A free market economy allocates resources through the price mechanism with minimal government, whereas a mixed economy combines the market with an active state. The claim that the free market is superior rests on its efficiency; whether it holds depends on how the market's failures are weighed.
The case for the free market's superiority. The price mechanism is a remarkably effective coordinator. Through signalling, incentives and rationing, prices direct resources to where consumers want them, and the profit motive plus competition push firms to cut costs, raising efficiency. Because firms compete for custom, consumers enjoy wide choice, falling prices and constant innovation. Crucially — Hayek's argument — the knowledge needed to run an economy is dispersed among millions of people and cannot be gathered by any central planner; the price system uses this scattered information automatically, which is why heavily planned economies suffered chronic shortages and surpluses while market economies grew. Adam Smith's 'invisible hand' captures the result: self-interest, coordinated by prices, tends to benefit society. On these grounds the free market allocates most goods better than a bureaucratic state could, and excessive government can blunt incentives and cause government failure.
The case against — why the mixed economy is usually superior. The free market fails in predictable ways that a mixed economy is designed to fix. First, it under-provides public goods such as defence and street lighting, because firms cannot easily charge for non-excludable goods — so a pure market leaves society without them. Second, prices ignore externalities: pollution imposes costs on third parties that the market does not price in, leading to over-production of harmful goods. Third, unchecked markets allow monopoly power, letting large firms raise prices and restrict output at consumers' expense. Fourth, and most fundamentally, the market answers 'for whom' by ability to pay, so it can generate severe inequality — the concern at the heart of Marx's critique that capitalism enriches owners of capital while leaving others with little. A mixed economy keeps the market's efficiency for most goods while the state provides public and merit goods, taxes externalities, regulates monopolies and redistributes income — correcting exactly these failures.
Evaluation and judgement. The verdict turns on what we mean by 'superior' and on the value we place on efficiency versus equity. If the sole criterion is allocative and productive efficiency for private goods, the free market is hard to beat, and too large a state can indeed cause government failure and weak incentives. But 'superior' for an economy must also include public goods, the environment and fairness, on which the pure free market plainly fails. There is also a practical point: a pure free market has never existed, so the real choice is not free market versus mixed but how far along the spectrum to sit. On balance, a mixed economy is generally superior, because it retains the market's powerful efficiency and incentive advantages while using the state to correct market failure and limit inequality. The free market is superior only under narrow conditions — where externalities and public goods are minor and inequality is not a concern — which rarely describe a whole economy. The strongest position is that the market should be the default allocator, with the state intervening where, and only where, markets demonstrably fail.