2.8 (Micro) Market failure: Negative externality production: Solution 2: Carbon tax (Pigouvian tax)

Video tutorial for IB Economics students illustrating how to draw & analyze a negative externality of production model with the applied example of the market for electricity generated by coal-fired power stations

Solution 2:
And the impact of a Carbon tax (an indirect Pigouvian tax on carbon) as a government means to correct the overallocation of resources to the production and consumption of the good or service, which has led to the negative externality

Note:
IB Econ Paper analysis at 10:56 (negative externality of production)​​
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Analysis
* Graph A: Market for electricity generated by coal-fired power stations

* x-axis measures Qs & Qd of electricity generated by coal-fired power stations
* y-axis measures the price of electricity generated by coal-fired power stations

* S1=MPC (marginal private cost), upward sloping according to the law of supply
* MPC= private cost of the private firm employing resources (labor, coal, etc.) that are exclusive and rivalrous to the firm (private goods)

* D1=MPB (marginal private benefit)= MSB (marginal social benefit), downward sloping according to the law of demand
* MPB= private benefit of the household that is consuming electricity; household consumption of electricity is a private good as it is excludable and rivalrous
* MSB= social benefit of households consuming electricity; household consumption of electricity does not lead to an assumed welfare loss

* S1=D1 (Point A), provides an equilibrium free market price (Pm) & an equilibrium free market quantity (Qm) where Qs=Qd

* But, the free market price of Pm does not reflect the true costs of production as the negative impacts of carbon emitted into the atmosphere (common access resource), the environment, ecosystems, plant, wildlife, human health, and economies (climate change impacts) are not reflected.
* Pm=MPC, and does not include MSC (marginal social costs) of production

* S2=MSC (Point B), which reflects the quantified social cost of the damage caused by the emission of carbon by coal-fired power stations

* Thus, at Qm, MSC is greater than MSB, generating a welfare loss (shaded area) representing the quantified cost and damage of carbon emissions into society

* Social optimum would be achieved where MSC=MSB
* MSC=MSB provides the socially optimum price of Popt= MPC+MSC
* MSC=MSB provides the socially optimum quantity of Qopt; as a result of an increase in price from Pm to Popt, Qd would decrease from Qm (Point A) to Qopt (Point C)
* Thus allocative efficiency would be achieved at MSC=MSB eliminating the free market failure

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IB Econ Paper analysis of Solution 2: Carbon tax (indirect Pigovian tax on carbon) at 12:53​​

* The central government then decides to intervene by applying a Carbon tax (indirect Pigouvian tax on each unit of carbon emitted into the atmosphere)

* The Carbon tax has the effect of shifting the supply curve inward by the amount of the tax on each unit of carbon emitted by the firm from S1 to S2=MSC1=(MPC+tax)=(S1+tax)
* Taxes are a non-price determinant of supply as it is an additional cost of production for the firm
* S2=D1 (Point C), provides a new equilibrium price paid by consumers at Pc=Popt1 (increased price paid by consumers from Pe to Pc, and a new and reduced equilibrium quantity at Qopt1 where Qs=Qd
* Thus Qd has decreased (law of demand) from Qm to Qopt as a result of an increase in price (Pm to Pc)
* And Qs has decreased (law of supply) from Qe to Qopt as a result of a decrease in price received by firms (Pm to Pp)

* The carbon tax has the effect of incentivizing the firm to lower their carbon emissions as a means to reduce the carbon tax, thus the firm may decide to invest in green technology that generates electricity through renewables (solar power, wind power, etc.). As a result of these investments in green technology, the electricity generating firm is able to lower their carbon emissions, and also lower their carbon tax bill enabling the firm to increase output and lower price.

* S3=D1 (Point D), provides a new and lower equilibrium price paid by consumers at Pc=Popt2 and a new and increased equilibrium quantity at Qopt2 where Qs=Qd

* Thus the Carbon tax (indirect Pigouvian tax on each unit of carbon emitted by coal-fired power stations) is effective in achieving social optimum where MSC=MSB providing the social optimum quantity (Qopt) and price (Popt)