Computational Experience with the Model

A substantial amount of computational experience has been acquired with the UK model.

The majority of execution time in solution is spent in function evaluation, particularly in evaluating the market demands for commodities at candidate price vectors. This suggests that execution times are sensitive to the functional forms which are used to describe demand patterns and this seems to be borne out by experience. If steps taken across a simplex have associated with them a fixed number of function evaluations per step, even if the number of steps remain constant for higher dimensional problems (which typically does not happen) the increased time spent in function evaluation per step will cause execution times to rise considerably.

The amount of execution time needed to numerically determine a competitive equilibrium can therefore be directly related to ‘dimensionality’. In its crudest terms, this can be thought of as the overall size of the model, but in practice there are specific dimensions which can be identified as critical.

Two dimensions in the model are especially important.

(i) The Dimensionality of Function Evaluation:

This is the dimension in which calculations underlying market demand and supply functions must be made. On the demand side of the economy the critical features are the twin dimensions of the number of consumers and the number of commodities. In the model of the UK this is a dimension of 103 by 64.