\-lc note that make preference can be interpreted as the probability of 

 purchase of the make under the conditicns that the sum of the intrinsic 

 pulls on the buyer is the same for each make. This result can be 

 deduced from (1) and (2). 



2.3 Geographic effect . We hypothesize that pull falls off expo- 

 nentially with the distance between dealer and buyer. This is only one 

 of many possible relations but it appears to work well. Let 



x(i;j) = distance of the buyers in market segment i to dealer 

 J. 



h(ij) = a. e-^J^^^'J^ (3) 



Here a and b, are constants specific to dealer j. The constant a. 

 expresses the dealer's strength in his own immediate neighborhood.-' 

 The constant b tells how fast his sales fall off with distance. Using 

 (1), (2), and J (3), we get 



p(i j) _ q(l,m(:,1)) a c-^^<^^-^) J 



^k=l ^^ ' "^W) \ c '^ ^ ' ' 



2.4 Dealer sales and penetration . Let 



N(i) = number of buyers in market segment 1 (called the 

 potential of the segment) in a given time period. 



3(j) = expected sales of dealer j in the given time period. 



n(j) = expected penetration of dealer j In the whole city. 



Then 



s(j) = L^l^ N(i) p(i,j) (5) 



n(j) = s(j) / l^J^ N(i) (6) 



3. Fitting the Model to Data 



3.1 D.3 1 a . The model has been fit to R.L.Polk new car registrations 

 for April, May, and June 1963 in Cook County, Illinois (fleet sales elim- 

 inated) . In order to maintain reasonable sample sizes with three months 

 of data, the analysis has been confined to 3 major makes (Ford, Chevrolet, 

 iiambler, Pontiac, PlymoaCh, Buicx, Oldsmobile, and Dodge) and to dealers 

 selling SO or more cars in the cimc period. This involves 47,670 cars 

 and 1&4 dealers, or 91. 5% of the carj and 627. of the dealers of the makes 



