We introduce a new model of user-based dynamic pricing in which decisions occur in real time and are strongly influenced by the budget constraints of users. This model captures the fundamental operation of many electronic markets that are used for allocating resources. In particular, we focus on those used in data centers and cloud computing where pricing is often an internal mechanism used to efficiently allocate virtual machines. We study the allocative properties and dynamic stability of this pricing model under a standard framework of cloud computing systems which leads to highly degenerate systems of prices. We show that as the size of the system grows the user-based budget-constrained dynamic pricing mechanism converges to the standard Walrasian prices. However, for finite systems, the prices can be non-degenerate and the allocations unfair, with large groups of users receiving allocations significantly below their fair share. In addition, we show that improper choice of price update parameters can lead to significant instabilities in prices, which could be problematic in real cloud computing systems, by inducing system instabilities and allowing manipulations by users. We construct scaling rules for parameters that reduce these instabilities.