We discuss the regulation of a multiproduct monopolist when the firm has pr
ivate information about cost or demand conditions. The regulator offers the
firm a set of prices from which to choose. When there is private informati
on only about costs, the firm should always have a degree of discretion ove
r its pricing policy. When uncertainty concerns demand, whether discretion
is desirable depends on how demand elasticities vary with the scale of dema
nds. If a positive demand shock is associated with a reduction in the marke
t elasticity, discretion is good for overall welfare; otherwise it is not.