The problem of simultaneous equation bias is examined in the context of the Cobb-Douglas production function and firm decision functions, assuming competition. Two extreme models are specified, depending on the nature of the disturbances in the relations. In one model, simultaneous equation bias does not occur; in the other model, it does occur. Asymptotic "least squares" estimates (estimates that would be obtained given an infinite sample) are presented for the latter case. In this case, (1) corrections for the bias of least squares estimates are derived for some specifications, (2) it is shown that there exists a fairly pronounced tendency for the least squares estimated elasticity sum to approach one, regardless of the true value of the elasticities.