Emergence of Organic Farming under Imperfect Competition: Economic Conditions and Policy Instruments

Mélanie Jaeck; Robert Lifran; Hubert Stahn

doi:10.1515/jafio-2013-0025

Published by De Gruyter June 5, 2014

Emergence of Organic Farming under Imperfect Competition: Economic Conditions and Policy Instruments

Mélanie Jaeck , Robert Lifran and Hubert Stahn

From the journal Journal of Agricultural & Food Industrial Organization

https://doi.org/10.1515/jafio-2013-0025

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Abstract

This paper explores the economic conditions for the viability of organic farming in a context of imperfect competition. While most research dealing with this issue has adopted an empirical approach, we propose a theoretical approach. Farmers have a choice between two technologies, the conventional one using two complementary inputs, chemicals and seeds, and the organic one only requiring organic seeds. The upstream markets are oligopolistic and the firms adopt Cournot behavior. The game is solved backward. The equilibrium distribution of the farmers between both sectors is obtained by a free-entry condition. Since multiple equilibria could exist, including the non-emergence of organic farming, we spell out viability conditions for organic farming. Then, using an “infant industry” argument, we propose several public policy instruments able to support the development of organic farming and assess their relative efficiency. Results could be useful to assess the conditions of emergence and viability of agricultural innovations in analogous contexts.

Keywords: agricultural inputs; organic farming; imperfect competition; technological choice; policy design

Appendix A

The sufficient conditions for optimality

Let us observe that the Hessian matrix of the profit function is given by H=A00B with

{A=k(n)⋅(f(3)(1n∑j=1msoj)⋅sojn2+(1+1n)⋅f(2)(1n∑j=1msoj))B=pc⋅(f(3)(1N−n∑j=1mscj)⋅scj(N−n)2+(1+1N−n)⋅f(2)(1N−n∑j=1mscj))

where f(n) stands for the nth derivative. Now remember that under market clearing the amount of seeds used by an organic farmer is so=1n∑j=1msoj, the same being true for conventional farming hence sc=1N−n∑j=1mscj. If we carry out this change of variables and introduce ef′′(s):=f(3)(s)⋅sf(2)(s) the elasticity of f′′, the previous Hessian becomes

H=k(n)n⋅f(2)soef′′(s0)⋅sojn⋅s0+1+n00pcN−n⋅f(2)sc⋅ef′′(sc)⋅scjN−n⋅sc+1+N−n

If both diagonal terms are negative, H is negative definite. Since f(2)s<0, it remains to check that

[19]{ef″(s0)⋅sojn⋅s0+1+n>0ef″(sc)⋅scj(N−n)⋅sc+1+N−n>0

This result is of course obvious when ef″(s)≥0. So let us consider the case in which ef′′(s)<0. Now let us first observe that at an optimal strategy of a Cournot player markets always clear. We can therefore say that n⋅s0 and N−n⋅sc are the aggregated quantities of the two kinds of seeds that are supplied, so that sojn⋅s0 and sojN−n⋅sc are market shares which belong by construction to 0,1. Moreover n and N−n are both greater than 1 otherwise one sector would not be activated. Finally remember that we have assumed that ef′′(s)>−2. If we make use of the three remarks, it immediately follows that conditions [19] holds

Appendix B

Proof of Lemma 1

Let us define ϕ(s,m,K):=1m⋅f′′(s)⋅s+f′(s)−K. It is easy to observe that:

∂ϕ(s,m,K)∂s=1m⋅f(3)(s)⋅s+f(2)(s)⋅1+1m=1m⋅f(2)(s)⋅ef′′(s)+1+m<0

since f(2)(s)<0,ef′′(s)>−2 and m≥1. Moreover we notice that:

lims→0ϕ(s,m,K)=f′(s)⋅1m⋅ef′(s)−Kf′(s)=+∞ since lims→0f′(s)=+∞ and ef′(s) remains bounded.
lims→+∞ϕ(s,m,K)=−K since lims→+∞f′(s)=0.

