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South African Journal of Economic and Management Sciences

versión On-line ISSN 1015-8812

S. Afr. j. econ. manag. sci. vol.13 no.2 Pretoria ene. 2010

 

PRICING MODELS

 

Econometric estimation of Armington elasticities for selected agricultural products in South africa

 

 

AA OgundejiI; A JoosteII; D UchezubaIII

IDepartment of Agricultural Economics, University of the Free State
IIDepartment of Agricultural Economics, University of the Free State and Market and Economic Research Centre, National Agricultural Marketing Council
IIIDepartment of Agricultural Economics, University of the Free State and Northern Cape Department of Agriculture Accepted January 2010

 

 


ABSTRACT

Price transmission behaviour is used to model the impacts of different trade regimes; if this behaviour is not modelled correctly, the trade impacts can be either under- or overestimated. Due to the lack of elasticities of substitution pertaining to selected imported and domestically produced agricultural products in South Africa, 'Armington' elasticities, using quarterly data from 1995-2006 and three different models, based on the time series properties of the data, are estimated in this paper. Considering the long-run elasticity results, soyabeans (whether broken or not) and meat of bovine animals (frozen) are the most sensitive import products, followed by maize, meat of bovine animals (fresh or chilled), sunflower seeds, and wheat and meslin. Regarding the short-run elasticity, soyabeans are the most sensitive import product, followed by meat of bovine animals (fresh or chilled); meat of swine (fresh, chilled or frozen) is the least sensitive import product.

JEL: F12


 

 

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Appendix A

Following Armington (1969) and much of the ensuing literature, it is assumed that consumer utility for goods in a country is separable from consumption of other products, and a simple CES sub-utility function is postulated to model demand for domestically produced and imported goods in that country:

U ( M,D) = α [ ßMσ-1)/σ + (1 - ß) D (σ-1)/σ] (A.1)

Where:

U = sub-utility over the domestic and foreign goods

M = quantity of imported goods

D = quantity of domestic goods

σ = constant elasticity of substitution between domestic and imported goods

α and ß = are calibrated parameters in the demand function

Assuming that 'p' equals price, prices of imports and domestically produced goods are denoted as pM and pD. In order to maximise expenditure, prices are made equal to the marginal utility derived from purchasing the associated products so that

Thus, differentiating equation (A.1) with respect to M and D yields the following:

Also,

Given that

and then can be rewritten as:

Rearranging A.3 gives

The first-order condition can be rewritten as:

y = a0 + a1(A.5)

Where y = ln(M/D), a0 = σ ln [ß/(1 - ß)], a1 is the elasticity of substitution between imports and domestic sales, and x represents ln(pD/pM).

 

Appendix B

 

 

 

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