Question

The table below provides information about three firms (A, B, C): CO2 Pollution produced by each firm and costs to clean up pollution (by unit).

Firm	Pollution produced by firm	Costs to clean up pollution (by unit)
A	70 units	$20
B	80 units	$25
C	50 units	$10

The goal is to reduce pollution to 120 units (by three firms). That is, each firm is allowed to produce 40 units of pollution.

Each firm is given 40 units tradable CO2 permits of for free! Let's assume each permit is traded at $24 in the market.

How much would the Cap & Trade system save compared to No Cap & Trade system?   

Answer 1

Solution

Firm	Pollution produced by firm	Costs to clean up pollution (by unit)
A	70 units	$20
B	80 units	$25
C	50 units	$10

The goal of the govt.is to reduce the total pollution to 120 units.

Under the cap system then each Firm has to reduce their pollution levels to 40 units each which means:

A will incur a cost of $600 ([70 - 40] * 20) to clean up the additional units of pollution it produces above the mandated level of 40 units

B will incur a cost of $ 1000 ([80-40] * 25) to clean up the additional units of pollution it produces above the mandated level of 40 units

C will incur a cost of $100 ([50-40] * 10) to clean up the additional units of pollution it produces above the mandated level of 40 units

Total cost incurred by the industry to control the pollution is : $1700

Given that under the trade system,,each firm is given 40 units of tradable CO₂ permits for free and the market value of each permit is $24.So,firms will trade (buy/sell) these permits only if they are mutually beneficial for them.Also,this trade system will also be more efficient in the sense it is beneficial both to the players & industry and the Govt. as well (in terms of value creation; more value creation / profitable an industry is,the more more would be the tax collected from them by the Govt.)

Here 1 permit is valid for only 1 unit of pollution

Firm C

C has 40 permits but produces 50 units of pollution.But since the cost to clean up pollution is $ only 10 / units but the market price of each permit is $24.

So,it can sell all its 40 permits in the market

Total cost it incurs on reducing pollution is 50 * 10 i.e., $500

But revenue is : $ 960 (40 * 24 ) so savings is $460

Firm B

It will require 40 additional permits.Since it's cost of reducing pollution is $25 which is more than the market price of permit.So it spends $ 960 (40 * 24)

Savings for Firm B = (40 *($25 - $24)) i.e., $40

Firm A

Here A will not buy the permits from the market since the market price of $24 is well above the cost it will incur for cleaning the additional units of pollution (i.e., $20 )

It will spend $600 ( 30 * 20 ) to clean up pollution

Total industry savings

$1700 - [ (50 * 10 ) - (0) - (30*20)]

$1700 - (500+600) i.e., $ 600

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