Market Failure

We define market failure as the condition in which the free market allocation of resources is allocatively inefficient — that is, the market fails to produce the Pareto-optimal quantity of Goods and services.

Formally, market failure occurs when the price mechanism does not equate marginal social benefit With marginal social cost:

$P \neq MSC \quad \mathrm{or equivalently} \quad MSB \neq MSC$

This leads to a deadweight welfare loss: the total surplus (consumer + producer + third-party) Is not maximised.

## 2. Types of Market Failure### 2.1 Externalities

We define an externality as a cost or benefit arising from production or consumption that Affects a third party who is not part of the transaction.

Negative externality: the social cost exceeds the private cost.

$MSC = MPC + MEC$

Where $MPC$ = marginal private cost, $MEC$ = marginal external cost.

Positive externality: the social benefit exceeds the private benefit.

$MSB = MPB + MEB$

Where $MPB$ = marginal private benefit, $MEB$ = marginal external benefit.

Consider a good with a negative production externality (e.g., pollution from a factory). The market Equilibrium is where demand (MPB) equals supply (MPC):

$\mathrm{Market equilibrium: } MPB = MPC \implies Q_{mkt}, P_{mkt}$

The socially optimal outcome is where marginal social benefit equals marginal social cost:

$\mathrm{Social optimum: } MSB = MSC \implies Q^*, P^*$

Since $MSC > MPC$ (there is an external cost), the social optimum quantity $Q^*$ is less than the Market quantity $Q_{mkt}$. The free market over-produces the good.

The deadweight welfare loss (DWL) is:

$\mathrm{DWL} = \frac{1}{2}(Q_{mkt} - Q^*)(MSC(Q_{mkt}) - MSB(Q_{mkt}))$

This is the area of the triangle between the MSC and MSB curves from $Q^*$ to $Q_{mkt}$.

For positive externalities (e.g., education, vaccinations), the analysis is reversed: $MSB > MPB$ So $Q^* > Q_{mkt}$. The free market under-produces the good, and the DWL triangle lies between $Q_{mkt}$ and $Q^*$.

Example: Pollution from a Chemical Factory

A chemical factory produces output $Q$ with marginal private cost $MPC = 20 + Q$ and marginal External cost $MEC = Q$. The marginal private benefit (demand) is $MPB = 80 - Q$.

• $MSC = MPC + MEC = 20 + 2Q$
• Market equilibrium: $80 - Q = 20 + Q \Rightarrow Q_{mkt} = 30$, $P_{mkt} = 50$
• Social optimum: $80 - Q = 20 + 2Q \Rightarrow Q^* = 20$, $P^* = 60$
• DWL $= \frac{1}{2}(30 - 20)(MSC(30) - MSB(30)) = \frac{1}{2}(10)(80 - 50) = 150$

The market over-produces by 10 units, creating a welfare loss of 150.

	Production	Consumption
Negative	Factory pollution ($MSC > MPC$)	Second-hand smoke, congestion ($MSC > MPB$)
Positive	Beekeeping near orchards ($MSC < MPC$)	Vaccination, education ($MSB > MPB$)

We define a public good as a good that is:

1. Non-excludable: it is impossible (or prohibitively costly) to prevent non-payers from consuming the good
2. Non-rivalrous: one person”s consumption does not reduce the quantity available to others

$Q_{total} = Q_{individual} \quad \mathrm{(non-rivalry)}$

Contrast with private goods: excludable and rivalrous (your consumption of an apple means I Cannot eat it).

	Rivalrous	Non-rivalrous
Excludable	Private goods (food, clothing)	Club goods (cable TV, cinema)
Non-excludable	Common resources (fish stocks, grazing land)	Public goods (national defence, street lighting)

Proposition: In a free market, public goods will be under-provided or not provided at all.

Proof. Suppose a public good costs $C$ to provide and benefits each of $n$ individuals by $B_i$. The socially optimal provision requires $\sum_{i=1}^{n} B_i \geq C$. However, each individual $i$ Reasons: “If others pay, I can enjoy the good without paying (non-excludability). If others don’t Pay, my contribution is insufficient to provide the good.” Therefore, it is individually rational For each person not to contribute — the dominant strategy is to free-ride. By the same logic, no One contributes, and the good is not provided, even when $\sum B_i \gg C$. $\blacksquare$

Quasi-public goods: goods that are largely non-rivalrous but are excludable (e.g., roads, Education, healthcare). These are often provided by the government because the market would Under-provide them.

We define information asymmetry as a situation in which one party to a transaction has more or Better information than the other.

Akerlof (1970) analysed the market for used cars. Sellers know the quality of their car; buyers do Not. There are two types of cars:

• “Peaches” (high quality): value to seller $= £8\,000$Value to buyer $= £10\,000$
• “Lemons” (low quality): value to seller $= £4\,000$Value to buyer $= £6\,000$

If buyers can distinguish quality, both types trade at mutually beneficial prices. But if buyers Cannot distinguish, and 50% of cars are peaches and 50% are lemons, the expected value to a Buyer of a random car is:

$E[V] = 0.5 \times 10\,000 + 0.5 \times 6\,000 = £8\,000$

Buyers are willing to pay at most £8,000. But at this price, sellers of peaches (£8,000 value to Seller) will not sell — only lemons are offered. Buyers, anticipating this, revise their offer Downward to £6,000. Now only lemons trade. The market for high-quality cars collapses — this Is adverse selection: asymmetric information drives high-quality products out of the market.

We define moral hazard as a situation in which one party alters their behaviour after entering Into an agreement, knowing that the other party bears some of the cost of that behaviour.

