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A Cambridge college possesses an ancient manuscript and has found an Oxford scholar who can translate it. The college wants to employ the scholar but is unsure about their efficiency. The scholar might be:

- A fast translator who takes [tex]n = 2[/tex] hours to translate [tex]n[/tex] pages, or
- A slow translator who takes [tex]n[/tex] hours to translate [tex]n[/tex] pages.

The scholar loses £10 per hour in outside compensation for any translation they do for the college. This means that from a contract requiring [tex]n[/tex] pages translated for a total payment of £[tex]t[/tex], the fast translator's utility is:

A. £[tex]t - 20[/tex]
B. £[tex]t - 10[/tex]
C. £[tex]\frac{t}{2} - 10[/tex]
D. £[tex]\frac{t}{2} - 20[/tex]

Answer :

Final answer:

The fast translator's utility, if they charge £10 per hour in lost outside compensation and takes 2 hours to translate n pages, would be £t - 20. The correct option is A. £t - 20 .

Explanation:

The calculation of the utility for the Oxford scholar who is a fast translator and charges \
£10 per hour in outside compensation is straightforward. If a fast translator takes \
n = 2 hours to translate n pages, then for n pages, the total hours worked would also be 2. Given that the scholar loses \n£10 per hour in outside compensation, the total cost in lost compensation would be £20 (2 hours \
\times \n£10/hour). Therefore, if the total payment for translation is £t, the utility of the fast translator would be £t - 20, corresponding to option A.

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