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Let $\pi$ be the fine that needs to be paid besides the parking fee (say, $\phi$) if he gets caught. Further, he may or may not get caught for not paying. So let $p$ be the probability perceived by John about whether he will be caught. Let $u(x)$ be utility function of paying for amount $x$, with $u(0)=0$, $u'(x)<0$.
If he pays the parking fee $\phi$ he ...
Virtually same question was already addressed at quantitative finance stack by user Matthew Gunn. The answer there can be summed as:
Financial economics is what economics calls finance. Finance is what finance calls finance.
Less flippantly though, there's a long debate on whether finance is a subfield of economics, ... Prof. Milton Friedman famously ...