We can therefore state that there exists a unique solution in sm,K to ϕ(s,m,K)=0 and the lemma is obtained by applying the preceding argument to each equation of system [7]

Appendix C

Proof of Proposition 2

Let us come back to the definition of ϕ(s,m,K) given in Lemma 1. If we now apply the implicit function theorem, we immediately observe that:

∂s(m,K)∂m=1m2⋅f″(s)∂ϕ(s,m,K)∂s>0 and∂s(m,K)∂K=(∂ϕ(s,m,K)∂s)−1<0

which proves the first part of the proposition. Let us now push m to infinite, the equation ϕ(s,m,K)=0 simply becomes f′(s)−K=0 since ef′(s) is bounded. Hence s=f′−1(K).

Appendix D

Proof of Lemma 3

The proof of Lemma 2 is immediate. Remember that the sign∂πok(n),co,m∂n=signk′(n). So let us study k(n)=p(n)⋅β(n). By computation we obtain

[20]k′(n)=p′(n)⋅β(n)+p(n)⋅β′(n)

[21]k′′(n)=p′′(n)⋅β(n)+2⋅p′(n)⋅β′(n)+p(n)⋅β′′(n)

Now let us observe that:

k′′(n)<0, since we have assumed that p′(n)<0 and p′′(n)<0, β′(n)>0 and β′′(n)<0.
limn→0k′(n)>0 because limn→0p′(n)=0 and β′(n)>0
limn→Nk′(n)<0 because limn→Nβ′(n)=0 and p′(n)<0

We conclude that there exists a unique n0 verifying k′(n0)=0, and therefore such that ∂πok(n0),co,m∂n=0. Moreover, since k′′(n)<0, πok(n0),co,m is ∩-shaped.

Appendix E

Proof of Proposition 4

Assume that maxnp(n)β(n)<cocb⋅pc, this means that ∀n, cop(n)β(n)>cbpc and we can deduce from Lemma 1 that ∀n, socok(n),m<sccbpc,m. If we now remember that γ(s):=f(s)−f′(s)⋅s is increasing since γ′(s)=−f′′(s)⋅s, we can say that ∀n, γsocok(n),m<γsccbpc,m. Now remember that co<cb, this implies, in case (i), that ∀n, p(n)β(n)<pc. It remains to mix these two observations in order to say that:
∀n, πok(n),co,m=p(n)⋅β(n)⋅γsocok(n),m<pc⋅γsccbpc,m=πcpc,cb,m
It is impossible to observe an equilibrium distribution which involves organic farming.
if maxnp(n)β(n)∈pc,∞ and since co<cb, we can say that ∀n, cop(n)β(n)<cbpc. With the same arguments as in point (i) and by simply reversing the inequalities we can conclude that ∀n,πok(n),co,m>πcpc,cb,m, i.e. organic farming always dominates conventional agriculture.
if none of these conditions is satisfied, organic farming occurs if and only if πocok(nmax),nmax,m≥πccbpc,m because π0 is ∩-shaped with respect to n.

Appendix F

Proof of Proposition 6

Let us recall that the outcome of our model can be reduced to three equations: the modified first-order conditions of the input providers, i.e. eqs [7] and the free-entry condition, i.e. eq. [12]. These equations, after the introduction of the different policy arguments, are summarized in eq. [18]. However to simplify the notations let us introduce ϕ(s)=1m⋅f′′(s)⋅s+f′(s), γ(s)=f(s)−f′(s)⋅s and κ(n,δ,λ)=k(n)+δβ(n)+λp(n). We can even notice that (i) ϕ′(s)<0 see Lemma 1, (ii) γ′(s)=−f′′(s)⋅s>0, and (iii) ∂nκ(n,δ,λ)<0 by construction. This last point requires an additional comment. In the comparative static exercise we are looking at what happens in a neighborhood of an equilibrium which has the property that n∗∈0,N and that all policy arguments are set to 0. So by construction at the equilibrium ∂nκ(n,δ,λ)<0, and since we apply the Implicit Function Theorem (IFT) from a local point of view, we can choose the neighborhoods such that ∂nκ(n,δ,λ)<0 at the new equilibrium.

