2120 final report.pdf - Agra CEAS Consulting

APPENDIX 2: THIRD COUNTRIESSo X is an aggregated input index and S is an aggregated output index. The value equilibriumequation sets the unit cost c Q of producing a unit of aggregated output equal to the unit revenue r Xearned per unit of the aggregated input X.A3.2.2.6. Output-constrained input demand of egg production(18) X 1 = c 1 (W 1 , W 2 , W 3 )S – demand for input X 1(19) X 2 = c 2 (W 1 , W 2 , W 3 )S – demand for input X 2(20) X 3 = c 3 (W 1 , W 2 , W 3 )S - demand for input X 3These equations are obtained by applying Shephard’s Lemma (Chambers, 1988) to the total costfunction.A3.2.2.7. Input supply to egg production(21) X 1 = g 1 (W 1 , T X1 ) - supply of input X 1(22) X 2 = g 2 (W 2 , T X2 ) - supply of input X 2(23) X 3 = g 3 (W 3 , T X3 ) - supply of input X 3These equations are the input factor supply equations.The model is estimated assuming that all types of eggs come from a single production sector which ischaracterised by the weighted average of the different systems in operation. We employ datacollected in Stage 1 of the study to apportion costs of egg production. When we ‘shock’ eggproduction by increasing or decreasing production costs we are explicitly assuming a change in themix of production systems. So, for example, an increase in other cost can be taken to mean lesstraditional cage egg production and more enriched or alternative (i.e., free range, barn) production.A3.2.3. Model in displacement formTo conduct policy analysis with our model it is shocked or displaced from its initial equilibrium as aresult of some exogenous change (e.g., demand or supply shift). By totally differentiating allequations in the model and expressing in elasticity form the model linearly relates changes in theendogenous variables to changes in exogenous variables (n Qc , n Qp , n Qa , n Qtc n Qtp , n Qta , t X1 , t X2 , t X3 ).Expressing as elasticities yields the following system of equations.(1*) EQ c = η (Qc Pc) (EP c -n Qc ) + η (Qc Pp) (EP p -n Qp ) + η (Qc Pa) (EP a -n Qa )(2*) EQ p = η (Qp Pc) (EP c -n Qc ) + η (Qp Pb) (EP p -n Qp ) + η (Qp Pa) (Ep a -n Qa )(3*) EQ a = η (QaPc) (EP c -n Qc ) + η (QfaPp) (EP p -n Qp ) + η (QfaPa) (EP a -n Qa )(4*) EQ tc = λ Sc ES c – λ Qc EQ c(5*) EQ tc = e c (EP tc -n tc )(6*) EP tc = e tc (αEP c + τ tc )(7*) EQ tp = λ Sp ES p – λ Qp EQ p(8*) EQ tp = e p (EP tp -n tp )(9*) EP tp = e tp (αEP p + τ tp )407