Data Envelopment Analysis under Variable Returns to Scale

Abstract

In this chapter we relax the assumption of constant returns to scale (CRS) which we have maintained up to this point. It is recalled (see Chapter 3) that under CRS we assumed that if (x, y) is a feasible input-output correspondence then so is (αx, αy), where α is a non-zero positive constant. The implication of the CRS assumption can be seen readily if we consider a single-input single-output situation. If the input is x and the output is y, x being non-zero, the CRS assumption means that average productivity, denoted by the ratio y/x is not dependent on scale of production. For example we may be assessing a set of tax offices using their operating expenditure as the sole input and the number of accounts each tax office administers as the sole output. Then if we assume that CRS hold a Pareto-efficient tax office A which administers half the number of accounts another Pareto-efficient tax office B administers should incur half the operating expenditure of tax office B. (This assumes both tax offices face the same prices for their inputs).