Data as an economic resource is increasingly relevant in an age of data-hungry parameterized models. The key property that sets classical data apart from traditional economic goods is the possibility of copying it at essentially no cost and without a record. The ability to store and transmit data as quantum states vulnerable to destructive measurement andunable to be generically copied has the potential to change this landscape. In this work, we use communication complexity lower bounds to demonstrate that encoding classical data in quantum states can mimic the behavior of a traditional, consumable economic good. We achieve this by proving that the quantum communication complexity of certain problems scales polynomially with the number of computational tasks performed using the data.This suggests that quantum networks hold the potential to enable novel types of data markets and incentive structures for the creation and distribution of \textit{classical} data.