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THE WELFARE IMPLICATIONS OF NITROGEN LIMITATION POLICIES

S. McCorriston and I. Sheldon*

The effects of nitrogen limitation policies on the UK fertiliser market are considered. Using a simulation model which incorporates some structural aspects of the UK fertiliser industry, the extent and distribution of the welfare effects of nitrogen tax and quota policies are estimated. The results show that, while farmers lose from both policies, the main fertiliser manufacturers may gain in the short run from a quota policy, while profits would be reduced with a nitrogen tax policy.

1. Introduction In recent years there has been discussion of proposals to limit fertiliser use as a means of inter alia reducing the cost of agricultural su port. For example, Marsh (1987), Rickard (1986) and Weinschenck (19875 have discussed the advantages and disadvantages of such policies for the agricultural sector. However, whilst such policies can be expected to reduce agricultural output, these restrictions will also have an impact on the market for fertilisers. The aim of this paper is to consider the potential effects of nitrogen limitation policies on the fertiliser market.

This paper uses a simulation model of the UK fertiliser market to estimate the welfare effects of nitrogen tax and quota policies. Such effects include not only the impact on farmers’ producer surplus, but also the profits of fertiliser firms and government revenue. Section 2 outlines the model, which attempts to characterise some structural aspects of the UK fertiliser industry. Whilst the model does not assume any specific form of oligopolistic behaviour, some features of imperfect competition are incorporated by distinguishing the dominant fertiliser firms from a fringe of smaller firms and by treating the products of these two sectors as imperfect substitutes. In Section 3 the model is used to simulate the welfare effects of nitrogen tax and quota policies in a partial equilibrium context. The results are discussed in Section 4 and some possibilities for extension of this research are suggested in Section 5.

2.

The theoretical foundations of the model of the UK fertiliser market adopted in this aper can be found in Dixit (1988). Dixit’s work is characteristic of

A Model of the UK Fertiliser Market

recent B evelomnents in the literature of international economics in attermtine. * Steve McCorriston and Ian Sheldon are lecturers in the Agricultural Economics Unit, University

of Exeter. They are grateful to David de Meza, Alan Swinbank, John Mclnerney and Alison Burrell for helpful comments on earlier versions of this paper, and also acknowledge the comments of an anonymous referee.

144 S. McCORRlSTON AND 1. SHELDON

to assess quantitatively the outcome of trade and industrial policies where markets are imperfectly competitive. Essentially this research has taken the form of simulation exercises which are conducted in a similar manner to computable general equilibrium models. In these, some of the model’s parameters are taken from external empirical sources for a given year and the remainder are calculated by a process known as calibration such that they are consistent with equilibrium in that year. Examples of the use of this technique are Cox and Harris (1986), Venables and Smith (1986) and Dixit (1987).

The UK fertiliser industry can be regarded as oligopolistic in structure with four firms (ICI, Norsk Hydro, UKF and Kemira*) accounting for over 80 per cent of market share (see McCorriston and Sheldon, 1987). Although these four firms dominate the manufacture of fertilisers in the UK, there are also a large number of blenders who import nitro en fertilisers and mix compound fertilisers for local and regional markets. gonsequently, in this model, the structure of the fertiliser industry is divided into two: the four major firms, and the blenders. It is also assumed that there is no entry or exit of firms. Dominant firms face constant average and marginal operating costs and blenders have a constant price-cost mark-up. The products of the two sections of the industry are deemed to be imperfect substitutes in agricultural production. They are differentiated by advertising, technical back-up, packaging and local availability. Also, imported urea and domestically produced ammonium nitrate differ in their nitrogen content per tonne.

