I can’t solve your problem, mainly because it is very unclear what your problem is. It seems to be that you think the section and subsection are being set in too big a font size, is that correct?
There are lots and lots of very kind and knowledgeable people here who are happy to help beginners like you, but you have to provide enough information. The most important of which is an MWE: a minimum, working example.
First, what you have provided is not a working example. It doesn’t compile, which you would have easily discovered if you had just tried to compile it yourself. The \end{centre} on the 2nd to last line has no corresponding \begin{centre}. So remove that.
Next, it should be minimum. Remove anything not relevant to your problem. So the maths doesn’t seem to be relevant. And your MWE doesn’t have any graphics or floats in it. So you can remove
\usepackage[dvipsnames]{xcolor}
\usepackage{graphicx}
\graphicspath{ {images/} }
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{float}
\usepackage{mathtools}
Let’s add some lorem ipsum text, and your MWE now looks like this:
\documentclass[12pt]{article}
\usepackage{lmodern}
\usepackage{ae,aecompl}
\usepackage[T1]{fontenc}
\usepackage[a4paper, total={6.5in, 8in}]{geometry}
\usepackage{titling}
\setlength{\droptitle}{-8em}
\usepackage{subcaption}
\renewcommand\rmdefault{lmr}
\begin{document}
\title{Problem Set 1 - Macroeconomic Theory}
\date{\today}
\maketitle
\section{The Ramsey-Cass-Koopmans Model}
Incididunt veniam non ipsum adipisicing aliquip id laborum nisi adipisicing consectetur
irure do. Aute veniam occaecat ipsum proident cupidatat Lorem mollit incididunt dolore
tempor laborum commodo. Ea sit nulla sunt veniam aliqua et magna aliquip dolor. Quis in
veniam ipsum et mollit dolor elit adipisicing labore Lorem eiusmod adipisicing esse
proident.
\subsection{The Ramsey Problem}
Qui qui ex officia consequat laborum nulla aliqua voluptate ea minim magna. Nostrud minim
exercitation deserunt sint voluptate amet aute laboris exercitation irure tempor
reprehenderit. Amet pariatur enim anim laborum. Proident consectetur duis sit
proident.
\end{document}
Now, if I compare the output of that with this even more minimal version
\documentclass[12pt]{article}
\usepackage[a4paper, total={6.5in, 8in}]{geometry}
\begin{document}
\title{Problem Set 1 - Macroeconomic Theory}
\date{\today}
\maketitle
\section{The Ramsey-Cass-Koopmans Model}
Incididunt veniam non ipsum adipisicing aliquip id laborum nisi adipisicing consectetur
irure do. Aute veniam occaecat ipsum proident cupidatat Lorem mollit incididunt dolore
tempor laborum commodo. Ea sit nulla sunt veniam aliqua et magna aliquip dolor. Quis in
veniam ipsum et mollit dolor elit adipisicing labore Lorem eiusmod adipisicing esse
proident.
\subsection{The Ramsey Problem}
Qui qui ex officia consequat laborum nulla aliqua voluptate ea minim magna. Nostrud minim
exercitation deserunt sint voluptate amet aute laboris exercitation irure tempor
reprehenderit. Amet pariatur enim anim laborum. Proident consectetur duis sit
proident.
\end{document}
I can see no difference in the font-size of the section and subsection.
So I am sorry to say that I just don’t understand what your problem is. You will need to try to explain it better.
But most importantly, learn how to create a proper MWE. More often than not, doing that can often lead to you discovering the cause of your problem and solving it yourself without even needing to ask here.
Sorry I couldn’t help more.
\documentclass...to\end{document}) that we can process that shows your problem. – Peter Wilson May 19 '20 at 18:21\usepackage{ae,aecompl}in any document written this century, the ae fonts were an early test release of what became T1 encoding. Certainly it makes no sense to load them and the lmodern package as you are then specifying two fonts both to be the main document font. also don't use$$in latex, it is not supported syntax. – David Carlisle May 21 '20 at 22:15