HABTM relationship MySQL tables for use in Rails

DROP TABLE IF EXISTS `products_tags`;
DROP TABLE IF EXISTS `tags`;
DROP TABLE IF EXISTS `products`;
 
CREATE TABLE `products` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `title` varchar(100) NOT NULL,
  `price` decimal(10,2) NOT NULL,
  PRIMARY KEY  (`id`)
)
 
CREATE TABLE `tags` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `title` varchar(64) NOT NULL,
  PRIMARY KEY  (`id`)
)
 
CREATE TABLE `products_tags` (
  `product_id` int(11) NOT NULL DEFAULT '0',
  `tag_id` int(11) NOT NULL DEFAULT '0',
  PRIMARY KEY  (`product_id`,`tag_id`)
)