Horizontally Differentiated Store Brands: Production Outsourcing to National Brand Manufacturers

Table 7

Equilibrium outcome under AMR scenario with assortment 𝐹.

	For 𝛽<1/7	For 𝛽≥1/7
𝑝𝑛	58	14𝛽^2−3𝛽+44(5𝛽^2+1)
𝑝𝑠	𝛽+48	−4𝛽^3+18𝛽^2−2𝛽+34(5𝛽^2+1)
𝑤𝑛	12	1+3𝛽^2−𝛽5𝛽^2+1
𝑤𝑠	𝛽2	−2𝛽^3+9𝛽^2−2𝛽+125𝛽^2+1
𝑚𝑛	12	𝛽2𝛽+145𝛽^2+1
𝑚𝑠	4−3𝛽8	2𝛽+145𝛽^2+1
𝑞𝑠	12(𝛽+1)	1−2𝛽^3−𝛽^2+2𝛽41−𝛽𝛽+15𝛽^2+1
𝑞1	1−3𝛽8(𝛽+1)	0
𝑞2 (=𝑞3)	18	𝛽2𝛽+145𝛽^2+1
𝜋1	17−15𝛽64(𝛽+1)	2𝛽+1^2165𝛽^2+1^2
𝜋𝑀	316	(2𝛽+1)^28(5𝛽^2+1)