A company is in the business of selling widgets. Widgets are sold for $20 each. The company has a choice between 2 technologies: technology A that has a fixed cost of $100 and a variable cost of $10 per widget. Technology B has a fixed cost of $ 200 and a variable cost of $5 in manufacturing the widgets. Which technology should the firm choose to maximize profits.

Question

BlackTom AI · Accepted Answer

Set profits equal: profit depends on revenue minus total cost, and the margin per unit equals price minus variable cost. With price P = $20, Technology A has fixed cost FA = $100 and variable cost vA = $10; Technology B has FB = $200 and vB = $5.

1) Relevant concepts
- Total cost = fixed cost + variable cost × quantity (q).
- Profit = Revenue − Total cost = P·q − (F + v·q) = (P − v)·q − F.
- Choose the technology with the higher profit at the anticipated output (demand) q. If profits are equal at some q*, either is fine at q*, but below or above that q* one dominates.

2) Step-by-step reasoning
Compute profit functions:
- ProfitA(q) = 20q − (100 + 10q) = (20 − 10)q − 100 = 10q − 100.
- ProfitB(q) = 20q − (200 + 5q) = (20 − 5)q − 200 = 15q − 200.

3) Intermediate calculations (finding the threshold q where profits are equal)
Set ProfitA = ProfitB:
10q − 100 = 15q − 200
Bring q terms to one side: −100 + 200 = 15q − 10q
100 = 5q
q = 100 / 5 = 20.

4) Why the correct answer is correct
At q = 20 both technologies yield the same profit:
- ProfitA(20) = 10·20 − 100 = 200 − 100 = $100.
- ProfitB(20) = 15·20 − 200 = 300 − 200 = $100.
For q > 20, ProfitB grows faster (slope 15 vs 10), so B yields higher profit. For q < 20, ProfitA yields higher profit because its lower fixed cost makes it cheaper at low volumes.

5) Why other options are incorrect
- "Technology A if demand is 10 units or more..." is wrong because the crossover is at 20 units, not 10.
- "Indifferent between the two technologies" is incorrect except exactly at q = 20; generally they differ.
- "Technology B if demand is 14 units or more..." is incorrect because 14 < 20; B becomes better only at 20 or more units.

6) Conclusion
Therefore the firm should choose Technology B if demand is 20 units or more, and Technology A otherwise — which matches the provided answer.

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