As the penetration of wind and solar resources deepens, grid operators must deal with increasing levels of variability and intermittency. While it becomes necessary to increase the reserves requirements to effectively manage such a resource mix, the speed at which the reserves can respond becomes of critical importance. Renewable resource power outputs such as those of wind units can change rapidly and grid operators need to ensure that the market outcomes produce resource dispatches that not only meet the load but are capable also to respond to any changes due to such variability that may occur within the hour of the corresponding market outcomes. We study to what extent the units that are able to provide the reserves can based on their respective up-and-down ramping capabilities appropriately respond to the variability in the loads and renewable resource outputs within the specified response time. We impose these requirements on the total ramping capabilities and introduce appropriate constraints in the market clearing formulation. We investigate the impacts on the resulting market dispatch outcomes and assess the economic costs over longer periods of operation. We illustrate the proposed approach with case studies in which we quantify the impacts of the incorporation of such ramping capability constraints to markets with real-sized power systems and evaluate the economics of the changes in the market outcomes.