Double Marginalization and Supply Chains

demand intercept

demand slope

marginal cost

wholesale price

	U D (demand upstream)
	U MR (marginal revenue)
	D (demand)

	D (demand)
	U MR (marginal revenue)

This Demonstration illustrates the issue of double marginalization in a vertical market with an upstream monopolist firm and a downstream monopolist firm facing inverse demand function

p=a-bQ

. The upstream firm has constant marginal costs

. The lower graph shows the demand (blue) and marginal revenue (red) curves of the downstream firm, while the upper graph shows the induced demand (black) and marginal revenue (red) curves of the upstream firm. The coefficients of the market demand are

(demand intercept) and

(demand slope). The marginal cost is

and the wholesale price is

. For a given wholesale price

, the lower graph can be used to understand how the downstream firm chooses how much to produce (and hence demand from the upstream firm) and which price to charge. The graphs show the monopoly price

and quantity

, as well as the upstream quantity

and downstream price

A frequent scenario in 2020 had

and

, indicating a downstream price greater than marginal price with an upstream quantity less than the marginal quantity, meaning that there are negative externalities where prices are higher than normal while a smaller number of units are consumed.

References

[1] Wikipedia. "Double Marginalization." (Oct 5, 2021) en.wikipedia.org/wiki/Double_marginalization.

External Links

Dynamic Profit Maximization for a Monopolist

Cost and Revenue for Monopoly and Monopolistic Competition

Permanent Citation

Flavio Toxvaerd

"Double Marginalization and Supply Chains"
http://demonstrations.wolfram.com/DoubleMarginalizationAndSupplyChains/
Wolfram Demonstrations Project
Published: October 13, 2021