional price canges: (6) Wat is difficult is saying anyting definitive about te sign of (5) in te context of a general I J model. As a result, we will generally use more restrictive models involving some combination of low dimensionality and/or strong structure on tecnology or ouseold factor portfolio structure. However, before turning to suc restrictive models, we first discuss te introduction of trade policy into tis framework. Houseold Preferences over Tariff Policy We will model a single political outcome tat affects te (non-proibitive) tariff levels in all import industries of a small, open economy. Furter, we will impose te restriction tat relative import prices are eld constant, so tat a ouseold's consumption of import industry goods (bot imported and domestic import competing) may be represented by a composite commodity x m (representing ouseold spending on importable commodities). Note tat tis is consistent wit our empasis in te next capter on cange in te protectiveness of te tariff 7
system, not in te dispersion witin te system. A cange in policy will terefore affect a tariff level index t, wic ten affects a ouseold's welfare troug bot price and income as follows In te second line we eliminate utility units and use Roy s identity as in te derivation of equation (1). To get te tird line we use te definition of p (=ð (1 + t)), from wic it follows m m tat Noting tat p = ð(1 + t) so p/ð = (1 + t), tis may be rearranged to get were ù is te wealt effect (te import price elasticity of income) and á is te consumption M effect (te proportion of ouseold income spent on x m) of a cange in import prices. To get tis in te same form as equation (3), divide bot sides by ã and multiply by t: M (7) Te first term on te rigt and side is positive, so te sign of equation (7) is dependent upon te 8
sign of (ù - á ), wic as we saw above is an income equivalent of te price cange. If tis M M expression is positive, and tere are no oter costs associated wit inducing a cange in te tariff, a one percent increase in te tariff raises te real income of ouseold. Under te assumptions of our model, ouseold prefers an increase in te tariff. Te alert reader will ave noticed tat equation (7) does not take account of tariff revenue. If tis were te final form of te caracterization of preferences over te tariff, we 5 would be assuming implicitly tat tere is no benefit from increased government revenue. For a variety of reasons tis seems sensible. In most countries, te sare of tariff revenue in government revenue is extremely small and migt reasonably be ignored in te political calculus of most citizens. Alternatively, we migt believe tat government expenditure is sufficiently 6 wasteful tat tere is no beneficial effect. For example, we migt imagine tat tariff revenue is burned, used to construct monuments tat yield no ouseold utility to any ouseold, or used to trow a party for politicians and bureaucrats (wose welfare receives a zero weigt in social welfare). At te oter extreme, we migt want to consider a case in wic ouseolds benefit from te tariff revenue. For example, te government migt provide public or private goods tat are positively valued by ouseolds. Rater tan develop a detailed model of government 5 In our political models we will generally not pursue issues related to active seeking of te revenues from te tariff. Te main argument for te lack of a political connection is tat tariff revenue goes into general revenue, so tere is no reason to assume any connection between te politics of tariff-seeking and te politics of revenue-seeking. But note tat tis issue is distinct from tat of weter or not to incorporate tariff revenue in ouseold utility from a tariff. 6 It sould be recalled tat our general equilibrium framework does incorporate any costs tat derive from economic distortions created by te tariff. 9
production, we will adopt te simple expedient of assuming tat te government simply 7 redistributes te income back to ouseolds, witout any waste. If we denote by T te value of tariff revenue redistributed to ouseold ouseold income is now made up of two components: revenue from rental on its endowment of factors; and redistributed tariff revenue. Tat is: (8) A particularly convenient assumption is tat every ouseold receives a sare of tariff revenue (ö ) equal to its sare of national income: (9) so (10) Substituting (9) and (10) into (8) allows us to write ouseold income as a simple sare of national income: (11) Using equation (11) we can rewrite te ouseold indirect utility function: 7 Note tat tis is in no way a maximally positive assumption. We could assume tat te government provides public goods tat raise social welfare above tat derived from simple redistribution. Similarly, te assumption of 100% waste is not maximally negative: te government could produce public bads tat reduce welfare beyond tat associated wit total waste of revenue. 10
