content_image/344025.jpg content_image/344031.jpg content_image/344032.jpg
## MATHEMATICAL MODEL 

## Purchase intention for individual person 

<img src='content_image/344025.jpg'>

Based on the observation of the movie hit phenomena in Japanes market, we present a mathematical model to explain and predict hit phenomena. First, instead of the number of audience N ( t ), we introduce here the integrated purchase intention of individual customer, J$_{i}$ ( t ) defined as follows, 

<img src='content_image/344031.jpg'>

here the suffix j corresponds to individual person who has attention to the movie. Sub- stitute (4) into (1), we obtain, 

<img src='content_image/344032.jpg'>