Now let us build the function:

Φ(so,sc,n,τ,σ,s,λ)=(ϕ(so)−co−σκ(n,δ,λ),ϕ(sc)−cb+τpc,κ(n,δ,λ)⋅γ(so)−pcγ(sc))

And since an equilibrium is given by Φ(so,sc,n,σ,τ,s)=0, let us apply the IFT. By a simple exercise of computation and by bearing in mind that ϕ(so)=co−σκ(n), we observe that:

∂(so,sc,n)Φ=[ϕ′(so)0ϕ(so)⋅∂nκ(n,δ,λ)κ(n,δ,λ)0ϕ′(sc)0κ(n,δ,λ)⋅γ′(so)−pc⋅γ′(sc)∂nκ(n,δ,λ)⋅γ(so)]

and

∂(τ,σ,δ,λ)Φ=[01κ(n,δ,λ))ϕ(so)⋅(β(n)+λ)κ(n,δ,λ)ϕ(so)⋅(p(n)+δ)κ(n,δ,λ)−1pc00000(β(n)+λ)⋅γ(so)(p(n)+δ)⋅γ(so)]

Now let us observe that the determinant of ∂(so,sc,n)Φ given by:

det(∂(so,sc,n)Φ)=ϕ′(sc)⋅∂nκ(n,δ,λ)⋅[ϕ′(so)γ(so)−γ′(so)ϕ(so)]<0

Being non-zero, we can therefore apply the IFT and we know that ∂(σ,τ,δ)(so,sc,n)=−∂(so,sc,n)Φ−1⋅∂(σ,τ,δ)Φ (at least locally). Moreover it is a matter of fact to check that:

(∂(so,sc,n)Φ)−1=1D[γ(so)−pcγ′(sc)ϕ(so)κ(n,δ,λ)⋅ϕ′(sc)−ϕ(so)κ(n,δ,λ)0Dϕ′(sc)0−γ′(so)κ(n,δ,λ)∂nκ(n,δ,λ)ϕ′(so)pcγ′(sc)ϕ′(sc)⋅∂nκ(n,δ,λ)ϕ′(so)∂nκ(n,δ,λ)]

withD=ϕ′(so)γ(so)−γ′(so)ϕ(so)<0

We therefore obtain that:

∂(τ,σ,δ,λ)(so,sc,n)=1D−γ′(sc)ϕ(so)κ(n,δ,λ)ϕ′(sc)−γ(so)κ(n,δ,λ)00Dϕ′(sc)⋅pc000ϕ′(so)⋅γ′(sc)ϕ′(sc)⋅∂nκ(n,δ,λ)γ′(so)∂nκ(n,δ,λ)−β(n)+λ⋅D∂nκ(n,δ,λ)−p(n)+δ⋅D∂nκ(n,δ,λ)

Since γ(s),γ′(s),ϕ(s),κ(n)>0 and ϕ′(s),∂nκ(n,δ,λ)<0 at an equilibrium, we can conclude that:

sign∂(σ,τ,δ,λ)(so,sc,n)=−+00−000++++

References

Batte, M. T., N. H.Hooker, T. C.Haab, and J.Beaverson. 2007. “Putting Their Money Where Their Mouths Are: Consumer Willingness to Pay for Multi-Ingredient, Processed Organic Food Products.” Food Policy32:145–59.10.1016/j.foodpol.2006.05.003Search in Google Scholar

Boccaletti, S., and M.Nardella. 2000. “Consumer Willingness to Pay for Pesticide-Free Fresh Fruit and Vegetables in Italy.” International Food and Agribusiness Management Review3:297–310.10.1016/S1096-7508(01)00049-0Search in Google Scholar

