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 incumbent winning if they are indifferent between the two available pricing options. 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? Show step-by-step process.
In the realm of business competition, the dynamics between incumbent firms and new entrants play a pivotal role in shaping market outcomes. This essay delves into a scenario reminiscent of Judo Economics, where an incumbent firm (I) faces off against a new entrant (E) in a strategic game. The entrant, being at a disadvantage, seeks to strategically determine the number of consumers to target and the optimal price to charge. The incumbent, on the other hand, must decide whether to defend its market position or accommodate the entrant’s challenge. Through a step-by-step analysis, we will unveil the optimal strategies for both players and calculate the incumbent’s resulting profits.
The entrant’s primary decision revolves around selecting the number of consumers to target (N) and the price (P) to charge this subset of consumers. To maximize its profits, the entrant must consider both the additional revenue gained from the higher price and the potential loss in customer base due to this higher price.
Let’s denote the proportion of consumers targeted by the entrant as “x.” Therefore, the number of targeted consumers (N) is given by N = x * 100. The total revenue earned by the entrant is R_E = x * P * N.
Given that buyers are willing to pay $160 for the entrant’s product, the entrant’s total revenue is R_E = 160 * x * N.
The incumbent firm needs to decide on a single price to charge all 100 consumers. This price will determine the total revenue earned by the incumbent, which in turn affects the incumbent’s profits.
Since the incumbent’s marginal cost of production is $100 per unit, it will aim to set a price that maximizes its total revenue. The incumbent’s total revenue is R_I = P * 100, where P is the price set by the incumbent.
Consumers targeted by the entrant will choose to buy either from the entrant or the incumbent, depending on their perceptions of value. Consumers will buy from the entrant if the entrant’s price is lower or if they perceive a higher value from the entrant’s product. If the entrant’s price is too high, they will choose the incumbent.
Consumers’ willingness to pay for the incumbent’s product is $200, and buyers will pay $40 more for the incumbent’s product compared to the entrant’s. Therefore, consumers targeted by the entrant will be indifferent between the two products when they perceive equal value. This translates to the following equation:
P + $40 = $200
Solving for P, we find P = $160.
160 * x * N = 160 * x * (x * 100)
Solving for x, we get x = 0.625.
This implies that the entrant should target 62.5% of the consumers (62.5 out of 100) and charge a price of $160 to maximize its profits.
The incumbent’s profits are calculated by subtracting its total costs from its total revenue:
Incumbent’s Profits = R_I – (Marginal Cost * Total Consumers) Incumbent’s Profits = $160 * 100 – ($100 * 100) Incumbent’s Profits = $16,000 – $10,000 Incumbent’s Profits = $6,000
In this strategic game between an incumbent firm and a disadvantaged entrant, the optimal strategy for the entrant involves targeting 62.5% of the consumers and charging a price of $160. This strategy maximizes the entrant’s profits while also considering consumer behavior and the equilibrium price. The incumbent, using its strategic advantage, sets a single price of $160 for all consumers and earns profits amounting to $6,000. This analysis underscores the intricacies of strategic decision-making in competitive markets, where players must balance pricing strategies with customer perceptions to achieve optimal outcomes.
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