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Solutions Judo Competition PDF

In a competitive market scenario, the new entrant (E) targets 50 customers and sets a price of $162.49 to maximize profits, while the incumbent (I) decides to accommodate rather than fight, resulting in a profit of $6,250 compared to $6,249 if they had fought. The analysis shows that the relationship between the number of targeted customers (N) and price (P) is crucial for determining the incumbent's strategy. Ultimately, the incumbent benefits more from accommodating the entrant's presence in the market.

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José Rafael Giraldo Tenorio
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25 views2 pages

Solutions Judo Competition PDF

In a competitive market scenario, the new entrant (E) targets 50 customers and sets a price of $162.49 to maximize profits, while the incumbent (I) decides to accommodate rather than fight, resulting in a profit of $6,250 compared to $6,249 if they had fought. The analysis shows that the relationship between the number of targeted customers (N) and price (P) is crucial for determining the incumbent's strategy. Ultimately, the incumbent benefits more from accommodating the entrant's presence in the market.

Uploaded by

José Rafael Giraldo Tenorio
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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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). Both have constant marginal costs of production of $100. There are 100
identical buyers who each would be willing to pay $225 dollars for the good. 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 chose 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
customers (N) to target and sets a single price (P) to those targeted customers. 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.

What price should the entrant charge and how many customers will they target?

Number of customers targeted by the entrant: 50

Price charged by the entrant: $162.49

We look forward to the end of the game to find the relationship between N and P so that for the incumbent
the profit for accommodating is greater than the profit to fighting.

 A  F
(225 − 100)(100 − N )  (P − 100)100
125(100 − N )  (P − 100)100
(12,500 − 125 N ) /100  P − 100
125 − 1.25 N  P − 100
P  225 − 1.25 N

Now the entrant will maximize profits [ N (P− 100)] , subject to the constraint above.

max  E = N (P − 100) s.t. P  225 − 1.25 N


 max  E = N (225 − 1.25 N − 100) = 125 N− 1.25 N 2

To maximize profits for the entrant take the derivative of the of the above profit function and sets it equal
to zero.

This study source was downloaded by 100000761548063 from CourseHero.com on 05-04-2025 10:00:14 GMT -05:00

https://www.coursehero.com/file/129938455/solutions-judo-competitionpdf/

125 N− 1.25 N 2 = 125 − 2.5N
N

125 − 2.5 N = 0
N = 50

This is gives us the number of customers, N, that maximizes profits. Now we can find the price:

P  225 − 1.25(50) = $162.50


P = $162.49

Let’s confirm that the incumbent is better off accommodating that fighting.

 A = (225 − 100)(100 − N )
= (225 − 100)(100 − 50)
= 125  50
= $6, 250

 F = (P − 100)100
= (162.49 − 100)100
= $6, 249

The incumbent will accommodate since that produces a slightly higher profit.

This study source was downloaded by 100000761548063 from CourseHero.com on 05-04-2025 10:00:14 GMT -05:00

https://www.coursehero.com/file/129938455/solutions-judo-competitionpdf/
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