We consider elastic resource provisioning in the cloud, focusing on in-memory key-value stores used as caches. Our goal is to dynamically scale resources to the traffic pattern minimizing the overall cost, which includes not only the storage cost, but also the cost due to misses. In fact, a small variation of the cache miss ratio may have a significant impact on user perceived performance in modern web services, which in turn has an impact on the overall revenues for the content provider using such services. We propose and study a dynamic algorithm for TTL caches, which is able to obtain close-to-minimal costs. Since high-throughput caches require low complexity operations, we discuss a practical implementation of such a scheme requiring constant overhead per request independently from the cache size. We evaluate our solution with real-world traces collected from Akamai, and show that the TTL approach is able to track the optimal cache configuration and achieve significant cost savings specially in highly dynamic settings that are likely to require elastic cloud services.