It is important to note that the parameters and appear in both the MDCEV probability expression (Equation 6) as well as the standard discrete choice probability expression for the choice of make/model (Equation 8). This creates the jointness in the multiple discrete and single discrete choices. The values are dissimilarity parameters indicating the level of correlation among the vehicle makes/models within vehicle type k. When for all k, the MDCEV-MNL model collapses to an MDCEV model with a fixed satiation parameter for all make/model alternatives within vehicle type k.
(12)
and 
appear in both the MDCEV probability expression (Equation 6) as well as the standard discrete choice probability expression for the choice of make/model (Equation 8). This creates the jointness in the multiple discrete and single discrete choices. The 
for all k, the MDCEV-MNL model collapses to an MDCEV model with 
for all make/model alternatives within vehicle type k.