Cap and trade is a method of regulatory intervention to reduce carbon emissions. Here, the system sets a maximum value for the emissions (cap). It also provides allowances, in emission permits, to firms to cover each unit of CO2 (or any other pollutant) produced. The company can redeem one for every emission unit or trade it to another party, who can then use it.
The regulator can issue permits to the firm in two ways. It can give away permits for free (based on some criteria) or auction them. Allocating permits based on past emissions is called grandfathering.
Mathematically, economists proved that the fee of permits has no impact on the price of the product. If p is the price, q is the output, c(q) is the cost of production, pp is the permit cost, and A is the free permit.
1) For zero free permit
profit = p q – C(q) – ppq
The firm maximises its profit with respect to quantity,
d(profit)/dq = p – C'(q) – pp = 0
price of the product, p = C'(q) + pp
2) For ‘A’ free permits
profit = p q – C(q) – (ppq – A)
The firm maximises its profit with respect to quantity,
d(profit)/dq = p – C'(q) – pp = 0; A is a constant and its derivative is zero.
price of the product, p = C'(q) + pp
So, in both cases, the product’s price is the marginal cost + the price of the permit. The auction, at least, gives the government some money that can be used to support the people who are the worst affected by the price rise.
