A can of soda costs \(\$ 1.25\) in the United States and 25 pesos in Mexico. What is the peso-dollar exchange rate (measured in pesos per dollar) if purchasing-power parity holds? If a monetary expansion causes all prices in Mexico to double, so that a soda now costs 50 pesos, what happens to the peso- dollar exchange rate?

The exchange rate is a crucial concept in international economics that represents the value of one currency in terms of another. For instance, if we consider the case of the United States (US) and Mexico, the exchange rate dictates how many Mexican pesos one would need to buy one US dollar.

Using the principle of Purchasing Power Parity (PPP), if a soda costs $1.25 in the US, and the same soda costs 25 pesos in Mexico, we can establish the exchange rate by dividing the price in pesos by the price in dollars, resulting in \(\frac{25 \text{ pesos}}{1.25 \text{ dollars}}\) which simplifies to 20 pesos per dollar. PPP implies that, excluding trade barriers and transaction costs, the exchange rate will adjust so that identical goods cost the same in both countries when prices are expressed in a common currency.However, this theoretical rate can vary in real-world scenarios due to factors such as inflation, interest rates, and government policies. When the price of an item changes in one country and not the other, as in the case of a monetary expansion that doubles the price of a soda in Mexico to 50 pesos, the exchange rate will also adjust. Thus, the new exchange rate would be \(\frac{50 \text{ pesos}}{1.25 \text{ dollars}}\), equaling 40 pesos per dollar, reflecting the depreciation of the peso relative to the dollar.

Monetary expansion refers to the increase in the money supply within an economy, typically initiated by the central bank. When a country undergoes monetary expansion, more local currency is available, and this often leads to inflation, or an increase in the general price level of goods and services. This phenomenon can be observed in the example within our exercise.

When Mexico experiences monetary expansion, and the price of a soda doubles from 25 to 50 pesos, it's evident that more pesos are now required to buy the same good. This is a direct consequence of the increased money supply. While this can stimulate economic activity in the short term, there's a risk that if the supply of money grows too quickly, the purchasing power of the currency may decrease. This devaluation is harmful as it can diminish consumer and international investor confidence, leading to a scenario where the currency is worth less relative to foreign currencies.

Understanding how monetary expansion affects exchange rates is vital. A country with a rapidly expanding money supply may see a rapid depreciation of its currency if the expansion is not matched by growth in the output of goods and services, as illustrated when the exchange rate between the peso and the dollar changed with the doubling of prices in Mexico.

International economics is a field of study that covers economic transactions between countries, including trade, investment, and currency exchange. Purchasing Power Parity is one concept within this field that allows for the comparison of economic productivity and standards of living between countries by adjusting for their different price levels.In our example, the relationship between the US and Mexico demonstrates how changes in domestic economic conditions can have international implications. An increase in prices due to monetary expansion in Mexico not only impacts the local economy but also the exchange rate with the US. If the increase in prices was uniform across all goods and services, it could indicate a devaluation of the Mexican peso relative to the US dollar, assuming no change in the US prices.

Such dynamics underscore the interconnectedness of national economies and the importance of policies that maintain stable exchange rates. High inflation can lead to a loss of competitiveness in international markets and may warrant a response from policymakers to regain balance and ensure stable trade relations. These intricacies of international economics demonstrate why constant monitoring of cross-border economic activities and adjustments of monetary policies are essential for maintaining global economic stability.