Although the model assumes no specific form of oligopolistic behaviour on the part of firms, such as either Cournot or Bertrand, firms’ reactions to one another are treated as a Nash equilibrium with conjectural variations. In a Nash equilibrium, each firm sees its strateg as being optimal given the strategies of other firms (see Vickers, 1985j. The notion of conjectural variations captures the possible beliefs each firm has about other firms’ strategies (see Waterson, 1984). For example, if firms have Cournot conjectures, they set output in order to maximise profits with the belief that other firms will keep their output constant. Consequently, in the model, the price-quantity equilibrium is always a Nash equilibrium implying a certain form of oligopolistic behaviour on the part of firms, i.e. whatever their oligopolistic strategy, firms cannot do better than the e uilibrium outcome. It should be noted that firms’ conjectures are assume 2 to be constant and hence are unaffected by changes in policy (see Appendix for further discussion).

Since the focus of the policy simulations is on the demand system, we first present the relevant demand equations and then show their derivation. The aggregate derived demand functions for fertilisers are given as:

where all parameters are positive and (B,B,-K*) > 0 which corresponds to imperfect substitutability between the firms’ products. p1 and pz are prices and Q1 and Qz are quantities where subscripts 1 and 2 refer to the dominant firms and blenders respectively. The corresponding inverse derived demand functions are:

Kemira have recently acquired UKF‘s production capacity in the UK.

THE WELFARE IMPLICATIONS OF NITROGEN LIMITATION POI.ICIES

pI = a, - blQ, - kQ2

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(3)

(4)

where all parameters are positive and (b,b,-k2) > 0.

Following the theoretical work of Dixit (1988) and Harris (1985), the demand equations (1) to (4) are consistent with the aggregate production function for farmers:

f(Ql,Q2) = a lQ1 + a2Q2 - Wb,Q,’ + b,Q,Z + 2k Q,Q2) ( 5 )

which exhibits the property of positive but diminishing marginal productivities. The demand system is derived by maximising with respect to Q I and Q, the aggregate profits rF for farmers:

Other specifications may also be consistent with the demand system, but it should be noted that no inputs other than the two forms of fertilisers have been considered in ( 5 ) , and that farmers’ output prices have been normalised to one in (6).

The parameters in equations (1) to’(4) can be calculated by using data on actual prices and quantities and also data on elasticities, which is the process of calibration. Focusing on equations (1) and (2), there are five unknown parameters A,, A,, B,, B, and K. Since actual prices and quantities give two relations between them, three furtner relations are required to solve the system.

Following Dixit (1987), expressions for the price elasticity of demand and elasticity of substitution can be derived and then set equal to empirically observed values. In the case of the price elasticity o f demand, since the products of the dominant firms and of the blenders are being treated as imperfect substitutes, i t is interpreted as being the effect of an equiproportionate rise in the price of the two products on total fertiliser expenditure Q . Therefore, letting p, = Plop and p2 = P,OP, where P,oand P20are initial prices and P is the proportional change factor, the aggregate expenditure for fertilisers can be written as:

Q = PIoQ, + P;Q, (7)

146 S. McCORRISTON AND 1. SHELDON

Given that in the calibration pI and p2 are the initial prices, and substituting equations (1) and (2) into (7), the aggregate expenditure index can be written as :

The total market elasticity of demand for fertiliser, E, is then defined and evaluated at the initial point where the proportional change factor P equals 1. By differentiating (8) with respect to P, and multiplying by P/Q, the elasticity is given as:

(9) 1 BlP21 + B2Pz2 - 2KPlP2

Q € = - [

Expression (9) is then set equal to the observed value of E. The elasticity of substitution would normally be defined as:

which gives a fourth relation between the parameters when set equal to an empirically observed value for a. However, as Dixit notes, equations (1) and (2) in general define the ratio Ql/Q2 as a function of the vector (pI,p2) and not in terms of the ratio p,/p2. In order for Q,/Q, to be a function of pI/p2, at least locally, then the parameters must satisfy the following final relation:

which implies homotheticity of the production function. Given the definition of a in (10) and using equations (l) , (2) and (11), the final expression for the elasticity of substitution can be derived as:

U = &(B,B, - KZ)

(B, E- K) (B2- K- P2 ;? Using price, quantity and elasticity data as presented in Table 1, the model

was calibrated for the year 1985. p1 and pz are the average selling prices of the dominant firms and blenders over the year 1985 based on reported prices in the UK farming press. Q, and Q2 are derived from Fertiliser Manufacturer Association data and other farming and trade sources. The value of the elasticity of demand E is based on an estimate made by Metcalf and Cowling (1967), although more recent estimates by Burrell (1989) suggest a similar value. No estimate of a is available for the UK, so a value of 2.00 is assumed. This is based on the observation that potentially a large proportion of blenders’ materials can be imported, hence the value for u reflects the degree of substitutability between domestic and imported fertilisers and corresponds with an estimate made by Higgs (1986) for Australia of 1.7.

