Equation (2.1) says that trade between any two countries is proportional to the product of their GDPs. Does this mean that if the GDP of every country in the world doubled, world trade would quadruple?

International economics is a field of study that examines how countries engage with one another through trade, finance, and monetary interactions. It helps to understand how goods and services flow across the international borders and the impact of governmental policies on trade activities. One of the essential frameworks used in international trade analysis is the gravity model of trade, which posits that larger economies tend to trade more with each other while the distance between them acts as a deterrent.

Understanding this model is crucial for comprehending the dynamics of global trade patterns. By examining the variables that the gravity model incorporates, such as GDP, distance, and sometimes other factors like shared borders or trade agreements, economists can predict trade flows and craft policies that facilitate international economic growth. As such, it's a pivotal tool in the domain of international economics, applying physical principles to economic behavior to illustrate and forecast trade activities.

The GDP, or Gross Domestic Product, of a country is one of the primary indicators of its economic strength and a key factor in assessing the potential for trade with other nations. In the gravity model of trade, the relationship between GDP and trade is explicit: the GDP of two trading countries affects the trade volumes between them. To put it simply, the model suggests that wealthier nations, or those with higher GDPs, have a higher capacity for both exports and imports.

This is because economies with larger GDPs typically produce more goods and services, which can then be traded internationally. Furthermore, these economies also have greater demand for imported goods and services. The GDP-trade relationship is foundational, explaining why economically sizable countries are often at the nucleus of international trade networks. Therefore, understanding GDP movements is paramount for businesses, policymakers, and researchers engaged in international trade.

Trade flow analysis involves examining the movement of goods and services across countries, identifying patterns, and understanding the factors that drive these flows. It takes into account numerous variables, with GDP being a principal one as highlighted by the gravity model. The application of the gravity model in trade flow analysis gives economists a formulaic approach to estimating the volume of trade between countries based on their economic size and distance.

However, it's worth stressing that doubling the GDP of countries doesn't merely double the trade flow—according to the model, it would actually quadruple it, due to the multiplicative relationship of the GDPs of trading partners. This fundamental insight serves to underline the non-linear dynamics of trade and the importance of scale in the global economy. Hence, for analysts and policymakers, understanding the intricacies of such relationships is vital for forecasting trade patterns and making informed decisions on trade policies.