Q.Suppose the exchange rate between the Rupee and the dollar was Rs. 30 = 1$ in the year 2010. Suppose the prices have doubled in India over 20 years while they have remained fixed in USA. What, according to the purchasing power parity theory, will be the exchange rate between dollar and rupee in the year 2030.

The purchasing power parity (PPP) theory states that the exchange rate between two currencies should adjust to reflect changes in their relative price levels, so that a given basket of goods costs the same in both countries when measured in a common currency.

The real exchange rate is defined as:

where $e$ is the nominal exchange rate (domestic currency per unit of foreign currency), $P^*$ is the foreign price level, and $P$ is the domestic price level. Under PPP, the real exchange rate remains constant over time.

In 2010, the exchange rate was $e_{2010} = 30$ (Rs. per dollar). By 2030, Indian prices have doubled, so $P_{2030} = 2 \times P_{2010}$, while US prices remain unchanged: $P^*_{2030} = P^*_{2010}$.

For PPP to hold, the real exchange rate must be the same in both years:

Substituting the price changes: …

The purchasing power parity (PPP) theory rests on a simple arbitrage idea: if goods cost different amounts in two countries after converting currencies, traders would buy where it's cheap and sell where it's expensive until prices equalize. In the long run, exchange rates should adjust so that a dollar buys the same real quantity of goods whether you spend it in New York or convert it to rupees and spend it in Mumbai.

The key is to distinguish between the nominal exchange rate (how many rupees trade for a dollar) and the real exchange rate (the relative purchasing power of currencies). PPP asserts that the real exchange rate should remain constant — meaning nominal rates must move to offset any difference in inflation between the two countries.

In 2010, the exchange rate is Rs. 30 = 1$. Over the next 20 years, Indian prices double — the price level rises by a factor of 2. US prices remain fixed, so the US price level has a factor of 1 (no change).

Step 1: Identify the inflation factors.

• India: $\frac{P_{\text{India, 2030}}}{P_{\text{India, 2010}}} = 2$
• USA: $\frac{P_{\text{USA, 2030}}}{P_{\text{USA, 2010}}} = 1$

Step 2: Apply the PPP formula.

The new exchange rate must adjust in proportion to the relative inflation:

$E_{2030} = E_{2010} \times \frac{\text{India inflation factor}}{\text{USA inflation factor}} = 30 \times \frac{2}{1} = 60$ …