J Econ (2013) 109:303–313 DOI 10.1007/s00712-012-0294-4 On inferior inputs and marginal returns Paolo Bertoletti · Giorgio Rampa Received: 30 September 2011 / Accepted: 4 June 2012 / Published online: 15 July 2012 © Springer-Verlag 2012 Abstract An input is inferior if and only if an increase in its price raises all marginal productivities. A sufficient condition for input inferiority under quasi-concavity of the production function is then that there are increasing marginal returns with respect to the other input and a non-positive marginal productivity cross derivative. Thus, contrary to widespread opinion, input “competitiveness” is not needed. We discuss these facts and illustrate them by introducing a class of simple production function functional forms. Our results suggest that the existence of inferior inputs is naturally associated with increasing returns, and possibly strengthen the case for inferiority considerably. Keywords Inferior and normal inputs · Marginal productivity · Homotheticity JEL Classification D11 · D21 · D24 1 Introduction An “inferior” input is one the demand for which decreases with output, at given prices. Clearly, this feature is a property of the cost-minimizing “conditional” demand system, x (w, y ), where x is a vector of n inputs whose positive prices are given by w, and y indicates the output level. 1 We will discuss the case for an inferior input by assuming that the production function y = f (x ) is twice differentiable, strictly increasing and 1 Formally, the case of an inferior consumption commodity, whose characteristic depends on the Hicksian “compensated” demand system, h(p, u), where h is a vector of goods whose prices are indicated by p and u is a utility index, is completely analogous: see e.g. Fisher (1990). P. Bertoletti (B ) · G. Rampa Dipartimento di economia politica e metodi quantitativi, Facoltà di Economia, University of Pavia, Via San Felice, 7, 27100 Pavia, Italy e-mail: paolo.bertoletti@unipv.it 123