2120 final report.pdf - Agra CEAS Consulting

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APPENDIX 2: THIRD COUNTRIESInputsFeed, Labourand OtherEggProductionCagedShelldAlternativeTrade with ThirdCountriesProcessedFigure A3.1: Schematic Diagram of the EDM ModelA3.2.1. Model assumptionsTo implement the EDM we make the following assumptions:1. all sectors are profit maximisers;2. all multi-output production functions are separable in terms of inputs and outputs; and,3. all production functions are characterised by constant returns to scale.These assumptions allow us to characterise an industry allocation problem in two parts: costminimisation and revenue maximisation (Varian, 1994). Zhao et al., (2000a) derive the formaleconomic representation of a multi-input/output industry under these assumptions. Our model isbased upon the same formal structure. We are also assuming that the forces of supply and demanddetermine the price of eggs.A3.2.2. Model definitionsNext we define the variables, parameters and notation used in the modelNotation:Let:c = caged;p = processing; anda = alternative404
APPENDIX 2: THIRD COUNTRIESEndogenous Variables:Xi (i=1,2,3) are inputs (Feed, labour and other)Wi (i=1,2,3) are input pricesQ c Q p and Q a , are quantities demanded of caged shell, processed and alternative shellS c, S p and S a are quantities supplied of caged shell, processed and alternative shellQ tc Q tp and Q ta are the net import/export of caged shell, processed and alternative shellP c P p and P a are prices of caged shell, processed and alternative shellP tc P tp and P ta are world prices of caged shell, processed and alternative shellX is an aggregated input index of egg productionQ is an aggregated output index of egg productionExogenous Variables:N X – demand shifter in market Xn - Amount of shift in Nx as a percentage of price of xTx – supply shifter in market XT – Amount of shift in Tx as a percentage of price of xZ tx – tariff shifter in market Xτ tx – amount of shift as a percentage of priceParameters:Elasticities η – demand elasticity of variable x with respect to change in price y β xy – Allen’s elasticity of product transformation between output x and output y xy – Allen elasticity of substitution between input x and input y ε - supply elasticity of variable x with respect to change in price y ei – import supply/export demand elasticity (i=c,p,a) e ti – price transformation elasticity (i=c,p,a)Cost/Revenue Shares: κ X – cost shares of inputs γ – revenue share of outputsGiven the above assumptions and the description of the egg sector, the EDM consists of thefollowing 23 equations.A3.2.2.1. Domestic demand(1) Q c = Q c (P c , P p , P a , N Qc , N Qp , N Qa )(2) Q p = Q p (P c , P p , P a , N Qc , N Qp , N Qa )(3) Q a = Q a (P c , P p , P a , N Qc , N Qp , N Qa )405
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