"Economics" is a subject, body of knowledge, that deals with the production, consumption and distribution of resources/wealth. (Although it has an "s" at the end of the word, it is a singular noun.) "Economy" refers to how a country or region produces, consumes and distributes wealth/resources. A student can specifically examine the economy of a country or region, yet the broader subject matter that students study at a university is called "economics." Students take classes in the "Economics Department" and are typically described as "economics students" because of the body of knowledge they study. A single person is described as an economics student or a student of economics. "Economic" is an adjective. While one can refer to "economic policy, questions, matters, predictions," the adjective is not used for people. A person is not "economic." Instead, a person can be described as "economical" which means that the individual is careful about how he/she personally uses resources and/or spends money. Thus, your teacher was wrong because one can't describe someone as "a student of..." (plus an adjective). It is incorrect to say, for example, "a student of legal," "a student of religious." Instead, the phrase, "a student of..." requires a noun to follow it: e.g., a student of religion, a student of law, a student of foreign languages, a student of economics. The subject matter noun can also be used descriptively: a religion student, law student, foreign languages student. Hope this helps clarify things for you.