(12) Equation (12) identifies tree main cannels troug wic te tariff affects ouseold welfare: directly troug its effect on te price vector; and indirectly troug its effect on total national income and its effect on te sare of ouseold in national income. Since ouseold welfare is decreasing in p and increasing in ouseold income, equation (12) makes it clear tat te effect of te tariff working troug p and à is qualitatively identical for all ouseolds. If te 8 country is economically small, bot of tese effects are negative. Tus, to te extent tat ouseolds experience qualitatively different effects, it must be because ouseold income sares are differentially affected. It is now easy to see tat allocation of tariff revenue on te basis of pre-policy income sare as te analytical virtue of allowing us to focus our analysis on effects tat work troug te effect of te tariff on return to ouseold endowments. In te next section we use a simple 2-factor 2-good HOS model of te underlying economy to develop our intuition. Te Mayer Model of Houseold Tariff Preferences in an HOS Economy Our analysis to tis point suggests tat, to get a usable caracterization of ouseold preferences, we will ave to adopt more constraining assumptions. In one of te most important papers in te literature on endogenous trade policy, Wolfgang Mayer (1984) developed one suc 8 As we sall see in Capter 13, if te country is economically large, ten it must ave an optimal tariff. Tus, from an initial position of free trade, à can be increased by a positive tariff. Of course, if te analysis begins wit te government levying te optimal tariff, à must fall wit a cange from tat policy. Furtermore, te Metzler paradox refers to a situation in wic te imposition of a positive tariff causes te domestic price of te imported commodity to fall. 11
9 model. Te underlying economy is taken to be an internationally small, HOS economy. Tat is, tere are two factors of production labor (L) and capital (K); fixed endowments of bot; bot factors are of uniform quality, and bot are perfectly and instantaneously mobile between sectors. Tere are two sectors caracterized by neoclassical production functions j y j = f (K j, L j), were bot factors are essential and te functions are linear omogeneous, twice differentiable, and strictly concave. Tere is no joint production and no production externalities. Recall from Capter 4 tat if tere are only two goods, tere is only a single relative price, and only relative prices matter to ouseold and firm decision-making. Tus we assume, witout loss of generality (relative to tis very simple model), tat good 1 is te importable in te initial equilibrium and we will write te relative price as Since we ave assumed tat te economy is small in international markets, te world price is fixed at ð, so if te quantity of imports of good 1 is M, and protection is by ad valorem tariff at rate t [so p = ð(1 + t)], we can write total tariff revenue as: (13) Since our goal is to develop a model of political-economy driven by endowment differences among ouseolds, we will abstract from taste differences by assuming tat all 9 We sould also note tat te representation of ouseold preferences in equation (12) is also found in tis important paper. 12
ouseolds sare identical, omotetic preferences. Tis implies tat, faced wit te same relative price p, all ouseolds will consume goods 1 and 2 in te same proportions. Tis will dramatically reduce problems of aggregation across ouseolds. Furtermore, all ouseolds will sare te same direct and indirect utility functions. Note, owever, tat because we are going to assume tat ouseolds own differing portfolios of capital and labor, it will not be te case tat utility is equalized across ouseolds, nor, more importantly, will it be te case tat ouseolds sare te same preferences wit regard to te tariff. Wit regard to ouseold factor portfolios, we will assume tat every ouseold is endowed wit one unit of L and some non-negative quantity of K L = 1 and K 0, H. Bot factors are infinitely divisible and perfectly mobile between te two industries. Tus, as in te previous section, ouseold income is derived from factor income and redistributed tariff revenue: (14) Te sare in tariff revenue is again given by ouseold sare in national income, and because tere are now only two factors, we can rewrite equation (9) to read: (15) Tis allows us to rewrite equation (11) as: (16) 13
As a result, we can rewrite te indirect utility function as: were te only difference between (17) and (12) is tat p is no longer a vector. Wen te tariff rate is canged, all ouseolds experience te same price and aggregate income effects, but if ouseold factor endowments differ teir income sares will be differentially affected. To find te effect of a tariff increase on ouseold welfare, substitute p = ð(1 + t) into (17) and differentiate wit respect to t to get: (18) To get tis result: we use Roy s identity to substitute -x 1 for and ten we use te fact tat wit identical omotetic preferences te demand of t ouseold for a commodity is just te product of its income sare and aggregate demand for tat product (i.e. x = ö D ). 1 1 To get an expression for Ã/ t, we need te national income identity: (19) Now differentiate (19) wit respect to t to get (20) 14
To get te second line of (20) we: Substitute p = ð(1 + t) and differentiate w.r.t. t to get and use D 1 = (y 1 + M), to get te first term; and use te fact tat and te fact tat by te small country assumption, to get rid of te oter terms. Substitute (20) into (18) to get (21) Tus, tere are two cannels troug wic ouseold welfare is affected by a tariff increase: canges in te tariff-weigted value of imports, and canges in te ouseold income sare, We know tat a tariff reduces imports, so te first effect is negative, but te second effect depends on te ouseold factor-endowment relative to te national factor endowment. Unfortunately, tere is not sufficient structure in te HOS model to ensure concavity of v ( ) in t. Tus, assuming tat v ( ) is strictly concave in t, te ouseold optimal tariff is found were Rearranging (21), we get an expression for te ouseold optimal tariff 10 (22) Since - ( M/ t) > 0, te ouseold optimal tariff is positive, zero, or negative as a iger tariff 10 Appendix 1 develops tis analysis for te general case, empasizing te difficulties wit getting determinate results. 15