THE WELFARE IMPLICATIONS OF NITROGEN LIMITATION POLICIES

Table 1 Calibration Data PI 126.00 (Utonne) P2 120.00 (Utonne) Q I 1,268,000 (tonnes) Q2 317,000 (tonnes) E 0.65 a 2.00

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Having calibrated the model, the parameter estimates shown in Table 2 are consistent with equilibrium in the UK fertiliser industry in 1985. This year was chosen for the calibration in that it represented a ‘typical’ year for the UK fertiliser market. If 1986 had been chosen, the results could have been substantially different due to the high level of im orts from Eastern bloc

trade restrictions that were then imposed would have affected the results. Equally 1985 could have been atypical, due to the effects of milk quotas, but these types of problems are likely to affect any period for which the model was calibrated. Given the parameters, the model can now be used to simulate the effects of nitrogen restrictions.

countries (see McCorriston and Sheldon, 1988). If 1 8 87 had been chosen, the

Table 2 Demand Parameters Aggregate Demand Inverse Demand

Functions Functions A , 2,092,200 a, 320 A2 523,050 a2 305 Bl 7799 b, (10-ql.38 B2 3104 b, (10-4)3.47 K 1321 k (10-5)5.68

3. Simulation Results

Nitrogen Taxes In this section the effects of an ad valorem tax on fertilisers are simulated. Two cases are considered; a 10 per cent tax and a 25 per cent tax on the original prices. These will have the effect of shifting the fertiliser supply curve upwards by the amount of the tax, thereby raising prices and reducing quantities, as shown in Table 3.

Table 3 Outcomes of Fertiliser Taxeson Fertiliser Prices and Quantities Sold Pre-tax I0 per cent tax 25 per cent tax

p1 Utonne 126 139 158

Q1 tonnes 1,266,000 1,185,580 1,061,950 pz [Utonne] 120 132 150

Q2 [tonnes] 317,000 296.395 265,487,

Given this increase in fertiliser prices, the effects on economic welfare can be examined by calculating the changes in farmers’ producer surplus as given by (6) and fertiliser firms’ profits using equations (13) and (14):

148 S . McCORRISTON AND I . SHELDON

where n, and are the profits of the dominant firms and blenders respectively and Q; and Q; are the post-tax uantities. cI , the operating costs for the

the blenders’ operating costs, are assumed to be 210 below the selling price minus the tax in order to reflect bagging and transport costs. Government revenue R from the tax is given by (15):

dominant firms, are assumed to be 9 100honne (see Challinor, 1987), whilst c2,

R = t(piQ; + P~Q;) (15)

where t is the ad valorem tax on fertiliser.

The net welfare effect of the tax policy is calculated by summing ( 6 ) , (13), (14) and (15). The results are presented in Table 4, relative to estimated actual welfare in 1985 as calculated at equilibrium. The burden of the tax falls largely on the farmers, although the fertiliser firms also face reduced profits. These losses are largely transferred to the government as revenue, but there are net social welfare losses of approximatelyf3 million and f9.9 million respectively.

Table 4 Welfare Outcomes of Fertiliser Taxes in 1985 (f million) Pre-tax (level) 10 percent iax (change) 25per cent lax (change)

Producer Surplus 152.36 -19.15 -45.41 Dominant Firms’ Profits 32.91 -2.14 -5.36 Blenders’ Profits 3.17 -0.21 -0.52 Government Revenue - + 18.50 +41.42 Net Welfare - -3.00 -9.93

Nitrogen Quotas An alternative policy to restrict the use of nitrogen is that of quotas. There has been little detailed discussion of how nitrogen quotas would be implemented and clearly there would be administrative problems with both consumption and production quotas. In this simulation, the latter case is considered, affecting the supply side of the fertiliser market. It is assumed that the level of imports will not increase following imposition of the quota.

