The random-coefficients logit model generates a flexible pattern of substitutions between pro-
ducts. Consumers have different price disutilities that will be averaged to a mean price sensitivity
and cross-price elasticities are not constrained by the individual level logit assumption. Once the
individual demand parameters have been estimated, the aggregate market shares and price elas-
ticities of the demand can be recomputed by simulation in order to be used for the estimation of
price-cost margins using the different supply models presented in section 3. Expressions for own
and cross-price elasticities are given in Appendix 7.4.
4.2 Identification and Tests Across Supply Models
Let’s consider in this section the problem of identification of retail or wholesale margins and
test across the different supply models with a known demand function and market shares and
observed retail prices for a set of T markets. Remark that from the conditions obtained before for
the price equilibrium in case of two part tariffs contracts, the identification of fixed fees is never
possible and thus only "variable" margins (as opposed to margins obtained from fixed fees) and
marginal costs can possibly be identified. Profits of retailers and manufacturers are not identified
up to a constant exogenous to the horizontal and vertical competition modelled here.
The different supply models of section 3 give different restrictions on the supply side and in
particular on wholesale and retail price-cost margin vectors denoted Γ and 7 respectively. Depen-
ding on the model, the implied restrictions do not lead to the same degree of identification or
underidentification of price-cost margins.
4.2.1 Linear pricing models :
In the case of linear pricing between manufacturers and retailers, both manufacturer level and
retailer level price-cost margins are straightforwardly identified with (2) and (4).
4.2.2 Two-Part Tariffs contracts without RPM
In the case of two part tariffs contracts without RPM between manufacturers and retailers, we
have seen in section 3.2.2 that both the manufacturer level and retailer level price-cost margins are
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