# Double Marginalization Loop

This Market Simulation uses a loop to illustrate the problem of Double Marginalization.

From Wikipedia:

A common example of such an externality is double marginalization. Double marginalization occurs when both the upstream and downstream firms have monopoly power and each firm reduces output from the competitive level to the monopoly level, creating two deadweight losses. After a merger, the vertically integrated firm can collect one deadweight loss by setting the downstream firm’s output to the competitive level. This increases profits and consumer surplus. A merger that creates a vertically integrated firm can be profitable.

When the Wholesaler sets a Profit Maximizing Price, it must first know the Retailer’s Demand for the Product. But the Retailer can only start selling the Product when it knows the Wholesaler’s Price. And the Retailer will also want to set their own Profit Maximizing Price based upon it’s Cost – that is, the Price it must pay to the Wholesaler.

Hence an iterative loop is required to find an equilibrium between the Wholesaler’s Price and the Retailer’s Price.

The loop starts by setting an initial test Margin for the Retailer of \$20. As End-Customers need to pay the Retailer this \$20, their Willingness To Pay (WTP) for the Product, as seen by the Wholesaler, will be reduced by \$20. The Wholesaler can then use the Manufacturing Cost, along with this “Retailer WTP Matrix”, to set their Profit Maximizing Price.

The Wholesaler’s Profit Maximizing Price becomes the Retailer’s Cost (we are assuming that the Retailer doesn’t have any other Costs). The Retailer can use this Cost, along with the true “Customer WTP Matrix” to set their own Profit Maximizing Price.

Initially the Wholesaler’s Price and the Retailer’s Price will not be in balance, and the Quantity the Retailer expects to sell will not equal the Quantity the Wholesaler expects to sell. But the loop will pass back the Retailer’s Profit Maximizing Price to the Wholesaler until the Demand seen by the Wholesaler equals the Demand seen by the Retailer. When this happens the “Price Equilibrium” will have been found.

To illustrate the problem of “Double Marginalization”, the total Profitability of both the Wholesaler and the Retailer is added together. This is then compared to the Profit that would be generated if the Wholesaler and the Retailer were to merge into a single company and set a single Profit Maximizing Price.

This Market Simulation illustrates that total Profitability could be more that doubled if the Wholesaler and the Retailer were to merge and the “Double Marginalization” problem were eliminated.

This Case Study provides a high-level overview of the workflow without detailed explanation. It assumes you are already somewhat familiar with KNIME and Market Simulation. If not, start by reviewing the Building Blocks and Community Nodes.

# #1 Wholesaler Price

The Wholesaler calculates the Demand they see from the Retailer by calculating a “Retailer WTP Matrix”:

Retailer WTP = Customer WTP – Retailer Margin

Using this “Retailer WTP Matrix” along with their Manufacturing Cost, the Wholesaler can calculate their Profit Maximizing Price.

# #2 Retailer Price

The Retailer sets their Cost equal to the Price charged by the Wholesaler:

Retailer Cost = Wholesaler Price

Using the true “Customer WTP Matrix” along with their Cost, the Retailer can calculate their own Profit Maximizing Price.

# #3 Price Equilibrium

Each loop iteration, the Retailer’s Profit Maximizing Price is passed back for the Wholesaler to calculate the Demand that they see for the Product. This then allows both the Wholesaler and the Retailer to each set their own Profit Maximizing Prices.

The loop continues until a Steady State Price Equilibrium is found. At this Price, the expected Quantity sold by the Wholesaler is equal to the expected Quantity sold by the Retailer. Neither Wholesaler nor Retailer want to change Price.

The equilibrium is met when the Wholesaler sets their Price = \$80 (this is the Retailer’s Cost) and the Retailer sets their Price = \$109.40. The Wholesaler’s per unit Profit = \$80 – \$50 = \$30, while the Retailer’s per unit Profit = \$109.40 – \$80 = \$29.40.

At this point, the combined total Profitability generated by both the Wholesaler and the Retailer is \$115,680. This will next be compared to the potential Profitability that they could generate if the Wholesaler and Retailer were to merge. See below.

# #4 Merged Company

If the Wholesaler and the Retailer were to merge then they would set a single Profit Maximizing Price. This would eliminate the “Double Marginalization” problem.

The Profit Maximizing Price the merged company would charge End-Customers would be \$95. This is considerably cheaper than the \$109.40 Price the End-Customers paid the supply chain Retailer above.

The Total Profitability generated by merged company is predicted to be \$256,860. That is about \$30,000 more than the \$223,527 combined Profitability generated above by the Wholesaler-Retailer supply chain.