10. A TYPOLOGY OF WELFARE EFFECTS: REGIONAL PERSPECTIVE

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1 Printed=04/10/02 12:04, Filename=Ch10.doc; Version date: 17-Sep-02 14: TYPOLOGY OF WLFR FFCTS: RGIONL PRSPCTIV Introduction The nomenclature of policy effects is rich and confusing. Terms of trade effects, trade creation and diversion, dynamic effects, scale effects, growth effects are but a few of the terms applied by various authors to various channels. To provide a unified terminology for our policy analysis, this chapter presents a framework for organising our thinking about how policy changes can affect welfare. We do not specify the connections between particular policies and the changes in the various endogenous variables; we simply identify and label the various channels through which policy changes may affect welfare. James Meade pioneered the basic approach employed here. The current application is an extension of Dixit and Norman (1980 Chapter 6) and Helpman and Krugman (1989 Chapter 2.7) Organisation of the Chapter The chapter starts with a framework that allows general preferences, before specialising the organising framework to Dixit-Stiglitz preferences in Section Both of these sections assumes factors supplies are fixed to allow us to focus on the static effects. The next two sections expand the framework to allow the accumulation of factors (typically capital). Thus section 10.4 allows one-off changes in capital stocks in response to policy changes, so-called medium run growth effects, while the final section allows for one-off changes in the rate of capital accumulation, thus encompassing the possibility of long-run growth effects Organising Framework We start by deriving an organising framework for general preferences. We focus on the welfare of the north and work with a utilitarian social welfare function that counts the utility of all residents located within the northern region. Since we work with small changes around an equilibrium, we implicitly assume that the economy starts at a stable, interior equilibrium ssumptions We assume two regions (north and south), two sectors ( and M), and two factors (K and L). The -sector is Walrasian while the M-sector is monopolistically competitive and produces differentiated products. ach region s supply of L is fixed and cannot cross regional borders, but the other factor, K, may be inter-regionally mobile or not, depending upon the model (we consider both cases below). t this point we work with general preferences given by intertemporally separable preferences: (10-1) t t=0 e ρ V [p, n, ]dt Geopo 10-1

2 where ρ is the constant discount rate, p and n are the vectors of consumer prices and the number of varieties in each sector, and is total consumption expenditure. xpenditure is home income less home savings, where income is the sum of home factor income, net revenue from tariffs and other import barriers (assumed to be returned lump-sum to consumers) and pure profits, i.e.: (10-2) = wl + rk + Tm + Π S where w and r, and L and K are the prices and stocks of home's labour and capital, m is the vector of sectoral trade (imports enter with a positive sign, exports with a negative sign), Π is pure profit, and S is savings. lso, T p-p*, where p* is the border price, i.e. the price that the country actually pays for imports and the price it actually gets paid for exports. Thus p* need not equal the world price, for example, when there are frictional trade barriers such as transport costs the price the north pays for its imports is the price received by the exporter plus these costs. Pure profits are related to the vector of local prices, p, the vector of sectoral outputs, Q, and the vector of average cost functions, a[w,r,x], according to: (10-3) cwrx i[,, i] Π= ( p aq ) ; awrx i[,, i], Qi nx i i x where Q i is a typical element of the sectoral output vector Q, a i is a typical element in the vector of sectoral average costs a, defined as the total cost of a typical firm (all domestic firms within a sector are assumed to be identical) c i [w,r,x i ] divided by typical firm output x i. s usual, total cost is a function of w, r and firm output x. Notice that pure profits are decomposed here. That is, Π is defined as if all goods in a particular sector were sold at the domestic (i.e. local) price, p. For perfect competition sectors and for sectors marked by Dixit-Stiglitz monopolistic competition, this does not matter since in both cases, firms charge the same producer price in all markets (perfectly competition firms never price discriminate across markets, and non-discrimination, i.e. mill pricing, is optimal under Dixit-Stiglitz competition). However, for oligopolistic sectors (which is a possibility with the linear model of Chapter 5), producer prices can vary across markets. For such sectors, the profitability of price discrimination shows up in the term (p-p*)m in (10-2) Calculations Totally differentiating V and converting utils into euros (by dividing through by the scalar V ) yields: dv Vp Vn Vn (10-4) = ( ) dp+ dn+ d = Cdp+ dn+ d V V V V i 1 For example, suppose markets are segmented and there are costs to exporting, so a profit-maximising oligopolist would typically charge a lower producer price for exports. Then the total profit of the firm would be p a q a plus p b q b minus a[w,r,q a +q b ](q a +q b ), where the a indicates the producer price and quantity for local sales and b indicates the producer price and quantity for exports, but in notation of (10-3), the profit is p a (q a +q b )-a[w,r,q a +q b ](q a +q b ) + (p b -p a )q b with the last term showing up in the trade rents term. Geopo 10-2