Burton, M., D.Rigby, and T.Young. 2003. “Modelling the Adoption of Organic Horticultural Technology in the UK Using Duration Analysis.” The Australian Journal of Agricultural and Resource Economics47(1):29–54.10.1111/1467-8489.00202Search in Google Scholar

Dimitri, C., and L.Oberholzter. 2005. “Market-Led Versus Government Facilitated Growth.” Development of the U.S. and E.U. Organic Agricultural Sectors, USDA, WRS 05-05. www.ers.usda.gov.Search in Google Scholar

Dimitri, C., and N. J.Richman. 2000. “Organic Food Markets in Transition, H.A. Wallace Center for Agricultural and Environmental Policy.” Winrock Inter.Search in Google Scholar

Eerola, E., and A.Huhtala. 2008. “Voting for Environmental Policy under Income and Preference Heterogeneity.” American Journal of Agricultural Economics90(1):256–66.10.1111/j.1467-8276.2007.01042.xSearch in Google Scholar

Fulton, M., and K.Giannakas. 2001. “Agricultural Biotechnology and Industry Structure.” AgBioForum4(2):137–51.Search in Google Scholar

Gil, J. M., A.Gracia, and M.Sanchez. 2000. “Market Segmentation and Willingness to Pay for Organic Products in Spain.” International Food and Agribusiness Management Review3:207–26.10.1016/S1096-7508(01)00040-4Search in Google Scholar

Hanson, J. C., E.Lichtenberg, and S. E.Peters. 1997. “Organic Versus Conventional Grain Production in the Mid-Atlantic: An Economic and Farming System Overview.” American Journal of Alternative Agriculture12(1):2–9.10.1017/S0889189300007104Search in Google Scholar

Hayenga, M. 1998. “Structural Change in the Biotech Seed and Chemical Industrial Complex.” AgBioForum1(2):43–55.Search in Google Scholar

IFOAM. 2009. “Definition of Organic Agriculture.”http://www.ifoam.org/growing organic/definitions/doa/index.html.Search in Google Scholar

Jaeck, M., and R.Lifran. 2009. “Preferences, Norms and Constraints in Farmers Agro-Ecological Choices.” Case study using choice experiments survey in the Rhone River Delta, France’, Montpellier, LAMETA, Working Paper, DR2009-16.Search in Google Scholar

Johnson, S. R., and T. A.Melkonyan. 2003. “Strategic Behavior and Consolidation in the Agricultural Biotechnology Industry.” American Journal of Agricultural Economics85(1):216–33.10.1111/1467-8276.00114Search in Google Scholar

Just, R. E., and D. L.Hueth. 1993. “Multimarket Exploitation: The Case of Biotechnology and Chemicals.” American Journal of Agricultural Economics75(4):936–45.10.2307/1243981Search in Google Scholar

Kleffer, R., W.Lockeretz, B.Commoner, M.Getler, S.Fast, D.O’Leary, and R.Blobaum. 1977. “Economic Performance and Energy Intensiveness on Organic and Conventional Farms in the Corn Belt: A Preliminary Comparison.” American Journal of Agricultural Economics59(1):1–12.10.2307/1239604Search in Google Scholar

Kristallis, A., and G.Chryssohoidis. 2005. “Consumers’ Willingness to Pay for Organic Food: Factors That Affect It and Variation per Organic Product Type.” British Food Journal107:320–43.10.1108/00070700510596901Search in Google Scholar

Lammerts van Bueren, E. T., and J. R.Myers, eds. 2011. Organic Crop Breeding. Chichester: Wiley-Blackwell.10.1002/9781119945932Search in Google Scholar

Martini, E. A., J. S.Buyer, D. C.Bryant, T. K.Hartz, and R.Ford Denison. 2004. “Yield Increases During the Organic Transition: Improving Soil Quality or Increasing Experience?” Field Crops Research86(2–3):255–66.10.1016/j.fcr.2003.09.002Search in Google Scholar

Mayen, C. D., J. Va. ndBalagtas, and C. E.Alexander. 2010. “Technology Adoption and Technical Efficiency: Organic and Conventional Dairy Farms in the United States.” American Journal of Agricultural Economics92(1):181–85.10.1093/ajae/aap018Search in Google Scholar

