Question

A monopoly manufacturer sells its product through a network of n retailers, to each of whom it has assigned an exclusive territory. Within their territory, the retailers are themselves monopolies. Sales of each retailer are q = (a - bp)s1/2, where p is the retail price, s is the level of service provided by the retailers, and a and b are parameters that are identical for all retailers. The retailers choose both p and s so as to maximize their profits. Each unit of services provided costs them $1 and the manufacturer charges them a wholesale price of m for each unit of the product, but otherwise they have no costs. What level of p and s do they choose? What level of m does the manufacturer choose if its unit costs of production are constant at c?

Answer 1

Answer:

1st part: Here MC = m + $1, since each unit of service requires these two costs. Given, q = (a - bp)s x (1/2) By rearranging, p = (as - 2q) /bs The price (p) must be greater than MC by each retailer to stay in the business. Therefore, the level of p is as below: {(as - 2q) /bs} > (m +1) 2nd part: p = (as - 2q) /bs TR = p X 5 = (as - 2q) /b MR = Derivative of TR with respect of s MR = a/b MC = m +1 The profit maximizing level of s is as below: MC = MR M +1 = a/b