NAME_______________________________________________________________
FE461 Practice Problem
Sixth Homework Set
Due May 1st
1. Assume there is a market in which there is 1 Manufacturer and 1 Retailer; assume the
inverse demand for the retailers is given by P = 100 – Q. Further assume the
Manufacturer faces the following total costs: CM(Q) = 10Q and the Retailer faces the
following total costs: CR(Q) = QPW + 10Q, where PW is the “wholesale price” (the price
the manufacturer charges the retailer).
a) If the firm are vertically integrated, what is the PRetail and the firm’s profit?
MR = 100 – 2Q = 20 = MC
Q = 40
P = 60
Profit = (60 – 20)*40 = 1600
b) If the firms are vertically separated, what is the PRetail, PManufacturer, and each firm’s
profit? Show graphically.
MRR = 100 – 2Q = MC = Pw + 10  90 – 2Q = Pw = DM
MRM = 90 – 4Q = 10 = MCM
Q = 20
Pw = 90 – 2(20) = 50
PR = 100 – 20 = 80
Profitw = (50 – 10)*20 = 800
ProfitR = (80 – 50 – 10)*20 = 400
c) If the Manufacturer decided use “resale price maintenance” what minimum retail
price would it require the Retailer to charge if it wanted to achieve the same profits
you found in #a?
P = 60
2. Welfare Implications of Resale Price Maintenance
Gain in CS
P*
Loss in CS
MCR + S*
Gain in  or PS
PM
CM
Dwithout Adv
Qno adv
Qwith adv
Dwith Advertising
Q
a) Identify CS, PS before and after advertising (and note the change in CS and
change in PS) – then state if this increases welfare
P
Gain in CS
P*
Loss in CS
MCR + S*
Gain in  or PS
PM
CM
Dwithout Adv
Dwith Advertising
Qwith adv
Qno adv
Q
Identify CS, PS before and after advertising (and note the change in CS and change in
PS) – then state if this increases welfare