2 4.1 Linear Prices versus Vertical Restraints

2.1 4.1.1 Basic Framework

A single supplier, called the monopolist or the manufacturer, produces an intermediate good at a constant unit cost \(c\).
He is the only producer of this good.
He sells it to a single downstream firm, called the retailer.
The retailer resells the product.
\(p_{w}\) denotes the wholesale price and \(p\) the consumer price.
\(q\) denotes the quantity bought by the retailer; it also denotes the final consumption if the retailer does not throw away any of the intermediate good.
The consumers’ demand function is denoted \(q = D(p)\).

A linear price is a contract specifying only a payment, \(T(q) = p_{w}q\) from the retailer to the manufacturer.
A franchise fee, \(A\), gives rise to the simplest example of a nonlinear price. The retailer then pays \(T(q) = A + p_{w}q\)
Resale-price maintenance (RPM) is a provision in the contract dectating the choice of the final price, \(p\), to the retailer. Variants of this restraint are a price ceiling (\(p \leq \overline{p}\)) and a price floor (\(p \geq \underline{p}\)).
Quantity fixing specifies the amount, \(q\) to be bought by the retailer. Variants of this restraint are quantity forcing (\(q \geq \underline{q}\)) and quantity rationing (\(q \leq \overline{q}\))

Introduce the possibility of competition among several retailers on the same market.
New type of restraint: exclusive territories

Now assume that the downstream unit uses several inputs to produce the final good.
The downstream unit can be a producer, or can be a retailer who sells complementary products to the customer.
A new restraint: tie in, in which one of the input suppliers forces the downstream unit to purchase the other inputs from him.
The manufacturer can also impose a payment, called a royalty, proportional to the number of units sold downstream.

The retailer may sell goods that are close substitutes for the good supplied by the manufacturer.
The manufacturer may then impose exclusive dealing on the retailer, which prevents him form selling goods that compete directly with the manufacturer’s product.