Referencing the "economies of scope" model discussed on slides 47-50 in Lecture 1, 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 si: High Gloss Paint, HGP (sHG); Customized Paint, CP (sC); and Road Paint, RP (sR). 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 dHG, dc, and dR, 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, sHG = 20, sC = 25, sR = 15, r = 1, dHG = 0.5, dC = 1, dR = 0.5?

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