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Aa

Double Marginalization: No Integration

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Payoff Computation

Example

Example 1

The inverse market demand for bags of coffee is given by P = 12 - Q. The marginal cost to the wholesaler for coffee production is MC=$4.

Wholesaler sets a price of r=$7. The retailer then chooses Q. Given a market demand curve of P = 12 - Q if the retailer chooses Q=4 that means the market price is P=$8.

So ultimately profits are:

Retailer: Qx($P - $r) = 4x($8 - $7) = $4
Wholesaler: Qx($r - $MC) = 4x($7-$4) = $12


Example 2

We use the same inverse demand curve P = 12 - Q and marginal cost MC=$4.

Suppose the wholesaler sets a price of r=$5. Then, the retailer chooses Q=6 units at r=$5. Given a market demand curve of P = 12 - Q if the retailer chooses Q=6 that means the market price is P=$6.

So ultimately profits are:

Retailer: Qx($P - $r) = 6x($6 - $5) = $6
Wholesaler: Qx($r - $MC) = 6x($5-$4) = $6

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