Most people assume that an economical writing style is one that is always brief, but a better way to think of it is as a style which is never unnecessarily long-winded. To a student, much academic writing can seem rambling and indirect, but this is largely because of unfamiliarity with the rhetorical situation and academic field which this writing is designed to address. Writing which appears short and pithy, such as Sun editorials or the bullet-point lists of Powerpoint presentations, can often in fact be very vague, because it makes little attempt to convey the writer's mental picture of the topic to the audience, and so really constitutes a writer-orientated mode of writing (this point is made at length in Edward Tufte's entertaining essay, The Cognitive Style of Powerpoint, Cheshire CT: Graphics Press 2003).
To achieve true economy of style, your essay needs to be designed around creative reading, ie organized in such a way that it anticipates and exploits the reader's inferences. One way to do this is to ask whether your reader really needs the level of detail your essay supplies, or whether they could simply fill in the details for themselves - lengthy summaries of plot, for example, are rarely necessary, because your reader can usually be assumed to have read the novel.
Another way of avoiding unnecessary explanations of material that your reader can be presumed to know is to consider whether areas of argument could be simply signalled by the use of key-words referring to key issues in the academic field to which the question relates. Since your reader is familiar with the field, key-words can act as a kind of shorthand to indicate the context, or rhetorical situation, of your argument - but you need to be sure that you're not failing to meet the tutor's expectations by referring to these subjects in such an abbreviated way.