There is a coin score indicated in the opening player notes for each episode that needs to be reached by the end of the scenario. You always start rated as an Animal Handler and work your way through ratings such as Promising Business Man, Captain of Industry, Notable Tycoon and the highest accolade, Merchant Prince. You can pause and see your rating as the episode progresses. Your final episode score and Merchant Rating will appear at the end of the scenario. You may also rate in the high scores.
Regular game play across all episodes indicates that any regional map with a merchant family starting in it has an equal chance of achieving Merchant Prince. That said; it is obvious that some starting locations are more central and have resources that facilitate an easier start. Planning a strategy and sticking to it are the key.