This paper generalises Kumbhakar's (1996a) single product shadow profit function to a multiproduct one, which in contrast to Berger, Hancock, and Humphrey (1993) is consistent with a firm's profit maximising behaviour. By estimating a parametric translog profit function, which does not require special assumptions about the error distribution, and using panel data from Taiwan's banking industry, the following conclusions can be drawn: (i) Parameter estimates from the translog functional form are more robust than those from the Fuss (non-logarithmic) form. (ii) More than half of all potential variable profits are found to be lost due to inefficiencies. (iii) Greater reduction in profit results from deficient output revenues than from a suboptimal input mix. (iv) The model finds technical progress during the sample period. (v) A type of ‘weakly’ optimal scope economies is detected, which suggests that the joint production of the two products can increase profits for some banks while not hurting the profits of others.