Example

After purchasing comprehensive car insurance, a driver may take more risks (driving faster, parking In unsafe areas) because the insurance company bears the cost of accidents. The driver's behaviour Changes _because_ they are insured — this is moral hazard.

When a single firm (monopoly) or a small number of firms (oligopoly) have significant market power, They restrict output and raise prices above the competitive level. This creates a deadweight loss (analysed in detail in Topic 4).

Occupational immobility: workers cannot move between jobs due to lack of skills, Training, or qualifications.

Geographical immobility: workers cannot move between regions due to housing costs, family Ties, or information gaps.

Both types of immobility prevent the market from clearing, leading to structural unemployment and Inefficient allocation of labour.

Markets reward factors of production according to marginal productivity. Those who own scarce, Highly productive factors (skilled labour, capital, land) receive higher incomes. Without Redistribution, this can lead to extreme inequality — which many consider a form of market failure Because:

1. Unequal incomes $\Rightarrow$ unequal access to education, healthcare, opportunities
2. High inequality may reduce aggregate demand (the rich have a lower MPC)
3. Social and political instability

The Lorenz curve plots the cumulative share of income received by the cumulative share of the Population, ordered from poorest to richest.

If income were perfectly equally distributed, the Lorenz curve would be the 45° line (line of Perfect equality). The greater the deviation (bow) of the Lorenz curve from the 45° line, the Greater the inequality.

We define the Gini coefficient as:

$G = \frac{A}{A + B}$

Where $A$ is the area between the 45° line and the Lorenz curve, and $B$ is the area under the Lorenz curve.

Since $A + B = \frac{1}{2}$ (area of the triangle below the 45° line):

$G = \frac{A}{A + B} = 2A = 1 - 2B$

Gini Value	Interpretation
$G = 0$	Perfect equality
$G = 1$	Perfect inequality (one person has all income)
$0.2 - 0.3$	Relatively equal (e.g., Nordic countries: 0.25-0.28)
$0.3 - 0.4$	Moderate inequality (e.g., UK: 0.35)
$0.5 - 0.6$	High inequality (e.g., South Africa: 0.63)

### 4.1 Pigouvian Taxation

For a negative externality, the optimal Pigouvian tax equals the marginal external cost at the Socially optimal quantity:

$t^* = MEC(Q^*)$

Proof of optimality. With a specific tax $t$ per unit, the firm’s private cost becomes $MPC + t$. The firm produces where demand equals private cost plus tax: $MPB = MPC + t$. For this to Equal the social optimum ($MPB = MSC = MPC + MEC$), we need $t = MEC$ at the optimal quantity. $\blacksquare$

The tax internalises the externality: the firm now faces the full social cost of its production And reduces output to $Q^*$.

Example: Carbon Tax

A coal power plant produces electricity with $MPC = 10 + Q$ and $MEC = 0.5Q$ (carbon emissions Damage). Demand: $P = 100 - Q$.

• $MSC = 10 + 1.5Q$
• Social optimum: $100 - Q = 10 + 1.5Q \Rightarrow Q^* = 36$, $P^* = 64$
• Optimal tax: $t^* = MEC(36) = 18$
• With tax, firm faces: $MPC + t = 10 + Q + 18 = 28 + Q$. Equilibrium: $100 - Q = 28 + Q \Rightarrow Q = 36$ ✓

For positive externalities, a Pigouvian subsidy equal to the marginal external benefit can Internalise the externality and increase output to the social optimum.

Limitation: subsidies require government revenue (from taxation), which may itself create Distortions.

The government can directly regulate production or consumption:

• Quantity regulation: e.g., banning smoking in public places, setting emission limits
• Price regulation: e.g., price ceilings (rent control), price floors (minimum wage)
• Quality standards: e.g., minimum building standards, food safety regulations

Evaluation: regulation can be effective but may be:

• Inflexible (doesn’t allow firms to find least-cost solutions)
• Costly to enforce (monitoring and compliance)
• Subject to regulatory capture (regulated firms influence the regulator)

The government sets a total quantity of pollution allowed and issues permits that firms can trade Among themselves. This combines quantity regulation with market efficiency:

• Firms with low abatement costs reduce pollution and sell permits
• Firms with high abatement costs buy permits instead
• The equilibrium permit price equals the marginal abatement cost across all firms

Advantage: achieves the environmental target at minimum cost to society.

The government directly provides public goods (defence, street lighting) and merit goods (education, Healthcare) that the market would under-provide.

Government can reduce information asymmetry by:

• Mandatory labelling (nutritional information, energy ratings)
• Product safety standards
• Employment laws (preventing discrimination)
• Financial regulation (requiring disclosure)

We define government failure as the situation in which government intervention to correct a Market failure worsens the outcome.

1. Regulatory capture: the regulatory agency becomes dominated by the industry it regulates, acting in the industry’s interest rather than the public’s
2. Information problems: governments face the same information constraints as markets. They may not know the optimal tax rate or the true marginal external cost
3. Bureaucracy and inefficiency: government agencies lack the profit motive and may be slow, costly, and unresponsive
4. Unintended consequences: e.g., rent control reducing the supply of housing, agricultural subsidies encouraging overproduction
5. Political constraints: short election cycles incentivise policies with immediate visible benefits but long-term costs
6. Principal-agent problems: government officials (agents) may not act in the public’s (principal’s) interest

## 6. Critical Evaluation

Merit goods: goods that the government believes consumers should consume more of, because Consumers underestimate their private benefit (due to imperfect information or myopia). Examples: Education, healthcare, vaccinations.

Demerit goods: goods that the government believes consumers should consume less of. Examples: Alcohol, tobacco, illegal drugs.