GDP versus GNP (Gross Domestic Product and Gross National Product)
GDP is concerned with the region in which income is generated. It is the market value of all the output produced in a nation in one year. GDP focuses on where the output is produced rather than who produced it. GDP measures all domestic production, disregarding the producing entities' nationalities.
In contrast, GNP is a measure of the value of the output produced by the "nationals" of a region. GNP focuses on who owns the production. For example, in the United States, GNP measures the value of output produced by American firms, regardless of where the firms are located.
"In China, a large part of GDP takes place in foreign-owned factories. If we want to mesaure the standard of living in China, wouldn't it be better to use GNP than GDP to allow for this?"
In prinicple you are right. Any profits earned by foreign firms in China ultimately benefit the owners of the foreign firm, rather than people in China. These profits are included in China's GDP, but not in China's GNP. GNP would therefore make a better measure of Mainland China's standard of living.
Increase in exports of a country will lead to increase in both GDP and GNP of the country. Correspondingly, increase in imports will decrease GDP and GNP. However, sometimes increase in exports might only lead to increase in GDP and not GNP. The exact relationship will depend on the nationality status of the company doing the export or import. Eg. if Microsoft Corporation has a 100% owned subsidiary in India, and that office exports US$2 Billion worth of services out of India, then US$2 Billion will be added to the GDP of India. However, it will not be added to the GNP figure since the export is done by a US company and not an Indian company