This paper shows that optimal consumption is weakly increasing in the borrowing ceiling, while savings and the welfare losses caused by borrowing constraints are weakly decreasing. More important, the strict inequalities may hold even at high saving levels at which the constraints are not expected to bind any time soon. In essence, the paper shows that one can make a smooth transition between the two extremes of free and no borrowing. Further, quantitative versions of the theory demonstrate that the distortive impact of borrowing constraints depends upon all the parameters of the economic environment in a complicated way. Copyright 1994 by Ohio State University Press.