High School

Assume that we have an entry situation like that in the Judo Economics example. There is an incumbent firm (I) and a new entrant (E). Now we will look at the outcome if the entrant is at a disadvantage.

- The incumbent has constant marginal costs of production of $100, while marginal costs for the entrant are $120 per unit.
- There are 100 identical buyers who are willing to pay $200 for the incumbent’s product, but only $160 to buy from the entrant. Overall, buyers will pay $40 more for the incumbent’s product.
- Any consumer can buy from the incumbent, but only those targeted by the entrant can buy from the entrant. Those consumers targeted by the entrant can choose to buy from the incumbent or the entrant and will choose the lowest price (with the incumbent winning ties).

At the first move of the game, the entrant decides how many consumers (N) to target and sets a single price (P) to those targeted consumers. The incumbent then sets a single price for all 100 consumers, deciding to defend the market or accommodate the new entrant. Consumers then purchase the good.

1. How many consumers should the entrant target, and what is the optimal price?
2. What are the incumbent’s profits in this scenario?

Answer :

The entrant in the Judo Economics example targets a certain number of consumers who can choose to buy from the entrant or the incumbent at the lowest price (with the incumbent winning ties). To determine the optimal price and the number of consumers the entrant should target, let's go through the different scenarios that could play out.

Scenario 1: Entrant targets 1 consumer. The price set by the entrant is $160. The incumbent will set a price of $200 for all 100 consumers to defend the market. The entrant's revenue would be $160 and the incumbent's revenue would be $20,000 ($200 x 100 consumers).

Scenario 2: Entrant targets 2 consumers. The price set by the entrant is $160. The incumbent will set a price of $200 for all 100 consumers to defend the market. The entrant's revenue would be $320 ($160 x 2) and the incumbent's revenue would be $19,840 ($200 x 99 + $160 x 1).

Scenario 3: Entrant targets 3 consumers. The price set by the entrant is $160. The incumbent will set a price of $200 for all 100 consumers to defend the market. The entrant's revenue would be $480 ($160 x 3) and the incumbent's revenue would be $19,680 ($200 x 98 + $160 x 2). And so on...

We can conclude that the entrant should target all 100 consumers, as they will lose money by targeting fewer consumers. The optimal price would be $160. If the entrant sets a higher price, the incumbent will defend the market and the entrant will only receive revenue from the consumers they targeted (which is less than 100). If the entrant sets a lower price, the incumbent will accommodate the entrant and set the same price, resulting in the entrant only receiving revenue from the consumers they targeted. The incumbent's profits in this scenario would be $16,000 ($200 - $100 marginal cost) x 100 consumers.

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