Two levels of quota are considered, a 5 per cent level and 10 per cent level. Given that there IS no basis for predicting how the burden of such quotas would be distributed between the two sections of the fertiliser industry, three

ossibilities are presented. Case 1 divides the distribution of the uota equally

dominant firms and Case 3 distributes the quota in accordance with market share, i.e. 80 per cent of the 5 per cent production quota falls on the dominant firms. Such a policy results in the fertiliser supply curve becoming vertical at the quota level. The new levels of supply and the corresponding equilibrium prices are shown in Table 5.

getween the two sections, Case 2 assumes the quota is impose a only on the

W E WELFARE IMPLICATIONS OF NITROGEN LIMITATION POLICIES 149

Clearly the distribution of the quota affects the price increases of the dominant firms and the blenders. For example, in Case 1 the change in the blenders’ price is highest, and the change in the dominant firms’ price lowest, relative to the other two cases. This is due to two effects; a higher burden of the quota on the blenders and the effect of the elasticity of substitution. If the products of the two sectors were more substitutable, there would be less of a divergence between prices.

Table 5 Outcomes of Quotas on Fertiliser Quantities and Prices Case I Case 2 Case 3

Equal Distribution Dominant Firms Only to Market Share Distribution According

Quota Cut: Pre-Quota Sper cent IOper cent Sper cent IOper cent Sper cent lOper cent Q I (tonnes) 1,268,OOO 1,228,375 1,188,750 1,188,750 1,109,500 1,204,600 1,141,200 Q2(tonnes) 317,000 277,375 237,750 317,000 317,000 301,150 285,300 pl(fYtonne) 126.00 134.00 142.00 137.00 148.00 136.00 146.00 p,(f/tonne) 120.00 136.00 152.00 125.00 129.00 129.00 138.00

The net welfare effects of these price changes can again be calculated by summing equation (6 ) for farmers’ producer surplus and equations (13) and (14) for fertiliser firms’ profits where prices and quantities refer to post-quota levels. The results are shown in Table 6 , relative to estimated actual equilibrium welfare for 1985.

Table 6 Welfare Outcomes of Fertiliser Quotas in 1985 (f million) Case I Case 2 Case 3

Equal Distribution Dominant Firms Only to Market Share Distribution According

Quota Cut: AdualWelfme Spercent lopercent Spercent lopercent Spercent lopercent Producer

Dominant Firms’ Profits 32.97 +8.79 +16.96 +11.01 +20.29 +10.40 +18.38 Blenders’

Net Social Welfare

Surplus 152.36 -14.64 -28.45 -14.99 -28.90 -15.03 -28.26

Profits 3.17 -0.40 -0.79 0.00 0.00 -0.16 -0.32

Change - -6.25 -12.28 -3.98 -8.61 -4.79 -10.20

As with taxes, the burden of the welfare effects is borne mainly by farmers, their losses being broadly the same in all three cases. However, the dominant firms increase their profits, the extent depending on the level and distribution of the quota. Interestingly, the blenders’ profits fall in Cases 1 and 3 despite the increase in their prices. This follows from the assumption made about the blenders’ mark-up over costs. Again there is a net social welfare loss which varies with the level and distribution of the quota.

150 S . McCORRlSTON AND I . SHELDON

4. Discussion It is important to treat the simulation results presented in this paper as being suggestive of the extent of the welfare changes due to fertiliser tax and quota policies since the results depend on the specification of the model and the particular year for which it was calibrated. From the analysis, a number of points should be noted. First, due to a lack of relevant data, somewhat rigid assumptions have been made regarding the cost structure of fertiliser firms and clearly firms’ profits will be sensitive to assumptions made about their costs. Second, by nature of the agricultural production function used, effects on the derived demand for other inputs have been ignored as have changes in agricultural output prices. Taking account of these factors would greatly increase the mathematical complexity of the model. Third, since the model is of a partial equilibrium nature, other effects of nitrogen limitation policies have not been captured. For example, lower fertiliser usage by farmers may reduce agricultural support costs and also lead to important environmental benefits.

