A justification is the reason why your thesis is valid. In economics, this typically involves explaining a theory which leads to the conclusion of your thesis.
A justification (theory) can come in many different forms:
A theoretical proposition can be explained in prose. This can be appropriate for simple concepts, but is often imprecise and it is a rare academic paper that does not rely on something more rigorous.
An example of a justification that can be satisfactorily described in words might be ‘an increase in income will lead to an increase in demand for normal goods’ (although even here an indifference curve diagram would make the same point with a greater degree of rigour).
Familiar to all A-level students (and all undergraduates after the first week of lectures), diagrams are a simple way of presenting a theory and explaining what happens. You can clearly show why an individual’s labour supply curve might ‘bend backwards’ at high levels of income with an indifference curve diagram to explain the work/leisure tradeoff precisely.
An example of an appropriate justification using diagrams would be showing that firms in a perfectly competitive market set prices equal to marginal cost in the long run.
There are two possibilities here. First, you can derive a simple mathematical result yourself, and discuss the implications of it. Second, you can state an equation and discuss the implications of it.
A simple example of the first would be to show that monopolies set prices above marginal cost. Let:
π(q) = p(q) – c(q) where π(q) is profit, p(q) is price, q is quantity and c(q) is cost
p = c'(q) – p'(q)q by taking derivatives with respect to q and setting π'(q)=0
And as dp/dq <0 for a monopoly selling ordinary goods ⇒ p > c'(q)
Actually, this can also be shown by a diagram – but in many other examples, maths is clearer. These might include accurate exposition of the principal-agent problem.