1)Referencing the "economies of scope", assume a production process is centered on a Base Product, B, which is a base paint product.The process can be changed to any of three other paint types, with switching cost of s_i: High Gloss Paint, HGP (s_HG); Customized Paint, CP (s_C); and Road Paint, RP (s_R). Marginal costs are c per unit for any of the four paint types. There are additional marginal costs of making the other paint types - These costs are r per unit of "distance" between B and the other products.There are shared costs, F for design, packaging, equipment of the paint types.In the absence of a single firm with shared costs, there would be four specialized paint firms, each with a cost of F for design, packaging, equipment.Initially, assume the unit of distance from B to HGP, CP, and RP is d_HG, d_c, and d_R, respectively.

a)Assuming the goal is to produce 50 units of each of the four products, derive an expression showing under what circumstances multi-product production by a single firm would be less costly than single-product production by multiple firms.

b)Using the expression above in part a., is multi-product production by a single firm less costly if F = 100, s_HG = 20, s_C = 25, s_R = 15, r = 1, d_HG = 0.5, d_C = 1, d_R = 0.5?

c)Explain the intuition behind your conclusion in part b.