A market failure occurs when the free market does not allocate resources efficiently, resulting in a loss of total welfare (dead‑weight loss, DWL).
Allocative efficiency – private market
In a perfectly competitive market the condition for allocative efficiency is
$$ P = MC_{private} $$where P is the market price and MCprivate is the marginal cost borne by the producer.
Allocative efficiency – with externalities
When a transaction creates external costs or benefits the socially optimal condition becomes
$$ MSB = MSC $$with MSB = marginal social benefit and MSC = marginal social cost. If the market only satisfies P = MC_{private} while MSB ≠ MSC, a market failure exists.
Intuitive picture of DWL
The dead‑weight loss is the “missing” benefit (or extra cost) that society could have enjoyed if the market had operated at the socially optimal quantity. It is the area between the marginal social benefit and marginal social cost curves that is not realised because the market is absent or distorted.
A missing (or incomplete) market exists when there is no market for a good, service or right that would increase overall welfare if it could be traded. Typical reasons are:
| Missing‑Market Category | Key Characteristic | Typical Example | Why the Market Is Missing |
|---|---|---|---|
| Positive Externalities | MSB > MPB (marginal private benefit) | Vaccinations, basic education, R&D | Beneficiaries cannot be forced to pay; producers cannot capture the full benefit. |
| Negative Externalities | MSC > MPC (marginal private cost) | Factory emissions, second‑hand smoke | Producers do not bear the full cost; victims cannot be compensated easily. |
| Public Goods | Non‑rival & non‑excludable | National defence, street lighting, lighthouse service | Free‑rider problem prevents voluntary provision. |
| Merit / Demerit Goods | Private benefit/cost diverges from social benefit/cost | Merit: primary education, health care; Demerit: tobacco, alcohol | Consumers underestimate (merit) or overestimate (demerit) the social effects; market price does not reflect MSB or MSC. |
| Missing‑Market Category | Key Characteristic | Typical Example | Why the Market Is Missing |
|---|---|---|---|
| Insurance / Contingent‑Claim Markets | Risk‑sharing across uncertain future states | Health insurance, crop‑yield insurance | Uncertainty and adverse selection make voluntary contracts incomplete. |
| Information Markets | Asymmetric information about quality or risk | Used‑car market, credit‑rating services | Buyers cannot verify product quality; sellers cannot credibly signal it. |
Assume a good would be supplied if a market existed (e.g., a public good). The socially optimal quantity Q* satisfies
$$ MSB = MSC $$If the market is missing, the actual quantity is Q = 0. The dead‑weight loss is the area between the MSB and MSC curves from 0 to Q*:
$$ \text{DWL}= \int_{0}^{Q^{*}} \bigl(MSB - MSC\bigr)\,dQ $$Graphically this is a triangle with base Q* and height MSB_{0} - MSC_{0}. The shortcut formula is therefore
$$ \text{DWL}= \frac{1}{2}\,(P_{MSB} - P_{MSC})\,(Q^{*}) $$For a positive externality the triangle lies **above** the private‑benefit curve; for a negative externality it lies **below** the private‑cost curve.
| Policy | How It Works | Advantages | Disadvantages / Potential Government Failure |
|---|---|---|---|
| Direct provision of public goods | Government produces and finances the good via taxation. | Eliminates free‑rider problem; ensures universal access. | Risk of over‑provision, bureaucratic inefficiency, fiscal burden. |
| Subsidies (positive externalities, merit goods) | Payment to producers or consumers to lower the effective price. | Encourages higher consumption/production; relatively easy to target. | Cost to the exchequer; possible DWL if subsidy exceeds marginal benefit; rent‑seeking. |
| Taxes (negative externalities, demerit goods) | Charge per unit of output or consumption equal to marginal external cost. | Internalises external cost; generates revenue. | May be politically unpopular; can create black markets; administrative complexity. |
| Tradable permits (e.g., emissions trading) | Allocate a total cap and let firms buy/sell permits. | Achieves the required quantity at lowest cost; creates a market where none existed. | Initial allocation can be contentious; monitoring and enforcement needed. |
| Regulation & standards | Set minimum quality, safety or emission standards. | Reduces information asymmetry; protects health and safety. | Can be inflexible; compliance costs may be high; may stifle innovation. |
| Compulsory insurance (e.g., motor vehicle) | Legal requirement to purchase insurance. | Ensures risk is pooled; prevents catastrophic losses. | May impose a burden on low‑income households; risk of moral hazard. |
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