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Evaluation of Alternate Aggregation Models for Rice Growing
Farmers of West Bengal
Paper presented at the National Workshop of National Commodity
Exchange and Derivatives on 10th October, 2007
At
India Habitat Centre (Annexe Building), New Delhi
Dr. Debabrata Lahiri
Associate Professor
Rural Development Centre
Indian Institute of Technology, Kharagpur
Introduction:
i)
Transport and marketing of food grains in most of the developing countries costs
more than 70 per cent of product values;
ii) Transport costs have been higher because of sparsely located villages and
weak infrastructure, which ensures that spatial price differences would have a
significant influence on market performance and affects of the supply;
iii) Economic models have typically ignored space, taking into account markets
as single points within which transport costs are zero (or are included in the
production cost);
iv) This has made difficult to include some of the key features like diversity
among farmers in terms of access to alternative markets;
v) A new continuous – space model, designed to capture both farm – to –
market and market – to –market transportation cost would be developed;
Preamble to the Model:
i) To make a continuous space model more acceptable, extreme assumptions about
the geography has to be made;
ii) For example, in the pioneering nineteenth century model of von Thunen, a single
demand point has been used and no structure of roads or navigable rivers (Hall)
considered;
iii) A somewhat similar geography has been used to study the spatial aspects of
market power (Greenhut and Ohta);
iv) Gersovit, in an attempt to combine continuous space model with policy
intervention has equally abstracted geography;
Assumptions:
i)
A constant elasticity function for marketed supply at the farm level;
ii)
From farm-to-depot marketing costs are a linear function of distance along
either main or feeder roads, and assuming that all farms has been distributed
across a circular zone;
iii) According to Bressler and King, actual market a shape of irregular polyhedrons
whose corners had been equidistant from the multiple market centres.
Circles joined by main roads have provided a simple, tractable
representation of the country’s actual geographical area;
The Model:
i)
The model allows many demand points; each of them corresponds to a place and
a depot or warehouse and also has a distinct supply zone;
ii) In addition the volume of supply would likely to vary in each region, reflecting its
distinct agro-ecological potential;
iii) Also the direction of transport between depots/warehouses is likely to vary,
reflecting the possibility of different patterns of transport;
iv) the model it has been assumed that non-participation of a farmer in the market
would be there by specifying a reservation price, or minimum opportunity cost of
market supply ;
v) Above this reservation price, sales have been specified as a constant-elasticity
function of the difference between the reservation and farm gate prices;
vi) When farm gate prices falls below the reservation price, farmers would be
locally self-sufficient and do not participate in the regional and national level market
–except their purchase would reflect aggregate demand at each depot/warehouse;
vii) Thus farm-level marketed surplus supply function per unit is basis (in terms of
kilo meters) would be:
€
Qi = ßi (Pf – Pr) ---------------------(1)
Where:
Qi = Rate of supply in metric tonnes per square kilometre;
Pf = Farm gate price;
Pr = Reservation price (which has been uniform across farms);
€ = Farm level elasticity of market supply with respect to the difference between
farm gate and reservation price (also uniform);
ßi = Region-specific constant which is calibrated so that the aggregate supply
relationship has been satisfied at a benchmark prices and quantities;
viii) Generally, reservation price Pr and the elasticity € may also vary from region to
region.
