If a Big Mac costs £3.50 in the UK and US$4.99 in the US. According to the Law of One Price, what should the GBP/USD exchange rate be, per an indirect quotation, expressing the value of £ in terms of US$?

Question

BlackTom AI · Accepted Answer

Law of One Price requires the same good to cost the same when expressed in a common currency. Therefore £3.50 converted into US dollars must equal US$4.99. Set the unknown exchange rate as US$/£ (US dollars per one British pound).

1) Relevant concepts
- Law of One Price: price_GBP × (US$/£) = price_USD.
- Indirect quotation here means expressing one pound in terms of US dollars (US$ per £).

2) Step-by-step reasoning and calculations
- Start with: £3.50 × (US$/£) = US$4.99.
- Solve for (US$/£): (US$/£) = US$4.99 ÷ £3.50.
- Compute the division: 4.99 ÷ 3.50 = 1.4257142857...
- Round to four decimal places: 1.4257.

Thus the exchange rate that equalizes the Big Mac prices is £1 = US$1.4257.

3) Intermediate steps shown
- 4.99 / 3.50 = (4.99 ÷ 3.50) = 1.4257142857...
- Rounded = 1.4257 (to 4 decimal places as in the answer option).

4) Why this is correct
- With £1 = US$1.4257, the UK price £3.50 converts to 3.50 × 1.4257 ≈ US$4.99, matching the US price and satisfying the Law of One Price.

5) Why the other options are incorrect
- US$1 = £0.7014 is the reciprocal (1 ÷ 1.4257 ≈ 0.7014). It expresses USD in GBP, not GBP in USD; it’s a different quotation direction.
- £1 = US$0.7014 is numerically wrong (it would mean the pound is worth less than one US dollar), not matching 4.99/3.50.
- US$1 = £1.4257 swaps the currencies and is the inverse of the correct rate.

Conclusion: The correct exchange rate (US$ per £) is £1 = US$1.4257, which matches the provided answer.

If a Big Mac costs £3.50 in the UK and US$4.99 in the US. According to the Law of One Price, what should the GBP/USD exchange rate be, per an indirect quotation, expressing the value of £ in terms of US$? Single choice

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