Method for predicting price based on Geographical market, Product, and Company
It may be usefull to put what you are doing in a formal context, that way you can look at some standard solutions to your problem.

You have obsvations of a (random) variable X (price), together with some explanatory variables L, C, P (L="location" = city, C=company, P=price). So your data consists of cuadruples $(C_i, L_i, P_i, X_i)$.  

You are assuming a $\mathbf{multiplicative}$ model:
$$ E(X|C,L,P) = \lambda \space f_C \space g_L \space h_P .$$

This model fits nicely in the context of generalized linear models, since:
$$ \ln (E(X|C,L,P)) = \ln(\lambda) + \ln( f_C) + \ln( g_L) + \ln( h_P) .$$ 

You are fitting the model by a variation of iterative scaling. I don't know if there is a probabilistic model that corresponds to that way of fitting the models. Both the multiplicative model and iterative scaling have long traditions, so the answer might be known.

In any case, once in the context of generalized linear models, you can fit the parameters making some assumptions on the error. Since $X$ counts the number of monetary units per item, you can start by trying a Poisson model (and a Poisson model with overdisperssion). It is also worth trying other GLM's.