Policy options-I:
i) If uniform price declared and the transport cost has been born by the
purchaser is different and within the regions, then under this pricing policy each
farm gets the same price, irrespective of the location;
ii) Then aggregate marketed supply for any ith depot/warehouse could be obtained
by integrating farm-level supply over the region;
iii) Expressing this form in polar coordinates yields supply function as a function
of price can be:
2Π Ri
€
Si (Ps) = f f ßi (Ps – Pr) dr dӨ
€
2
= Π ßi Ri (Ps – Pr) -----------------------------(2)
Where:
Π = is the trigonometric constant;
Pi, Ri = the radius of the supply region in kilometres so that the area of the resulting
circles equals the area of the actual (noncircular) geographical region;
Ps = is the uniform price;
The aggregate relationship between observed prices (Ps) and marketed quantities
(Si) can be calibrated to benchmark values by the choice of supply parameter
(ßi)
Options-II:
i) If the farm gate prices equals to the demand price at the regional
depot/warehouse minus farm-to-depot transaction costs;
i)
The rate of marketed surplus (in metric tonnes per square kilometre) would be:
€
€
Qi = ßi (Pf – Pr) = ßi (Ps – yr –Pr) ---------------------(3)
Where:
r = denotes the distance between the farm to regional depot/warehouses in
kilometres;
y = local market transaction costs in tonnes per kilometre. This local rate of y has
been substantially higher than the rate of interregional transport between depots
because of smaller shipments, shorter distances and bad quality roads.
Policy Options-III:
i) the farm gate price may be below the reservation price and the farm-level
marketed supply would be zero;
ii) In order to find out aggregate supply it must again integrate over all farm-level
supplies over the entire selling area, but has two possibilities:
(a) The selling area equals to the entire region;
(b) Or it does not;
If case (b) occurs then expressing in term of integral polar coordinates aggregate
supply function could be obtained for any depot/warehouse
i) The upper limit of integration has been the maximum of zero and the differences
between farm gate and reservation prices divided by the unit cost of transportation;
ii) Because the transportation cost has been positive, the limit of integration would
only be zero when the farm gate prices has been less than or equal to the
reservation price. In this case farm level marketed supply should also be zero.
Policy Options-III:
The reservation price has been uniform across regions and market demand
has been positive in the region, the farm gate price would always exceed the
reservation price in equilibrium:
Policy-IV:
i)
The balance of the model has been a traditional model endogenous price,
spatial-equilibrium model in the line of Takayama and Judge.
ii) The demand side of all policy scenarios would be represented by a constant
elasticity function at each depot/warehouse, representing only off-farm
consumption and calibrated so that demand relationship has been satisfied at
base-year market prices and quantities
This cope with the difficulty, the equilibrium has been solved by a sequence of
optimisation problems using the GAMS software package.
Data:
The following would be the data needs for different kind of scenarios this study
would be:
Supply of rice on per square kilometre basis for different regions within the state;
i)
Supply of rice on per square kilometre basis for different regions within the
state;
ii) Farm gate prices offered to farmers;
iii) Reservation price;
iv) Distance of the farms from the depots/warehouses
References:
i)
Hall, P. ed (1996): :Von Thunen’s Isolated State: An English Edition of Der
Isolierte Staat. Oxford: Pergamon Press;
ii) Greenhut, M.L., and H. Ohta (19750: “Theory of Spatial Pricing and Market
Access” Durham NC: Duke University Press;
iii) Gersovitz, M (1989): “Transportation, State Marketing and Taxation of the
Agricultural Hinterland” Journal of Political Economy, Vol. 97(October 1989):
pp. 1113 -37;
iv) Takayama, T and G.G. Judge (1964): “Equilibrium Among Spatially Separated
Markets: A Reformulation: Econometrica; Vol. 32, pp. 510-24;
v) -----------------------------------------(1971): “Spatial and Temporal Price and
Allocation Models, Amsterdam: North Holland;
vi) Takayama, T and G.G. Judge (1964): “Spatial Equilibrium and Quadratic
Programming”: Journal of Farm Economy; Vol. 46, pp. 67-93;
vii) Mwanaumo, Anthony, William A. Masters and Paul V. Preckel (1997): “A Spatial
Analysis of Maize Marketing Policy Reforms in Zambia”, Journal of Farm
Economy, Vol. 79, No: 3, pp. 514-523;
viii) Bressler, R.G., and R.A. King (1978): “Markets, Prices and Interregional Trade,
New York: Jojn Weily.