Recall from chapter 8 all the problems about the pfillip industry. In particular, recall that you solved in problem 3 for the market equilibria (in pfillip and kapitose) when the kapitose supply function was given by q = K/200. and the demand for pfillip was given by D(p) = 750- 150p. Now consider what will happen in these two industries if the supply of kapitose is controlled by a monopoly whose marginal costs for producing K units of kapitose are K/200. (You may well need to resort to numerical solutions.)
We did nothing in this chapter in the way of deriving testable propositions from the standard, model. Just so you don't get away without at least a taste of this:
Problem 3
Recall that in section 9.4 we considered a large manufacturing monopoly selling to individual retailing monopolies. There were eight retailers, three of whom face demand of the form p = 12 - 9x, and five of whom face demand of the form p = 12 - 6x. Well, it turns out that there are actually ten retailers - the eight described above and two more who face demand of the form p = 12 - 2x. Costs of production and sales are zero. The retailers are price takers in their dealings with the manufacturer. The manufacturer can set a fixed fee F and a per unit charge P; the retailers take these as given and decide .
(a) whether to participate at all, and
(b) if so, how many units to purchase. The fixed fee and per unit charge must be the same for all the retailers: no discrimination is allowed.
(a) What is the optimal fixed fee to charge if P is set at zero?
(b) What is the optimal fixed fee to charge if P = 1?
(c) What is the optimal fixed fee and per-unit charge?