Ketchup is a complement (as well as a condiment) for hot dogs. If the price of hot dogs rises, the quantity of hot dogs demanded (fall/rises), which (raises/lowers) the demand for ketchup. Because of the change in the equilibrium quantity of ketchup, the demand for tomatoes by ketchup producers (falls/rises), causing the equilibrium price of tomatoes to (increase/decrease). This means producers of tomato juice face (higher/lower) input prices, and the supply curve for tomato juice (increases/decreases). The resulting (rise/fall) in the price of tomato juice causes people to substitute (away from tomato juice and toward orange juice/away from orange juice and toward tomato juice), so the demand for orange juice (falls/rises).

Fall; lowers; falls; decrease; lower; increases; fall; away from orange juice and toward tomato juice; falls.

Explanation:

Ketchup is a complement and condiment in hot dogs. An increase in the price of hot dogs will cause its quantity demanded to fall. This will cause the demand for ketchup to decrease as well. The demand curve for ketchup will move to the left. This will cause the equilibrium quantity to fall. This will further cause a reduction in the demand for tomatoes by ketchup producers.

A decrease in demand will cause the equilibrium price of tomatoes to fall. A reduction in the price of tomatoes will lower the cost of producing tomato juice. The firms will be able to supply more at the same cost. This will cause the supply to increase. As the supply curve moves to the right, the equilibrium price of tomato juice will fall.

Orange juice is a substitute for tomato juice. The consumers will prefer the cheaper substitute. As a result, demand will move away from orange juice towards tomato juice. This will cause the demand for orange juice to fall.