Industrial Organization Contemporary Theory and Empirical Applications - Chap 17 Solution

Chapter 17

Question 1. Suppose that a car dealer has a local monopoly in selling a luxury sports car. The sports car

manufacturer is considered a monopoly for its class of automobile. The dealer pays m to the manufacturer for each car that it sells and charges each customer P. Market demand faced by the dealer is given by P = 200 - Q where p is measured in thousands of dollars.

a. Suppose the manufacturer's marginal production cost per-car is $50,000 (c = 50). What will be the quantity of cars produced by the manufacturer? What will be the price m charged to the dealer and the market price P charged to consumers?

b. Calculate profits to the dealer and to the manufacturer.

c. Discuss a two-part pricing scheme that the manufacturer could use to remedy the double-

marginalization problem in its relationship to the dealer. Specifically, what will be the

price m charged to the dealer under such an arrangement and how might profits be shared

between dealer and manufacturer?

a.

Start with retailer

Π- max decision

MR = MC

200 – 2Q = m

* Q = 100 – 0.5m

This is the Π- max quantity for retailer and the demand for the manufacture

Mfg’s problem

Get m interm of Q

m = 200 – 2Q

MR = MC

200 – 4Q = 50

* Q = 37.5

This is the Π- max quantity for manufacture

m = 200 – 2Q = 200 – 2*37.5 = 125

P = 200- Q = 200 – 37.5 = 162.5

Q = 100 – 0.5m = 100 – 0.5*125 = 37.5

b.

Profit outcomes

πM = 100*37.5 – 50*37.5 = 1875

πR = 175*25 – 125*25 = 1250

c.

If the retailer and Mfg are merged together

P = 200 – Q

MC = 50

Π- max decision

MR = MC

200 – 2Q = 50

* Q = 75

* P = 125

Π = 125*75 – 50*75 = 5625

If we use 2-part pricing contract, retailer pays $m per unit to the Mfg plus a lumpsum $T

Without contract Mfg earned 1875

* Mfg needs at least this back through T

* T > 1875

Without contract retailer earned 1250

* need to keep at least this amount...