3 where V p and V n are vectors of partial derivatives; the second expression follows from the first using Roy's identity. To calculate d, we totally differentiate the definition of, (10-2), and use T=p-p* to get: (10-5) d = Ldw + Kdr + rdk + (p p *)dm + mdp + mdp * + (p a)dq + Q(dp da) ds where: (10-6) c dw c dr a Qda = Q + Q +Q dx i i i i i i i i w xi r xi xi a i = Ldw + Kdr + Q i i dx i xi and the summation is over all sectors i; the second expression follows from the first by Shephard's lemma. Plugging (10-6) and (10-5) into (10-4) and using -C -m-qthe expression for home welfare changes simplifies to: dv/ V = (p p *)dm mdp* (10-7) + (p a)dq + Q( a )dx + ( V n / V )dn x + rdk ds where we employ the notation a/ x=a x. This expression (10-7) is our general organising framework Discussion The three rows of the (10-7) categorise welfare effects into three types. Walrasian effects: Trade price and volume effects The first row shows effects that occur even when one ignores scale economies and imperfect competition. s in the public finance literature, welfare effects in a Walrasian world stem from quantity changes times initial price wedges and price changes times net trades. We refer to the first as the trade volume effect and the second as the trade price effect (a.k.a. terms of trade effect). ICIR effects: Production rents, scale and location effects The second row shows the effects that appear when we assume the economy is marked by scale economies and imperfect competition (ICIR effects for short). The first effect is the production-rent effect. That is, if there are pure profits in a sector, increasing production in that sector tends to improve northern welfare. The second term is the scale effect. That is, since -a x is positive under scale economies average cost falls as output increases, increased scale tends to improve northern welfare. Geopo 10-3

4 The third term includes two distinct effects, the well-known variety effect (i.e. an increases the total number of varieties available tends to improve domestic welfare) and a location effect. The location effect captures the welfare implications of changes in the production location of a particular variety. For example, when trade is costly, northern welfare is higher when more varieties are produced domestically instead of abroad since this allows avoidance of the trade cost. Study of this location effect is best left to the next section where concrete analysis is made possible by adoption of Dixit-Stiglitz preferences. ccumulation and migration effects The third row constitutes the accumulation and migration effects. In most of the Part I models, the world human or physical capital stock is fixed, so savings is zero by definition. In such cases, rdk is the impact of migration on northern expenditure. In the constructed capital, and local and global spillover models, north s capital stock depends upon savings. In such cases the third line captures the welfare implications of induced capital formation and the induced savings that is required. In particular, induced capital formation has two counteracting welfare effects. higher capital stock raises income and thereby expenditure. This is reflected in the first term and it is the positive aspect of induced capital formation. However, induced capital formation means consumption must be foregone. This negative influence on the current flow of utility is captured by the second row-three term. Since the accumulation of human, physical and knowledge growth is the source of all per capita output growth, many authors refer to accumulation effects as growth effects, or dynamic effects. Interested readers can easily extend this framework to capture additional effects Dixit-Stiglitz Preferences In all but one of the Part I chapters, we assume Dixit-Stiglitz monopolistic competition and iceberg trade costs. These assumption simplifies the analysis greatly; this section exploits the resulting simplicity. Imposing symmetry on M-varieties made in the same nation and assuming only two nations, the Dixit-Stiglitz indirect utility function is: (10-8) µ µ w 1-σ 1-σ 1 µ 1-σ 1-σ V = ; P ( n ) p ; s n p + (1 sn) p* P where p and p* are the consumer prices of a typical domestic and imported differentiated variety (respectively), s n is the share of world varieties produced in north (i.e. s n n/n w where n is the number of varieties produced in north), is total northern consumption expenditure, µ is the constant fraction on expenditure spent on M-goods, and n w is the total mass (number) of varieties available. s usual σ is the constant elasticity of substitution between any pair of the differentiated varieties. In the one-period economy, expenditure is income, i.e. the sum of home factor income and pure profits, plus revenue from tariffs, taxes etc., less any subsidy or transfer payments. Since the models allow only frictional trade barriers, tariff revenue need not be considered. Moreover, we always assume that the government runs a balanced budget so taxes, subsidies and transfers sum to zero. Thus: Geopo 10-4

