6. SAMPLE PROBLEM NUMBER TWO


 6.1 A Two Commodity, Three-Region Model


 This problem is similar to the one above except that it is expanded
to include two commodities and has the asymmetric Q property. It will
demonstrate the structure of a general LCP market oriented problem and
clarify the input strategy. To recap from the last section, there are
essentially four steps to model development.
 1) Model specification--Deciding on commodities, regions, time
 periods, and functional relationships for the model. Formulating
 data tables with actual coefficients to be used.
 2) Tableau formulation--Making matrix "tableaus" of the model either
 as a whole or in sections to organize the data, clarify the matrix
 structure, identify errors, and allow for straightforward prepar-
 ation of computer input.
 3) Preparation of computer input--This involves the coding and
 punching of computer statements which give model coefficients
 and represent the model structure. This is the most tedious of
 the four steps and therefore is usually the source of most errors.
 It should be done systematically and carefully.
 4) Solving the model--This step includes inputting the model into the
 computer system properly, identifying and correcting errors,
 analyzing solution results, and developing and implementing a
 strategy for generating model scenarios based on different para-
 meter assumptions.
 The tangible results of these particular steps in creating sample
problem number 2 will now be duplicated.
 Consider two products, A and B with three spatially distant regions
separated by constant transportation costs. Commodities A and B are
considered to be substitutes for each other. Both producers and consumers
make decisions regarding each commodity on the basis of the current price
of the other. The demand and supply functions are shown in Table 3.
These again have quantities as the independent variables to fit into our
quantity formulated model. The inverse forms which are more familiar can
be derived from this set but will not be presented here.