This paper theoretically analyzes how income assistance/welfare benefits affect the aggregate disposable income of the benefit recipients when the government cannot observe the recipients' earning capability. If the recipients' earning capabilities are uniformly distributed, the model shows that the means-tested linear income assistance benefits do not increase the aggregate disposable income of the benefit recipients at all, regardless of the benefit size. Under a more realistic distribution of earning capabilities, the aggregate disposable income can decrease. The expenditure minimizing benefit reduction rate is strictly between zero and one.