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Difficulty: MediumIdentifying Necessary Assumptions

Coffee Importer: Our cooperative should immediately convert all conventional sun-grown coffee farms to shade-grown coffee. Although shade-grown farming yields 30%30\% fewer beans per hectare, shade-grown specialty beans sell for a 50%50\% premium over conventional beans. Therefore, making this complete conversion will undoubtedly increase the cooperative's overall profits.

Which of the following are necessary assumptions upon which the coffee importer's argument depends? Select all that apply.

  1. The total costs associated with cultivating and harvesting shade-grown coffee will not increase enough to completely offset the projected gains in revenue.Answer
  2. B
    The cooperative will not lose any of its current coffee buyers when it transitions exclusively to shade-grown coffee.
  3. C
    Shade-grown coffee farming requires significantly less expenditure on chemical fertilizers than sun-grown farming.
  4. D
    Any agricultural cooperative that shifts to producing a crop with a 50%50\% price premium will experience an increase in its overall profits.
  5. The cooperative will be able to sell its entire newly produced volume of shade-grown coffee at the projected 50%50\% premium rate.Answer

Answer

The correct answers are the options stating that the total costs of shade-grown coffee will not completely offset the revenue gains, and that the cooperative can successfully sell its entire volume at the projected premium rate.
Both correct statements pass the Negation Test. The argument's conclusion is that overall profits will increase. Profit inherently depends on both revenue and costs. If the total costs of shade-grown coffee increased enough to completely offset the revenue gains (the logical negation of the first correct option), profits would not increase, decisively destroying the argument. Furthermore, the mathematical revenue calculation depends on selling the beans at the stated 50%50\% premium. If the cooperative cannot sell its newly produced volume at this premium rate (the logical negation of the second correct option), the expected revenue won't materialize, again destroying the argument.

Step-by-Step Solution

1
Analyze the argument's structure and premises.
Premise: Volume drops by 30%30\% but price increases by 50%50\%. Conclusion: Overall profits will definitely increase.
Identifying the core components is necessary to spot the logical leaps made by the author.
2
Identify the primary logical gap regarding profit.
The argument conflates increased revenue (which mathematically rises by 5%5\%) with increased profit, completely ignoring potential changes in operating costs.
Profit is a function of both revenue and cost. A revenue increase only leads to a profit increase if costs do not rise to eclipse the gains.
3
Identify the secondary logical gap regarding market capacity.
The argument assumes the theoretical 50%50\% premium will hold steady even when the cooperative's entire yield shifts and hits the market.
Market dynamics can shift; increased supply of specialty coffee or lack of sufficient buyer demand might prevent them from selling all beans at the premium price.
4
Apply the Negation Test to the options.
Negating the correct options directly undermines the conclusion (e.g., if costs DO offset revenue gains, profits won't increase). Negating the incorrect options leaves the conclusion intact.
The Negation Test is the definitive method for confirming whether an assumption is strictly necessary.

Key Concept

Identifying Necessary Assumptions via the Negation Test and Profit/Revenue/Cost dynamics.
Estimated Time:1m 30s
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Topics

Identifying Necessary Assumptions

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