Double marginalization

In industrial economics, double marginalization occurs two firms at different levels of the supply chain possess market power and independently apply markups, resulting in a final price that is higher than it would be if the firms were integrated. Double marginalization is clearly negative from an economic welfare point of view, as the double markup leads to a final price is higher than the price that would maximize the firms' joint profit, lowering both producer and consumer surpluses. The situation arises from externalities: each firm does not fully take into account the impact of its pricing on the other firm.

Example

Consider an industry with an upstream manufacturer and a downstream retailer. The manufacturer does not sell directly to consumers, but through the retailer. Suppose that the consumer demand for the product is given by the function

Q

=

10

−

p

{\displaystyle \mathrm {Q} =10-p}

where

p

{\displaystyle p}

is the final consumer price, the manufacturer has a constant marginal cost of

c

=

2

{\displaystyle c=2}

, while the retailer does not incur any costs, other than the wholesale price paid to the manufacturer.

In the case that a single monopolist controls both the upstream and downstream operation, the price that would maximize its total profit

Π

=

(

p

−

2

)

(

10

−

p

)

{\displaystyle \Pi =(p-2)(10-p)}

is

p

=

6

{\displaystyle p=6}

, resulting in a quantity of

Q

=

4

{\displaystyle \mathrm {Q} =4}

and a total profit of 16.

In a non-integrated scenario, the monopolist manufacturer sets the wholesale price

w

{\displaystyle w}

, then retailer observes the retail price and sets the final price

p

{\displaystyle p}

. Given the wholesale price

w

{\displaystyle w}

, the retailer's profit is given by

(

p

−

w

)

(

10

−

p

)

{\displaystyle (p-w)(10-p)}

. Thus, its profit-maximizing price is

p

=

5

+

0.5

w

{\displaystyle p=5+0.5w}

, corresponding to the quantity of

Q

=

10

−

(

5

−

0.5

w

)

=

5

−

0.5

w

{\displaystyle Q=10-(5-0.5w)=5-0.5w}

.