raises, keeps constant, or lowers te ouseold income sare. Tus, we need to examine te link between t and te ö. It sould be clear tat te relationsip between t and ö will depend on te ouseold endowment, te economy s aggregate endowment and te production structure tat links tese togeter. Using te HOS structure, we can differentiate (15) wit respect to t to get 11 (23) We ave used te definitions: and Given te HOS s Stolper-Samuelson teorem tells us tat is positive (negative) if good 1 (te importable) is relatively labor (capital) intensive in production. From equation (23) we see tat a tariff increase results in a iger (lower) income sare for te t ouseold if tat ouseold, compared to te nation as a wole, is relatively well (poorly) endowed te wit import good s relatively intensively used factor of production. Using tis result and (22), we can conclude tat te ouseold optimal tariff is positive (negative) for ouseolds tat are relatively well (poorly) endowed wit te factor used intensively in te production of te importable good. Furtermore, te greater te difference between te ouseold and te national endowment ratios, te greater te deviation of te ouseold optimal tariff or subsidy from te nationally optimal tariff. Note tat te small country assumption means tat te nationally optimal tariff is zero. If every ouseold owned only L or K (te standard assumption in muc endogenous tariff teory), tere would be only two ouseold optimal tariffs--one for all K-owning ouseolds and one for all L- 11 Te details of tis derivation can be found in appendix 2. 16
owning ouseolds. Te optimal tariff rate is zero for eac ouseold for wic k = k. We can represent te effect of a cange in te tariff on real income as (24) For any given level of t, we can find te Houseold endowment ratio for wic tat tariff is optimal. We will denote tat Houseold endowment ratio Using (22) and (23), must be suc tat (25) Now use (21) to get an expression for (24) as (26) Now substitute from (25) for t and from (23) for ( ö / t), and manipulate to get (27) Again, recall tat te Stolper-Samuelson teorem tells us tat for a K- intensive importable good. Equation (27) tells us tat a given tariff increase raises (lowers) te t ouseold s real income as k exceeds (falls sort of) te capital-labor endowment of te 17
Houseold for wic te prevailing tariff is optimal-- It is also straigtforward to see tat, if good 1 is relatively K-intensive, Noting in te first two bracketed terms varies wit k, and te tird term is increasing in it. Te logic of tis is quite simple, and based on te Stolper-Samuelson teorem: As te price of te K-intensive importable is raised by te tariff, te rental rises relative to te wage. Tink of tis as exploitation of L by K: every unit of K extracts a benefit from every unit of L; ouseolds tat own only K always gain from an increase in t and ouseolds tat own only L always lose. All oter ouseolds ave a mixed relationsip to an increase in te tariff: teir units of K gain and teir units of L lose. Te ouseold optimal tariff balances tese gains and losses at te margin, wile movements away from te optimum involve greater losses to one of r te factors. Given te strict concavity of v ( ) in t and te linear omogeneity in {x 1, x 2}, (27) also sows tat All of tis tells us tat ouseold preferences are single-peaked over te tariff. Eac ouseold as a single most preferred tariff (i.e. te ouseold optimal tariff); and ouseold welfare declines monotonically away from tat optimum. In te next capter we pursue te implication of tis from te perspective of politicaleconomic analysis: if te tariff is set by a referendum, te equilibrium tariff will be determined at te ouseold optimal tariff of te median ouseold. Mayer makes te extremely useful point tat te median ouseold is determined in part by te underlying economy (our analysis to tis point) and in part by francise rules. Tat is, te relevant median preference is te participating median preference. First we will examine te unconstrained median, and ten we will consider some political structure-constrained medians. 18
We would expect an economically/politically rational individual to engage in two kinds of activities: directly productive and political. Wit costly political activity, an individual must make a trade-off between te gains from iger (or lower) industry price level and te cost of attempting to influence government output. An economically rational individual will devote resources to bot directly productive and political activities until te marginal benefit from eac equals its marginal cost. We ave spent te last couple of lectures caracterizing economic rationality and its implications in te context of simple general equilibrium models. In te next several lectures we caracterize te implications of political rationality, first in voting models and ten in lobbying models. Wat Evidence Do We Have on Houseold Trade Policy Preferences? 19
