Economics Question about Free Market Economy

Firstly...

you should say households do not have to pay income tax and secondly, you are right in terms of subsidy being a form of government intervention but subsidy is defined as a payment made by the government to pay part of producer's cost of production (with the aim of reducing their costs). And hence subsidy will mostly benefit producers and will indirectly affect consumers in terms of them paying lower prices as firm's cost of production is reduced.

It really depends on the context of the question....are you evaluating the advantages and disadvantages of free market in comparison to that of a public economy?

PS. Producers are part of households and as producers they pay what is so called indirect tax (tax on spending) - this tax can be specific or pigouvian depending on the government. And of course consumers also have to pay indirect tax but who pays more depends on the elasticities of demand.

Um...hm...I'm not quite sure what you mean by free goods...do you mean public, merit and demerit goods and in referral to market failure? If so you can say that the disadvantage of free markets is that public goods will be completely neglected (free rider problem) as these goods are not profitable at all (assume most firms are profit-maximising) and henceforth these goods will not be produced. Merit goods will also be underprovided as these goods are usually unprofitable whereas demerit goods like cigarettes and alcohols will be encouraged as they are addictive (inelastic PED) and hence free market will usually result into more inequality and market failure.

Yes you are right in terms of how subsidies will be neglected, but it's not much of an evaluation point here. You can say that without subsidies that:
1. Price of exports produced domestically will be higher relative to exports produced by other countries (and hence uncompetitive exports) which may lead to balance of trade problems (depending on the marshall lerner condition) - but this is going a bit too far and out of context
2. Some industries need subsidies like that of the sunset and sunrising industries (again a bit out of context as this is related to international economics)
3. Subsidies should be provided to firms who produces merit goods to correct market failure (subsidies can be used as a tool to correct market failure; indirect and direct taxes as well)

And yes austerity basically means a contractionary fiscal policy.