Market Failure and Externalities: Question 5

Worked solution

Part (a): Why the externality prevents allocative efficiency

Allocative efficiency is achieved where marginal social benefit equals marginal social cost, $MSB = MSC$, so that resources are directed to where they generate the greatest net benefit to society as a whole.

A coal-fired power station, however, makes its output decision based only on its own marginal private cost, $MPC$ (the cost of coal, labour and capital used to generate electricity) and the price consumers are willing to pay, which reflects only their marginal private benefit, $MPB$. It has no financial incentive to take account of the marginal external cost, $MEC$, that its carbon dioxide emissions impose on people elsewhere (and in the future) through climate change, since $MSC = MPC + MEC$.

Because the power station produces where $MPB = MPC$ rather than where $MSB = MSC$, and $MSC > MPC$ due to the external cost, output ends up higher than the socially optimal level: at the free-market output, the marginal social cost of the last unit generated exceeds its marginal social benefit. This is allocatively inefficient, resources are over-allocated to coal-fired electricity generation relative to what would maximise society’s net benefit, and represents a deadweight welfare loss.

Part (b): How significant is the resulting misallocation of resources?

The externality and the resulting misallocation. Because $MSC = MPC + MEC$ and the marginal external cost of carbon dioxide emissions is positive, the free market for coal-fired electricity settles where $MPB = MPC$ rather than at the socially optimal output where $MSB = MSC$. At the free-market output, marginal social cost exceeds marginal social benefit, so resources are over-allocated to coal-fired generation relative to the socially efficient level, and the gap between $MSC$ and $MSB$ over the units produced beyond the social optimum represents a deadweight welfare loss.

How significant is this misallocation?

• The size of the marginal external cost. Carbon dioxide emissions are associated with a wide range of long-lived, global damages (more frequent extreme weather, rising sea levels and losses to agriculture) that accumulate and persist for decades after the electricity is generated. The larger and more persistent the marginal external cost, the larger the gap between $MPC$ and $MSC$, and the greater the resulting over-allocation of resources and deadweight welfare loss.
• The price elasticity of demand for electricity. The socially optimal output is where demand meets $MSC$, while the free market produces where demand meets $MPC$; the quantity over-produced is the horizontal gap between these two points. For a given marginal external cost, that gap is larger when demand is more price elastic and smaller when demand is more price inelastic. Electricity has few close substitutes and is close to a necessity, so its demand tends to be relatively price inelastic, which means the quantity over-produced, and hence the deadweight welfare loss from the distortion, is relatively small for a given external cost. Had demand been more elastic, the same external cost would have produced a larger quantity distortion and a larger misallocation.
• Possible offsetting positive externalities. Reliable electricity supply from coal-fired stations may generate positive externalities elsewhere in the economy, for example by supporting hospitals, schools and other firms whose own output benefits third parties. To the extent that such benefits exist, they should be weighed against the negative externality from emissions, which would reduce the net misallocation of resources below what the carbon dioxide externality alone would suggest.
• Difficulty in valuing the external cost. Because the damage from carbon dioxide emissions is global, long-term and uncertain, it is very difficult to place a precise monetary value on the marginal external cost. This means the true size of the gap between $MPC$ and $MSC$, and therefore the true size of the misallocation and the deadweight welfare loss, cannot be measured with confidence; estimates could understate or overstate how serious the problem actually is.

Overall judgement. The misallocation of resources in the market for coal-fired electricity is likely to be significant, mainly because the marginal external cost of carbon dioxide emissions is large and persistent. That said, the price-inelastic nature of electricity demand means the quantity actually over-produced is not far above the social optimum, so the deadweight welfare loss from the distortion may be more limited than the sheer scale of emissions first suggests; and the difficulty of valuing a global, long-term external cost means the exact size of the welfare loss remains genuinely uncertain. On balance, the large external cost makes the misallocation significant, but its precise extent cannot be measured with confidence.

Final answers

• (a) The power station ignores the marginal external cost of its emissions, so it produces where $MPB = MPC$ instead of where $MSB = MSC$, causing over-production and allocative inefficiency
• (b) $MSC = MPC + MEC$ means the free market over-allocates resources to coal-fired electricity relative to the social optimum; the misallocation is likely significant mainly because the external cost is large and persistent, though inelastic demand limits the size of the quantity distortion and the external cost is hard to value, so its exact size is uncertain