There are a number of variables. Firstly, does an increase in price of hot dogs necessarily decrease sales of hot dogs. New products and formulations may increase the per unit price of the hot dogs. However, new demand may be created in the marketplace for these higher priced hot dogs that didn't exist before. In this case, the average price increase would accompany an increase in sales.
Let's say, for argument sake, that a price increase results in a decrease in sales of hot dogs. 7 billion hot dogs were sold in the USA from retail outlets in 2011(not including WalMart). Even with this large number of hot dogs, hot dogs are only a fraction of the demand for ketchup. Ketchup is only a fraction of the demand for processed tomato products. Tomato products are only a fraction of the demand for tomatoes.
A large increase in price of hot dogs may decrease demand for ketchup by a small percentage.
This small percentage in decreased demand for ketchup would in turn decrease demand for processed tomato products by a miniscule amount.
This miniscule decrease in demand for processed tomato products would in turn cause an infinitesimally small decrease in demand for tomatoes.