Horizontally Differentiated Store Brands: Production Outsourcing to National Brand Manufacturers

Table 6

Equilibrium outcome under ARM scenario with assortment 𝑆.

𝑝𝑛	3−𝛽^22√3𝛽^2−3√3𝛽−6𝛽^2−3𝛽+2436−12𝛽^2
𝑝𝑠	2√3𝛽−3√33−𝛽^2−6𝛽^2−6𝛽+2736−12𝛽^2
𝑤𝑛	3−𝛽^22√3𝛽^2−3√3𝛽−6𝛽^2+1836−12𝛽^2
𝑤𝑠	2√3𝛽−3√33−𝛽^2−3𝛽^2+918−6𝛽^2
𝑚𝑛	2−𝛽43−𝛽^2
𝑚𝑠	3−2𝛽√33−𝛽^2+3123−𝛽^2
𝑞𝑠	3−2𝛽√33−𝛽^2+3123−𝛽^2
𝑞1	—
𝑞2 (=𝑞3)	2−𝛽43−𝛽^2
𝜋1	3−2𝛽^2√33−𝛽^2+3^21443−𝛽^22
𝜋𝑀	16