Cotton output in India, the world’s third-largest exporter of the fiber, may reach a record this year as farmers increase the use of genetically altered seeds, likely posing competition for the U.S., the biggest supplier. [...] Higher exports may help India garner a bigger share of the Chinese market as the U.S., the Asian nation’s main supplier, is forecast to harvest a smaller crop after farmers switched their fields to more-profitable grains such as corn. Prices of cotton traded in New York have risen 12 percent in the past year.