
Ramsey Optimal Pricing?
Question :
4. It is 1920 and a railroad has monopolies on both coast to coast passenger travel (Q)
and transcontinental freight shipments (F). Its per period costs are given by:
C(Q,F) = 1000 + 10Q + 10F for Q, F > 0
C(0,F) = 800 + 10F for Q = 0, F > 0
C(Q,0) = 600 + 10Q for Q > 0, F = 0
The market demand curve for passenger travel is given by Q = 110 – pP. The market
demand for freight is much less elastic. For simplicity, assume that it is totally inelastic
at the quantity F = 100 for any price pF < 22. (At any price higher than 22, freight
demand drops to zero.)
a) (10 points) Calculate the (Ramsey optimal) freight and passenger rates that maximize
total surplus in this example subject to the condition that the railroad breaks even.