Abstract
This note provides a formula to compute the value of the mean utilities as a function of market shares in Bresnahan et al.'s (Citation1997) production differentiation models (PD-GEV) (1997). Such a formula avoids the time consuming contraction mapping procedure suggested by Berry et al. (Citation1995).
Acknowledgement
I am grateful to Professor Steinar Str⊘m for very helpful comments and discussions.
Notes
1 See for instance Goldberg and Verboven (Citation2001), Peters (Citation2003), Tovar (Citation2004).
2 This procedure is of course fundamental when closed forms do not exist.
3 The correlation coefficients are the complement of logsum coefficients.
4 The inequality on cross elasticity of substitution when dimension B and D competes simultaneously and symmetrically according to PD-GEV model is εBD, BD ≥ (εNBD, BD, εBND, BD) ≥ εNBND, BD with εNBD, BD ≥ or ≤εBND, BD
5 See for instance Moul (Citation2003). In this case mean utilities could be expressed as: