This unit is one of the harder econ subjects. You need to be able to understand the basic graphical/intuitive approaches to public finance, as well as the mathematical approaches, and be able to distinguish the strengths and weaknesses of the different models . If you're not comfortable deriving mathematical proofs, I do not recommend you taking it.
The unit has the following topics: Economic Efficiency, Public Goods, Poverty and Equality, Commodity Taxation, Externalities, The Role of the Public Sector, Income Taxation and Tax Evasion.
Economic Efficiency : You're introduced to the main 2 theorems of welfare economics. This will expose you to some concepts like pareto efficiency, competitive efficiency and you'll also be introduced to the edgeworth box that depicts the two theorems in a two person economy. There's a little bit of calculus in regards to proving the competitive equilibrium.
The role of the public sector: You're pretty much taught the role of the government, how they have to balance equity and efficiency but arn't able to do this in a world with an invisible hand.
Externalities: Pretty Much exposed to a few simple examples of externalities
Public goods: This topic is pretty big, and I'd highly recommend you understand the calculus behind the Samuelson condition, this pretty much shows the efficiency condition behind the two main ways of allocating the private provision of public goods between two people.
Poverty and Equality: This topic isn't a major focus as ranjaan teaches a lot of people taking his development economics unit. However you'll learn about the gini coefficient, some conditions that are described as the optimal equality measures. You'll also learn about some different measures, most notabley RGT, SEN. The major distinction was understanding the decomposable component of an inequality measure.
Commodity Taxation: This is the big bad boy of this unit. You need to understand the inverse elasticity rule, the ramsey rule as well as the equity consideration to commodity taxation ( the many person situation).
Income taxation: you learn about the income and substitution effects behind income taxes (slutsky rule), as well as why taxes must be below 100% and above 0% at the marginal rate. You also learn that the optimal income tax is 0 for the highest earning person in an economy.
Tax Evasion: not a big topic but teaches you that theirs a payoff for the government to target tax evaders.
Overall I absolutely loved this unit. Not the teaching , but I thoroughly enjoyed learning the content. To be absolutely honest, the essay is not super relevant to the exam, but it was enjoyable. Ranjaan doesn't record his lectures and his lectures can be dense and boring. I definitely fell asleep in a few classes. The tutorial work you get is super mathematical, and can be very confusing, but the exam is nothing like the mathematical problems you get in your tutorials each week. The major focus areas on the exam are on public goods, the theories of the public sector and commodity taxation and his "additional slides" mostly relating to public expenditure of the past 150 years or so as well as climate change and taxation within Australia. He can be a bit cheeky with some of the questions in the exam with these additional slides with questions like. "Derive public expenditure for the past 50 years with evidence and statistics", for 30 marks. So definitely know your stats inside and out. In preparation for the exam you should definitely do the practice exam and know what kind of questions are examinable. usually they'll come with different wording, so get a good grasp of the main topics.