5. Summary This paper has analysed possible welfare effects of a nitrogen limitation policy by examining changes in farmers’ producer surplus, fertiliser firms’ profits and government revenue following the introduction of either a nitrogen tax or production quota. The distributional aspects between these groups have largely been ignored in policy discussions. A particular feature of the simulation model used is that it allows a distinction between the two sections of the UK fertiliser industry and also the imperfect substitutability between their products. The results of the simulation show that, while farmers lose from both policies, the main fertiliser manufacturers may actually gain in the short run from a quota policy, whilst profits for both dominant firms and blenders would be reduced with a nitrogen tax policy.

Finally, some comments can be made on the possible direction of future research in this area. In particular, i t would be desirable to consider a wider range of agricultural policies affecting the fertiliser sector. As it stands, the model can only be used to simulate input supply restrictions and other policies such as trade and industrial policy that directly affect the supply side of the input market. In order to simulate the effects of policies that influence the derived demand for inputs, i t would be necessary to account for the shift in the demand function. Essentially, the parameters in the farmers’ production function would change, which is impossible to deal with in this model.

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Economics, 40 ( I ) , 1-20, Challinor, S. (1987). The UK Fertiliser Indust Situation and Outlook in: Lingard, J . (ed.)

Agricultural Input Industries, University ofr3k’wcastle. Cox, D. and Harris, R. (1985). Trade Liberalisation and Industrial Organisation: Some Estimates

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Feenstra, R. ( e x ) Empirical Methodsin International Trade. Cambridge, Ma: MIT Press. Dixit, A. (1988). Anti-Dumping and Countervailing Duties Under Oligopoly, European

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Higgs, P. J . (1986). Adaptation and Survivalin Australian Agriculture. Oxford: Oxford University Press.

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McCorriston, S . and Sheldon, I. M. (1987). EC Integration and the Agricultural Supply Industries in: Macmillan, M., Mayes, D. G. and van Veen, P. (eds.), European Integration and Industry, Tilburg: Tilburg University Press.

McCorriston, S. and Sheldon, I. M. (1988). Estimating the Effects of Anti-Dumping Policies on the UK Fertiliser Market, Department of Economics Discussion Paper, 88/05, University of Exeter.

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APPENDIX

I n this appendix, i t is shown that an expression for firms' conjectural variations can be derived and used to show the nature of oligopoly in the UK fertiliser market in 1985.

The profits function rI of a typical dominant firm is:

where q i is its output, pI and cI being its selling price and costs respectively. If profits ri are maximised with respect to q i , the first-order condition is given as:

where dpl/dql is the conjectural variations parameter, i.e. the firm's expectation of how market price pI will vary with changes in its output q i . Therefore, if firms play Cournot, they believe rival firms will not change output in response to a change in ql , hence dpl/dql = -bi, the slope of the inverse demand function. If the market was perfectly competitive, a change in one firm's output would have noeffect on market price, hence dpJdq, = 0.

Expression (A2) can be aggregated over the ni dominant firms, the first-order condition being given as:

where V is the aggregate conjectural variations parameter. For Cournot behaviour, V, = bl!n, and as n: increases, the more competitive is the Cournot outcome. For perfectly competitive behaviour, Vl = 0. Similar expressions can be derived for the blenders.

Given observations on prices, quantities and costs, the conjectural variations parameters for both dominant firms and blenders can be calculated for 1985. In this year both the dominant firms and the blenders were acting fairly competitively, i.e. V and V, were approaching zero. It is assumed that these conjectures remain constant following tbe implementation of policy. However, it is possible that, if the model had been calibrated for a different year, firms may have been behaving less competitively. In terms of the effects of the policies considered, this will not affect the direction of change, only the magnitude.