Answer Happy

Assume that we have an entry situation like that in the Judo
Economics example (attached).
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.
How many consumers should the entrant target, and what is the
optimal price? What are the incumbent’s profits in this
scenario? Use the example as a guide/starting point.
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. 11, >II, (225-100)(100-N)>(P-100)100 125(100-N)>(P-100)100 (12,500-125N)/100>P-100 125-1.25N > P-100 P<225-1.25N Now the entrant will maximize profits [NP-100)], subject to the constraint above. max II, - N(P-100) s.t. P<225-1.25N > max II, = N(225–1.25N-100)=125N-1.25N2 To maximize profits for the entrant take the derivative of the of the above profit function and sets it equal to zero.
ап 125N-1.25N2 =125-2.5N an 1.25 N° 125-2.5N=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. 11,= (225-100)(100-N) = (225-100)(100-50) = 125x50 = $6,250 II, -(P-100)100 = (162.49–100)100 = $6,249 = = The incumbent will accommodate since that produces a slightly higher profit.