Appendix 1 Single-Peakedness of Houseold Policy Preferences Te use of Black's teorem to establis an equilibrium at te most preferred tariff of te median voter requires tat ouseold preferences be single-peaked over te tariff. In te text we follow Mayer in assuming tat te ouseold indirect utility function is concave in t. In tis appendix we sow wy tis is not a general property of te neoclassical political-economy model. If tariff revenues are distributed to ouseolds, tere are two sources of income: returns to factor ownersip and ownersip of a sare of tariff revenues. Letting be te portion of te wealt effect coming from factor ownersip (i.e., te import price elasticity of factor income), ö be te sare of total tariff revenue going to te ouseold (no longer assumed to equal te sare of te ouseold in national income), E s be te elasticity of tis sare to canges in import prices, M be te quantity of imports, and E m be te price elasticity of import demand, we ave te following: If a ouseold's preferences are suc eiter á m > ù m or ù m > á m for all tariff levels, ten teir optimal tariff level is simply 0 or 1, respectively, and preferences are obviously single peaked. Given te usual assumptions regarding ouseold preferences for goods and services (as discussed above), te necessary condition for a ouseold optimal general tariff level to fall between 0 and 1, at a given tariff level is tat ù = á. In te neo-classical production models m m 20
(Heckscer-Olin or specific factors), tis could only appen wen a particular ouseold as just te rigt mix of ownersip of factors of production, for any given tariff most ouseolds would prefer to move [???is tis assertion dependent on concavity in t???]. Te sufficient condition for a ouseold optimal general tariff level is We now sow tat tis is true only if: (A2) Expression (A1) can be broken up into tree parts as follows: Consumption Effect: Te term represents te derivative of te consumption effect alone. By equation (21') of Turnovsky, Salit, and Scmitz (1980), we know: were ñ is te Arrow-Pratt measure of relative risk aversion, a local measure of curvature, ç m is te income elasticity of import industry goods, and e m is te own price elasticity of demand for 21
12 13 imports, Wealt Effect: Te term represents t wealt effect alone. First, we can derive wic implies tat 14 were Ù m is defined as te elasticity of te wealt effect wit respect to import prices. Next, 12 We ave defined: 13 Also, note tat since prices of non-imported goods are unaffected, te usual assumptions on preferences tat result in te indirect utility function begin quasi-convex in all prices don't imply anyting about te sign of te second derivative of utility wit respect to import prices as long as some non-imported goods are consumed. 14 Tat is, we define Ù m as: 22
we ave so tat Cross Effect: Te wealt effect interacts wit te consumption effect troug te term Using Roy's Identity, we know: Substituting equation (21') of Turnovsky, Salit, and Scmitz (1980) and rearranging, we ave: Combined Effect: Putting te tree above parts togeter, we ave All tree terms directly following te negative sign starting te expression on te LHS are positive. Tus, te expression in square brackets, wic is (A2) above, must also be positive for 23
te entire expression to be negative. Tis is wat we wanted to sow. 15 If te sufficient condition is assumed to old for all tariff levels, ten preferences are single peaked. If we represented te production side of te economy by te generalized specific factors model wit n industries, eac industry employing a specific and a mobile factor, K i and L, respectively, ten a ouseold's factor income is Were te factor quantities represent ouseold ownersip rater tan economy endowments. Defining te proportions of ouseold factor income coming from ownersip of K and L as â and â L, respectively, te portion of a ouseold's wealt effect coming from factor ownersip would be i i were te 's are output price elasticities of factor returns. 16 Tis raises an interesting issue wen ouseolds are assumed to old a fixed amount of a single specific factor (or eiter factor in te Heckscer-Olin model). Since all relative import prices are fixed, we may apply te composite commodity teorem to use price indexes p and ð as if m m 15 16 Tis is te assumption used in Mayer (1984). Tat is, and were ats (^) represent propor canges. Note tat for all import competing products j, we ave 24
tey were prices for single products. Since, in te specific factors model (or te Heckscer- * Olin model), a ouseold's ù m must be less tan zero or greater tan one (unless te ouseold's sare of tariff revenue is so ig tat teir revenue increase exceeds te lost income due to factor ownersip), tere will be no tariff level suc tat ù =á and terefore no optimal general tariff level between 0 and 1. Te optimal ouseold tariff would be eiter zero or one, respectively. Witout voting costs, eac ouseold must terefore be always for a iger tariff level or always for a lower tariff level. For te remainder of tis paper, we will simply assume tat some m m production model creates a cleavage were some ouseolds ave ù > 0 and oter ave ù < 0. Furter, at a given general tariff level individual ouseolds (or ouseold members) will simply ave preferences for a iger or lower general tariff level. We will depend upon assumptions regarding voting costs and te distribution of voter preferences (wic will assumed to be monotonic) to insure a political/economic equilibrium. m m 25
Appendix 2 Using te HOS structure, we can differentiate (15) wit respect to t, use te quotient rule and te cain rule to get Now use: and multiply out ð to get: Now expand te expression in square brackets, cancelling and collecting terms to get: Multiply and divide te term in parenteses by p / w, and use to get: 26
Finally, use te fact tat te SS elasticities can be written as to get: (23) Tis is te expression in te text. 27