2. Model 



2.L Dealer Pull . To some extent all dealers are attractive to 

 a person planning to buy a car. The attractiveness of a specified 

 dealer presumably is a function of dealer characteristics (such as 

 make of car sold, extent of advertising), buyer characteristics (such 

 as make preference), and distance from dealer to buyer. The attrac- 

 tiveness of a dealer will be called his "pull". Pull will not be a 

 directly observable quantity but will be used to develop expressions 

 that are. 



We shall assume that the number of car purchases is fixed for 

 the time period under consideration. We have not modeled the effect 

 of a dealer in creating sales that would not have occurred In hla 

 absence. Our data do not seem to lend themselves to the estimation 

 of this effect, and perhaps it is small in today's well developed 

 markets. 



Buyers will be separated into market segments. The pull of a 

 dealer on a buyer in a given segment will be broken into two parts; 



(1) an intrinsic pull independent of the make sold by the dealer and 



(2) the make preference of the buyer. Let 



S(^>j) = ^^'^ pull of dealer j on a buyer in market segment 

 i. i = 1, . . .,S j = 1, . . .,D. 



^^C^/J) = the intrinsic pull of dealer j on a buyer in 

 segment i. 



q(i,m) = the make preference of a buyer in segment i for 



make m. m = 1,...,M. We specify that q(i,m) > 

 and S^W q(i,m) -- 1. 



Let m(j) denote the make sold by dealer j. We stipulate that the 

 above quantities be related by 



g(i,j) = h(i,j) q(i, m(.i)) (1) 



Thus, the pull cf a dealer on a buyer is the dealer's intrinsic pull 

 weighted by the buyer's brand preference. 



2.2 Purchase probability . The probability that a buyer purchases 

 at a given dealer will be taken as the pull of that dealer on the buyer 

 divided by the total pull on the buyer. Let 



P(i^j) = the probability that a buyer in market segment i 

 purchases at dealer j. 



p(i,j) = g(i,j) / L^l^ g(i,k) (2) 



