Suppose a computer costs $500 in the United States. With the price of the computer given in local currency, the Indian rupee is _____ by ______%.

Question

BlackTom AI · Accepted Answer

PPP-implied exchange rate = 18,000 ÷ 500 = 36 rupees per dollar.

1) Relevant knowledge points and concepts
- Purchasing Power Parity (PPP) / law of one price: identical goods should cost the same across countries when prices are converted at the correct exchange rate. 
- If the market exchange rate differs from the PPP-implied rate, the currency is misaligned: market_rate > PPP_rate implies the domestic currency is undervalued; market_rate < PPP_rate implies it is overvalued.
- Percent undervaluation is commonly measured as (1 − PPP_rate / market_rate) × 100% (equivalently (market_implied_price − local_price) / market_implied_price).

2) Step-by-step reasoning
- Compute the PPP-implied rupee/dollar rate from local and US prices.
- Compare the PPP rate to the observed market exchange rate (given in the table).
- Convert the US price into rupees at the market rate as a cross-check.
- Compute the percent difference using the standard PPP undervaluation formula.

3) Calculations (intermediate steps)
- PPP rate = local price / US price = 18,000 rupees ÷ $500 = 36 rupees per $1.
- Market exchange rate = 45 rupees per $1 (given).
- Since 45 > 36, the rupee is undervalued.
- Percent undervaluation = (1 − PPP/market) × 100% = (1 − 36/45) × 100% = (1 − 0.8) × 100% = 0.2 × 100% = 20%.
- Cross-check: $500 × 45 = 22,500 rupees implied by market rate; difference = 22,500 − 18,000 = 4,500; 4,500 ÷ 22,500 = 0.20 = 20%.

4) Why the correct answer is correct
- The PPP-implied rate (36) is lower than the market rate (45), meaning each dollar buys more rupees than PPP suggests — the rupee is undervalued. The computed percentage difference using the standard PPP formula is exactly 20%.

5) Why the other options are incorrect
- b (undervalued; 12.5%): wrong percentage (calculation does not match the PPP comparison).
- c (overvalued; 9.1%): wrong direction (rupee is not overvalued) and wrong magnitude.
- d (overvalued; 20%): wrong direction (sign) despite matching magnitude.

6) Conclusion
- The Indian rupee is undervalued by 20%, confirming answer a. undervalued; 20.

Suppose a computer costs $500 in the United States. With the price of the computer given in local currency, the Indian rupee is _ by __%.单项选择题

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Suppose a computer costs $500 in the United States. With the price of the computer given in local currency, the Indian rupee is _____ by ______%.单项选择题