Under certain conditions, predation acts as a selective pressure that drives prey adaptation. In response, the predator can evolve counter-defenses to increase the likelihood of successful attack. Investment in such traits is often costly, so that there is a trade-off between trait investment and reproductive ability. There is some evidence that cost, at least for the prey, can vary with changes in the environment such as low resource availability. For our investigation, we assume that competition for resources is most likely to occur at high prey densities. The result is that as prey density increases, so does the cost for prey defense. Quantitative trait models are employed to examine the stability and dynamics of the system. We find that variable cost of prey defense tends to stabilize the system when the rate of prey evolution is either very fast or very slow.