Double marginalization

Consider an industry with the following characteristics -

$${\displaystyle {\text{Demand:}}\quad \mathrm {Q} =10-p}$$

$${\displaystyle {\text{Marginal Cost:}}\quad \mathrm {MC} =C'(\mathrm {Q} )=2}$$

$${\displaystyle {\text{Total Profit:}}\quad \pi =p\cdot \mathrm {Q} -c\cdot \mathrm {Q} }$$

In a monopolistic situation with a single integrated firm, the profit-maximizing firm would set its price at ${\displaystyle p=6}$, resulting in a quantity of ${\displaystyle \mathrm {Q} =4}$ and a total profit of ${\displaystyle \pi =16}$.

In a non-integrated scenario, the monopolist retailer and the monopolist manufacturer set their price independently, respectively ${\displaystyle p_{r}}$ and ${\displaystyle p_{m}}$.

• The retailer's profit (marginal profit * quantity sold) is given by ${\displaystyle (p_{r}-p_{m})(10-p_{r})}$. Thus, to maximize profits, it will set its price at ${\displaystyle p_{r}=5+0.5p_{m}}$.
• The manufacturer's profit is given by ${\displaystyle (p_{m}-2)(5-0.5p_{m})}$. Thus, it will set its price at ${\displaystyle p_{m}=6}$. The retailer will respond by setting its price at ${\displaystyle p_{r}=8}$.
• This results in a total quantity produced of ${\displaystyle \mathrm {Q} =2}$. The producer's profit is 4, and the retailer's profit is 8.

Not only the total profit is lower than in the integrated scenario, but the price is higher, thus reducing the consumer surplus.

There are numerous mechanisms to prevent or at least limit double marginalization. These include, among others, the following.

• Vertical integration: A merger of the company concerned ensures that pricing is chosen from a corporate point of view. Equivalent to this is a cartel of the companies concerned.
• Franchise fee: The first company sells the second the right to distribute their products through a one-off price, the so-called franchise fee, which is independent of the quantity sold. In addition, a price per piece sold will be charged. If this unit price is chosen to exactly match the marginal costs of production, it is best for the second company to choose the monopoly price for the final product. Profits make the first company here just above the franchise fee.
• Nonlinear pricing: The first company does not charge a quantity-independent price per item, but makes the unit price dependent on the total quantity sold. If the discount scheme is optimally selected, it corresponds exactly to the franchise solution.
• Resale price maintenance: The first company prescribes the second the selling price of the final product.
• Competition: If a manufacturer sells its products through competing dealers, competition among them reduces the second markup.

Note that the above mechanisms only solve the problem of double marginalization. From the point of view of overall welfare, however, the problem of monopoly pricing remains. It should also be noted that some of the solutions presented above, such as mergers or cartels, are damaging in horizontal competition but positive in vertical competition as described here, as they have the advantage of preventing the double markup.

The phenomenon of double markup was already anticipated in the 19th century by the French mathematician Augustin Cournot (1838). A first complete analysis can be found in Joseph Spengler (1950). Massimo Motta (2004) contains an understandable discussion of the topic.

• Cournot, Augustin (1838). Recherches sur les Principes Mathématiques de la Théorie des Richesses, English edition: Research into the Mathematical Principles of the Theory of Wealth, Edited by N. Bacon, New York: MacMillan, 1897
• Spengler, Joseph J. (1950). "Vertical Integration and Antitrust Policy", Journal of Political Economy 58, 347-352
• Motta, Massimo (2004). Competition Policy, Cambridge University Press