(Please refer to the "It Ain't Just About Peanuts" handout.)

Assume that Joe had this conversation with his accountant before deciding to enter the peanut business. What should the minimum selling price be for him to buy the fancy peanut rack and start selling peanuts? Is your answer different from the answer in Q3? Why or why not?

Question

(Please refer to the "It Ain't Just About Peanuts" handout.)

Assume that Joe had this conversation with his accountant before deciding to enter the peanut business. What should the minimum selling price be for him to buy the fancy peanut rack and start selling peanuts? Is your answer different from the answer in Q3? Why or why not?

BlackTom AI · Accepted Answer

Since the rack is an avoidable up-front fixed cost, the minimum price must cover the per-unit variable cost plus the per-unit share of the rack cost.

1) Relevant knowledge points and concepts
- Distinguish variable costs (cost per unit that change with output) from fixed costs (one-time or time-period costs that do not change with output).
- When a cost is avoidable (not sunk) and you decide to enter a business, you must cover total costs in the relevant decision horizon. The minimum price to justify buying the rack equals average total cost (ATC) = variable cost per unit (VC) + fixed cost per unit (F/Q), where Q is expected sales quantity.
- In Q3 the rack cost was treated as irrelevant (sunk) so the break-even price there equaled the variable cost per unit (VC).

2) Step-by-step reasoning
- Let VC = variable cost per peanut (or per unit), F = cost of the fancy peanut rack, and Q = number of peanuts (units) Joe expects to sell.
- If the rack is not purchased (or rack cost is sunk/irrelevant), the minimum price p3 = VC (to cover incremental cost).
- If Joe must buy the rack, the per-unit cost rises by F/Q. The new minimum price p = VC + F/Q.

3) Intermediate steps (algebra)
- ATC = (Total variable cost + Fixed rack cost) / Q = (VC*Q + F) / Q = VC + F/Q.
- Therefore p >= ATC implies p >= VC + F/Q.

4) Why the correct answer is correct
- Because F/Q is a positive amount whenever F>0 and Q is finite, p is slightly greater than VC. Thus the minimum selling price is slightly greater than the answer in Q3, since Q3 ignored the rack cost.

5) Why the other choices are incorrect
- “Same as Q3 because cost of rack is relevant” is contradictory (if relevant it changes the price).
- “Slightly less than Q3 because rack cost is irrelevant” is wrong: making a relevant cost would increase, not decrease, required price.
- “Same as Q3 because rack cost is irrelevant” would only be correct if the rack cost were sunk; here it is avoidable so it is relevant.

6) Conclusion
- The minimum selling price is slightly greater than the answer in Q3, because now the cost of the rack is relevant. This matches the provided answer.

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