Convexity are functions with an increasing slope.
Most of us are familiar with the eighth wonder of the world compound interest, without which the financial markets would not exist :
V(t) = V(0)(1+R) ^ t
Another variant of convexity is exponential decay. In these models, the slow begins at a negative value and increases towards zero. A half-life model can predict that your engineering degree would be halve its value every 4-5 years.
Concave models are the opposite being functions with a decreasing slope. One possible function is the log function :
V(t) = N log Rt
Where the slope of a concave function is positive, it models diminishing returns. When concavity is assume, there is also a preference for diversity and risk aversion. One day in Kulai JB is great, but 10 days in Kulai will bore the shit out of you.
The Solow Growth model predicts that output in a given economy :
Output = A(LK)^0.5