Rivalry and Excludability Private goods are excludable and rival. Excludable means the good can only be used by the consumer who buys it. The buyer owns the property rights over the good. A Milky Way is excludable because if consumer A buys it and eats it, no one else can eat it. Rival means the consumption by one individual reduces the amount available for others to consume. A Milky Way is rival because if consumer A buys it, that reduces the amount others can buy. Private goods include cars, food, toys, pens, houses etc.
Public goods are non-rival and non-excludable. Non-rival means the consumption by one individual does not reduce the amount available for others to consume. A street light is non-rival because if consumer A uses it for light, others can still use it for light too. Non-excludable means anyone can use the good even if they do not pay for it. A street light is non-excludable because anyone can use it without paying for it. Public goods include street lights, the army, parks, beaches, flood control systems, the police etc.
Free Rider Problem Markets fail to provide public goods because of the free rider problem. A consumer knows he can consume a public good for free if another consumer pays for it. Every consumer will reason like this and aim to free ride on consumers who pay, so no consumer will pay for the public good. Private firms cannot profitably provide public goods for free so they do not produce the public good. Market failure occurs because the market for public goods is missing, public goods are not produced.
Valuation Problem Market prices cannot be accurately estimated for public goods. A consumer undervalues price to free ride, a firm overvalues price to earn more profit. Market failure occurs because consumers and firms do not agree on prices so public goods are not produced.
Government Intervention The government must intervene to correct market failure. The government must estimate the amount of demand for public goods, estimate the price, and then tax consumers to raise the revenue to provide the good.