What can I expect in a Cambridge economics interview?

So this, of course, depends on the particular college you applied to, but there are some general themes that you can expect to encounter. 

1) You will probably have some form of general interview, often with a non-economist. This is to gauge your level of interest in economics and how well you would suit Cambridge. They might ask "What economics book have you been reading", and then ask you to expand on some of the key points of the book or challenge the conclusions. Be prepared for the basic questions such as "Why economics" or "Why Cambridge".

2) The Cambridge economics course is very heavy in maths (1 of the 5 papers we take in first year is entirely dedicated to maths and stats). Therefore, it is worth revising key maths concepts from C1-4 (especially if you have taken a gap year). But also be prepared for these concepts to be applied to economics.

For example, they may give you a cost function and a demand function, and then ask you to calculate the revenue function (so PriceQuantity - QuantityCost(per-unit)). Then, they may ask you to maximise this function, taking first derivates to find at what quantity profit is maximised. You should then also prove that this is a maximum, by taking second derivatives. So whilst the acutal maths may not be that hard (basic differentiation) the interviewers may apply it to unfamiliar situations. 

Graph sketching is also very common, as is integration.

3) At the end of the interview, they will usually ask if you have any questions. It is worth thinking about this beforehand, so you have some questions ready to ask. But make sure these aren't too obvious, or anything you could have easily found on the College's website.