The impact of some invasive species will not decline proportionately with their density when managed, for example a seed contaminant will continue to have a large impact until the density is reduced to a very low level. The level of optimal management effort depends on the relationship between the population density of the invader and the cost of impact caused by the invasive population. In management studies this relationship is often assumed to be linear; however, we have little empirical knowledge of this relationship and it could plausibly take several different non-linear forms. We examine how the optimal management effort level varies based on four functional forms of the cost of impact. The optimal management effort minimizes a total cost which is a sum of the cost of impact and an economic cost of management effort. If we apply an inaccurate cost of impact curve, the invested management effort is smaller or larger than the optimal level based on an accurate cost of impact curve. We calculated the increase of the total costs due to this over- or under-investment in management which indicates the value of information of the cost of impact curve. The value increases with the time scope of management and it also depends on what kind of inaccurate cost of impact curve is applied. Knowing the correct form of the cost of impact curve will enable managers to better prioritize species for control and make more efficient budget allocation decisions.