Double Marginalization and Supply Chains

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 . 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.

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