5 (10-9) = wl + rk + Π; w Π = ( p a[ w, r, x]) sn n x + ( p wa ) where x is the equilibrium firm size and we have used the assumption that the sector employs only L. Recall that we choose units of K such that n w =1, so n=s n, and we take as numeraire, so p = Calculations Totally differentiating (10-8) and dividing by V =1/P to convert utils into real euros yields: (10-10) dv dp = d V P Totally differentiating the definition of in (10-9) using n=s n n w yields: (10-11) d = [ Ldw + Kdr ( nx) da a dw] + [( nx) dp + dp + ( r Γ) dk] + [( p a) d( nx) + ( p wa ) d] ; da = a dw + a dr + a dx where Γ is a model-specific term that is discussed below. Note that after cancelling, the terms in the first large bracket equals zero since any rise in factor payments is cancelled by a corresponding drop in Π, and firm size is invariant in the Dixit-Stiglitz approach (i.e. dx=0). The terms in the third square brackets are also zero since all equilibria considered are marked by average cost pricing in both sectors. Thus d equals the terms in the second square brackets. valuating the second term in (10-10), using the definition of the price index in (10-8), we have: σ σ 1 σ 1 σ dp (1 µ ) p * p * µ p p* (10-12) = dp + µ sn dp sn dp * + ( ) dsn P p + 1 σ where we have used dn w =0 to simplify, and our normalisation to set s n *=1-s n. Using the demand functions, the first two terms become C dp, and ncdp+n*c*dp* (c and c* are home consumption of, respectively, a typical local and a typical imported variety). The final term becomes µ(s-s*)/(1-σ) times ds n, where s and s* are, respectively, the expenditure shares on a typical local M-variety and a typical imported M-variety; note that (s-s*) exceeds zero with positive trade costs. 2 Plugging (10-12) and (10-11) into (10-10), the welfare effects are: dv B µ (10-13) = mdp + ( s s*) dsn+ ( r Γ) dk V σ 1 where m is the trade vector, i.e. domestic consumption minus domestic production (sector by sector) and dp B is the change in the vector of border prices, i.e. (dp, dp and dp*). w r x 2 The local demand function for a typical local variety is p -σ /(np 1-σ +n*p* 1-σ ) times µ. Multiplying by p we have that s=pc/ equals µp 1-σ /(np 1-σ +n*p* 1-σ ). Geopo 10-5

6 Observe that in a symmetric equilibrium the gap between the expenditure shares on a typical local M-variety and a typical imported M-variety, namely, s-s*, is greater than zero in the presence of positive trade costs. This expression is our organising framework for the restricted set of assumptions that characterise most economic geography models Discussion xpression (10-13) shows that the CP, F and FC models contain at most three types of welfare effects. Border Price ffect The first term in (10-13) shows the traditional trade price effect (a.k.a., terms of trade effect); anything that lowers the price of imports, or raises the price of exports will improve north s welfare. Notice that the other classic effect, the trade volume effect, is not present since we are considering frictional barriers (i.e. the interior and border prices are identical so small changes in the volume of trade has not net welfare impact). Location ffect The second term in (10-13) might be called the location effect, or the cost-of-living effect. What is says is that holding the number of varieties constant (so that the classic variety effect is absence), shifting production of one variety from the south to the north improves the north s welfare. The size of the effect increases with trade costs. Specifically, the magnitude of the effect is proportional to the difference between the share of expenditure that falls on a typical north-made variety and the share falling on a typical south-made variety. Migration ffect The third term in (10-13) captures the welfare impact of migration and is thus modelspecific. In the CP and F models, an inflow of the mobile factor K, raises real income and so is counted as a benefit. In other words, Γ=0 in the CP and F model. The size of the migration effect depends upon capital s reward, r. We note here that our strict utilitarian approach i.e. adding up the indirect utilities of all northern residents is not the only sensible approach. Its merit is the fact that it corresponds to an observable quantity the north s real income. However, one might, for instance, focus solely on the welfare of the initially residence. If north had a direct democracy, or the northern government always acted in the interest of northern voters, the initial residents welfare would be determinant. lternatively, one might focus on average utility, but then our normalisation would take on an unwanted importance. In the symmetric equilibrium, our normalisations imply that r and the wage of the immobile factor, w, are unity. Thus migration, per se, has a neutral effect on are utility, but could as well have chosen normalisations that implied a positive or negative effect on average utility. In the FC model, however, capital income is repatriated so Γ=r*, where r* is what the north s capital earns if it migrates to south. Note however that since we are starting from a stable interior equilibrium, and r=r* in the FC model in such instances, the third term in (10-13) is zero. Geopo 10-6

