# MODELS OF MARKET ALLOCATION OF EXTERNALITIES, GENERALIZED COASE THEOREM

## EMISSIONS PERMIT MARKET

The worsening climate forced the UN to adopt the Framework Convention on Climate Change in 1992. The Kyoto Protocol was annexed to this Convention in 1997. Under the Protocol, the world's industrial countries committed themselves to reducing emissions of greenhouse gases by 5.2% compared to the 1990 level by the year 2012. Cutting emissions of greenhouse gases should, according to the Protocol, slow the pace of climate change and global warming. The Czech Republic ratified the Kyoto Protocol in 2001.

One of the main tools for reducing pollution is emissions trading. This system — consisting of Joint Implementation (JI) and the Clean Development Mechanism (CDM) — provides economic agents with market-based incentives to cut emissions of pollutants. The system also makes it possible for the state to intervene effectively to reduce carbon dioxide emissions, for example. The state issues permits only for the number of tonnes of greenhouse gas emissions it wishes to allow. In the Czech Republic, this amount is set in a National Allocation Plan.

Firms can trade the permits they do not use. The permits therefore function similarly to securities. They can be sold to other polluters who cannot keep within the limits.[1]

It is believed that this system will contribute to the allocation of environmental investments to areas of maximum effect and therefore reduce emissions overall.

Another stated advantage of the emissions trading system is that it enables resources to be pooled for environmental investments that a single firm would otherwise find very difficult to carry out.

In this section we will try to model the behaviour of an agent that is trying to avoid two risks: the risk of exceeding the emissions limit, and the risk of insolvency due to low profitability. The agent can reduce one of these risks at the expense of the other by buying or selling emissions permits.

We will use the following notation in the model:

Y is output of a firm,

q is the price of the product,

π is profit per unit of output,

b is the boundary of the zone of the threat due to low profitability,

G is the volume of emissions,

Y is emissions per unit of output,

G0 is the initial number of emissions permits,

w is the market price of a permit,

ξ is the number of permits bought (with ξ<0 sold).

The Pareto probability of extinction due to low profitability is

We assume that the firm is not allowed to exceed the emissions limit given by the number of permits it holds, i.e. there is a prohibitive penalty for exceeding this limit. The probability of extinction due to this reason is

The firm maximizes its probability of survival

Because the sum of the factors in the denominator is constant (and because a square has a larger area than any other rectangle with the same perimeter) it holds that the probability of survival is maximized by the sale of emissions permits at which the factors in the denominator are equal:

The optimum (survival-probability-maximizing) number of permits is therefore

If , the firm will buy permits. If, by contrast, , the firm will sell permits.

The standard market mechanism will then deliver the emissions permit price o) at which the number of permits demanded and supplied is equal, i.e. at which the following relation holds (where i is the index of the agent):

Under the stated (essentially realistic) assumptions the demand and supply functions of market agents are smooth functions and the equilibrium price ω* certainly exists and is unique, because with rising price ω both demand (the sum of positive ) and supply (the sum of negative ) for permits changes continuously and the gap between supply and demand on the emissions market is an increasing function of the permit price.

• [1] For instance, the biggest Czech polluter, the power company CEZ, earned more than a billion Czech crowns in this way in 2007. However, firms are not required to sell their permits within any time-limit. In 2007, for example, the market price of permits fell and many businesses held them speculatively in expectation of a rise in the market price.