McCorriston, S., C. W.Morgan, and A. J.Rayner. 1998. “Processing Technology, Market Power and Price Transmission.” Journal of Agricultural Economics49:185–201.10.1111/j.1477-9552.1998.tb01263.xSearch in Google Scholar

Offerman, F., and H.Nieberg. 2000. “Economic Performance of Organic Farms in Europe.” Organic Farming in Europe: Economics and Policy5:198.Search in Google Scholar

Oude Lansink, A., K.Pietola, and S.Bäckman. 2002. “Efficiency and Productivity of Conventional and Organic Farms in Finland 1994-1997.” European Review of Agricultural Economics29(1):51–65.10.1093/erae/29.1.51Search in Google Scholar

Park, T. A., and L.Lohr. 1996. “Supply and Demand Factors for Organic Produce.” American Journal of Agricultural Economics78(3):647–55.10.2307/1243282Search in Google Scholar

Rogers, R. T., and R. J.Sexton. 1994. “Assessing the Importance of Oligopsony Power in Agricultural Markets.” American Journal of Agricultural Economics76:1143–50.10.2307/1243407Search in Google Scholar

Rouviere, E., and R.Soubeyran. 2011. “Competition vs. Quality in an Industry with Imperfect Traceability.” Economics Bulletin31:3052–67.Search in Google Scholar

Saitone, T. L., R. J.Sexton, and S. E.Sexton. 2008. “Market Power in the Corn Sector: How Does It Affect the Impacts of the Ethanol Subsidy?” Journal of Agricultural and Resource Economics33(2):169–94.Search in Google Scholar

Shi, G. 2009. “Bundling and Licensing of Genes in Agricultural Biotechnology.” American Journal of Agricultural Economics91(1):264–74.10.1111/j.1467-8276.2008.01174.xSearch in Google Scholar

Shi, G., J. P.Chavas, and K.Stiegert. 2008. “An Analysis of Bundle Pricing: The Case of the Corn Seed Market.” Staffpaper No 529, Dep. of Agricultural and applied econ. University of Wisconsin.10.2139/ssrn.1272132Search in Google Scholar

Sipiläinen, T., and A.Oude Lansink. 2005. “Learning in Organic Farming – An Application on Finnish Dairy Farms.” XIth International Congress of the European Association of Agricultural Economists, Econpaper No 61.Search in Google Scholar

Weldegebriel, H. T. 2004. “Imperfect Price Transmission: Is Market Power Really to Blame?” Journal of Agricultural Economics55(1):101–14.10.1111/j.1477-9552.2004.tb00082.xSearch in Google Scholar

Wheeler, S. A. 2008. “What Influences Agricultural Professionals’ View towards Organic Agriculture?” Ecological Economics65:145–54.10.1016/j.ecolecon.2007.05.014Search in Google Scholar

Wynen, E., and G.Edwards. 1990. “Towards a Comparison of Chemical-Free and Conventional Farming in Australia.” Australian Journal of Agricultural Economics34(1):39–55.10.1111/j.1467-8489.1990.tb00491.xSearch in Google Scholar

Yiridoe, E. K., S.Bonti-Ankomah, and R. C.Martin. 2005. “Comparison of Consumer Perceptions and Preference toward Organic Versus Conventionally Produced Foods: A Review and Update of the Literature.” Renewable Agriculture and Food Systems20:193–205.10.1079/RAF2005113Search in Google Scholar

Published Online: 2014-6-5

Published in Print: 2014-1-1

Emergence of Organic Farming under Imperfect Competition: Economic Conditions and Policy Instruments

Abstract

Appendix A

The sufficient conditions for optimality

Appendix B

Proof of Lemma 1

Appendix C

Proof of Proposition 2

Appendix D

Proof of Lemma 3

Appendix E

Proof of Proposition 4

Appendix F

Proof of Proposition 6

References

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