7 10.4. llowing for Variable Factor Supplies The models studied above, namely the CP, FC and F models, all take the supply of K as fixed. Since capital accumulation is the essence of growth and growth is an important consideration in regional policy evaluation, we now expand our organising framework to allow for constructed capital. We first work with the CC model, where the long-run capital stock reaches a steady state level New Considerations The first change is to our definition of expenditure. Since capital can be constructed, expenditure on consumption goods is income less spending on capital construction. Thus: (10-14) = wl + rk + Π wli where, following the CC model, we have assume that the capital-construction sector uses only the immobile factor L. The second change is to realise that maintain K requires real resources, so the reward to K must be adjusted. In the CC model, the equilibrium reward to capital (what we called π in Chapter 6) is such that r=(ρ+δ)f. Moreover, increasing K requires real resources, so dk is not for free. Using the production function of the capital construction sector, i.e. the I-sector, we see that it takes F units of L to make a new unit of K and δf units of L to maintain one in steady state, so: (10-15) L = F(δ K + K& ) dl = δfdk + FdK& I The third change involves the impact that dk has on income when we recognise discounting and depreciation. Presuming that future real income is discounted at the rate ρ, and using our normalisation that w=1, (10-15) and r=(ρ+δ)f, the present value of income can be written as: I t= 0 ρt (10-16) e ( L + ρfk ) dt FdK& = w L + FK FdK& ρ where the term, time zero. Fd K & appears outside the integral since it is a one-off cost that is incurred at Finally, we note that we start off in a long-run equilibrium, i.e. and P are timeinvariant. Thus the present value of our indirect utility measure is: t 1 1 (10-17) e dt ( L FK FdK& ρ = + ) t= 0 P P ρ Using (10-17) instead of (10-8), we proceed through the same chain of calculation, but now we must take account of the connection between dk and the cost of its construction given by (10-15). The result is: dv B µ (10-18) = mdp + ( s s*) dsn+ ( F F ) dk V σ 1 Plainly, the third term is zero, so induced capital formation adds nothing to utility. This result Geopo 10-7

8 is quite intuitive. In the CC model, the capital stock rises up to the point where the value of an extra unit of K equals its cost. But then any change that induces the economy to build a marginal unit of capital will have no welfare effect, exactly because the value of the extra unit will be exactly offset by the cost of constructing it (see Baldwin 1992 for details) llowing for ndogenous Growth Next we expand the framework to allow for endogenous growth. This has two implications for our calculations. First, as in the LS model, F=1/K w, with =1 if we work with the GS model; thus, L I =s K (δ+g)/. Second, the discounting has to take account of the fact that the price index falls at a rate (gs K + g*s K *)µ/(σ-1), where g and g* are the rates of growth of K and K* respectively, and in the initial equilibrium, g=g*. Finally, r=(δ+ρ+g)f. With these changes, the present value of our indirect utility measure is: (10-19) t= 0 e ( ρ ag ) t P dt = 1 P ρ a( s K 1 g + s * K sk ( L g*) Using this and following the usual chain of calculations, we get: g) + FK FdK& ) (10-20) dv V = mdp B µ + ( s s*) dsn+ ( F F) dk + σ 1 1 al ( ρ ag ρ ag 1 ) dg The new term here is the fourth one. The coefficient on dg is positive, so this could be called the growth effect. This implies that faster growth is welfare improving. The intuition for this is straightforward. Private innovators ignore two externalities. First, being atomistic, they ignore the impact of their flow of innovations on the time path of the price index. Second, they ignore the learning externality in the innovation sector. For both of these reasons, the free market results in a growth rate that is socially sub-optimal. References Baldwin, R. (1992). "Measurable Dynamic Gains from Trade", Journal of Political conomy, vol. 100, 1, pp Dixit,. and V. Norman (1980) Theory of International Trade, CUP, London. Helpman,. and P. Krugman (1989) Trade policy and Market Structure, MIT Press, Cambridge. Geopo 10-8