Critical thresholds represent one of the most important diffusion indicators of epidemic outbreaks. However, we believe that recent studies have overemphasized ways that the power-law connectivity distribution features of social networks affect epidemic dynamics and critical thresholds. As a result, two important factors have been overlooked: resource limitations and transmission costs associated with social interactions and daily contact. Here we present our results from the simultaneous application of mean-field theory and an agent-based network simulation approach for analyzing the effects of resources and costs on epidemic dynamics and critical thresholds. Our main findings are: (a) a significant critical threshold does exist when resources and costs are taken into consideration, and it has a lower bound whenever contagion events occur in scale-free networks; (b) when transmission costs increase or individual resources decrease, critical contagion thresholds in scale-free networks grow linearly and steady density curves shrink linearly; (c) regardless of whether the resources of individuals obey delta, uniform, or normal distributions, they have the same critical thresholds and epidemic dynamics as long as the average value of usable resources remains the same across different scale-free networks; and (d) the spread of epidemics in scale-free networks remains controllable as long as resources are properly restricted and intervention strategy investments are significantly increased.