WITH new_users AS (
	SELECT DISTINCT ON (user_id) user_id, created_at
	FROM purchases
	ORDER BY user_id ASC, created_at ASC
), old_users AS (
	SELECT DISTINCT ON (user_id) user_id, created_at
	FROM purchases AS pc
	WHERE exists (
		SELECT 1 FROM purchases
		WHERE date_trunc('month', created_at) < date_trunc('month', pc.created_at)
		AND user_id = pc.user_id
	)
)
SELECT
	COALESCE(old_users.created_at, new_users.created_at),
	COUNT(DISTINCT new_users.user_id) AS new_user,
	COUNT(DISTINCT old_users.user_id) AS old_user
FROM old_users full outer JOIN new_users
	ON old_users.created_at = new_users.created_at
GROUP BY COALESCE(old_users.created_at, new_users.created_at)
ORDER BY COALESCE(old_users.created_at, new_users.created_at)