# How to deal with challenging exam questions and truly understand concepts?

In my university, as well as many others around the world, undergraduate Economics exams can often be quite challenging – necessarily so, given that this is higher education. My question is – how can I meet this challenge?

A common source of frustration after exams is that “these questions were so different from what we did in class!” Over the past few semesters, I’ve come to realise that a difficult Economics exam question is difficult because it challenges the assumptions with which we learnt the central concepts and/or introduces external conditions which makes it difficult to directly apply how we learnt it in class.

For instance, just as a very simple example, in intermediate microeconomics, while we may have learnt how to solve for the optimal basket for a consumer who has a Cobb-Douglas utility function, in exams we could be “suddenly” thrown a scenario where the consumer’s utility function is now a minimum (min) function when we have not seen a min function before. Given the necessary scaffolding so that we know how a min function works, we are expected to solve for the optimal basket.

Another example: in introductory Econometrics, the topic on "estimation" focused on estimating mean, variance etc...(typical stuff). In exams, we were asked to estimate a cumulative distribution function i.e. P(X<=x). While we had learnt distribution functions quite extensively, we were never asked to estimate it in class.

In some ways the above examples are over-simplified, but the point is to illustrate a few ways “typical” questions could be tweaked to be challenging.

So my question is – how do I study Economics more skilfully so that I can be able to face up to these sorts of questions during the exam? Alternatively, how do I truly understand the concepts so that I can answer the question no matter how it’s tweaked – in a realistic amount of time under exam conditions. I can’t possibly compile a list of all permutations and combinations of how the question might deviate from the typical examples – that would be too inefficient, especially since the “assumption challenging condition” could come totally unexpectedly. Students are often advised to “truly understand” the concepts – but I have not heard enough on how this can be achieved. How can I do this?

I'm saying this from the perspective of a guy who was a student and a TA.

## Understanding the material

Saying from the perspective of a TA, as you have hinted, the point of learning economics is not to memorize ways to drive equilibrium outcome for Cobb-Douglas utility function. The point, rather, is to understand how the demand function is derived (starting from the consumer's maximizing her utility). Often, in the process, simple utility functions have many simplifying assumptions involved (continuouity, differentiability, etc.) and recognizing this will help you become more aware of other things... a good example is when you have linear or quasilinear utility function so that you need to consider endpoints as well.

If you truly understand the material, then you have no need to memorize things. You can derive them all in the exam room.

Your question, of course, is how to do that. I feel that if you work on the example questions and focus not just on the mechanics (take derivative of this, solve for $$p_x$$, plug into demand, etc.) but rather truly think about what the economic agent (consumer, producer) is actually doing... what they want to achieve, and what their constraints are... what would the market demand look like... etc., that might help.

One more technique I use if I have some spare time is to tweak the questions myself. Instead of having this utility function, what would happen if the utility function looks like that instead? Sometimes you work it out and check with friends. Sometimes it doesn't work out (price becomes negative!) and you could figure out why the question you set up yourself doesn't make sense.

## Exam format

This leads me to my second point, and where I might feel a bit different from you (and that you didn't ask).

As a student, I often find exams too long. There are too many questions and the time is too short. The only thing, I felt, that the exam is testing is whether the student could memorize that, when met with this kind of problem, the demand function is in the form of this and that. Many of my friends resort to memorizing shortcuts.

I would have much prefer exams you have... something that tests the understanding of the material, rather than your memory of the material. Of course, with this kind of problem, there needs to be enough time so that students could carefully go through and really think about the problems.

Another former TA here, who also sat as student rep on department board meetings for a time. While user @Art gives a great perspective (and one I share, especially on exam format), the other angle is that the "game" of producing university undergraduates has rules that can often produce sub-optimal outcomes for everyone.

Instructors face pressures from the institution to maintain a certain grading distribution; at the same time, they face increasing pressures from students to act as if the college experience is a simple transaction - students pay tuition, and receive degrees. This is a hard balancing act to perform. There's a lot of literature out there on grade inflation, attempts to correct for it, unintended socio-economic consequences of kludgy corrections, and so on - Wellesley College is one rather famous example.

What I'd like to know is whether your courses are graded on a curve, or based on absolute performance. If a curve, then it's entirely possible that being stonewalled by exam questions is exactly the point; the thing about reducing students to a probability distribution is that it reduces grading to the role of a band-pass filter.

An instructor may be writing her exams in such a way that (pulling numbers out of my hat) 60% of students are expected to get the easy questions that test rote application of the course material, an additional 30% of students will get the more challenging questions that slightly extend the scope of learning, and maybe 10% of students will get the really tough problems that require thinking fast and mathing faster. How this breakdown looks for your institution ultimately will be determined by the dominant philosophy about whether its degree holders should know more than just what is put in front of them.

Unfortunately, as a student part of your strategy must be first to understand what grading game you are playing. It is uncommon to be graded on absolute performance, as this requires more fine-tuning of material and is more likely to produce outlier grades that can hurt a student's overall GPA as well as a faculty member's performance review.

What I have noticed in studying both STEM fields and economics, is that the 10% of students who get the really tough problems tend also to be the students who get their hands on past exams and take the time to understand how the bandpass filter is constructed. They use that material to understand the relative weight of curveball questions, as well as their flavor. They engage with the instructor outside of class, and ask for additional materials. They are of course bright people, but their exam performance is as much owing to preparing in a different way than the other students, as it is owing to "truly understanding the material".

This is not a satisfactory answer from the standpoint of really wanting to learn a topic - but if it's any consolation, the literature is overwhelmingly populated with results that involve highly tractable utility functions, reduced-form econometric models, and so on. Unless you're angling for a scholarships and/or a graduate spot at a highly competitive university, there is diminishing marginal utility to landing on the far-right tail of a grade distribution.