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Ricardian Rent Theory Analysis

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The purpose of this project is to utilize Ricardo’s theory of differential rent in environmental economics in a system of pricing of pollution permits where choice of technique of production (i.e. superior environmentally efficient technology or low-grade polluting machinery) determines whether the units operate under Ricardo’s ‘Land A’ system by earning and accumulating Certified Emission Reductions (CERs) and thereby the ‘rent’ they acquire on the sale of the same; or whether the industrial units operate under ‘Land D’ conditions and instead increase their costs by resorting to purchase of these carbon credits.

The rent factor here is not accounted for in institutionally determined mandates on environmental preservation, rather in that these units operate in a world with costly disposal of harmful substances and where pollutants and waste generated is not considered a free good anymore. Thus, the report argues that if cost of production is taken into account, the choice of technique cannot be only considered based in the cost of manufacturing inputs but also based on the environmental costs which in today’s world take a quantifiable and regulated form of carbon credits. Thus, Ricardian concept of differential rent can be used for analysis of environmental policies.

The model this report proposes an alternative to Leontief (1970) who in his works, on an environmental accounting system and environmental input-output tables showed the physical flow from the environment system to the economic system (i.e. input resources) and vice-versa (i.e. outputs of pollution).

However, in this report, we will deal with only one output, that is, carbon emission. Since pollution are introduced into the environment as by-products and tend to be generated in a certain proportion to the characteristic product of the industrial unit, the cost of production must be accounted for by same unit that accounts for the overall costs of manufacturing.

Reformulation of theoretical Assumptions borrowed from Leontief (1970) and Lager (2001):

Using the concept of choice of technology and regarding the application of the model as relevant in today’s world scenario, there are certain theoretical assumptions that are to be taken as given for the model to fit environmental policy decisions. These are:

  1. Firms access to all method of production is not restricted especially by size of the firm. Thus, firms are capable of switching to more (environmentally) efficient means of production.
  2. There are ‘n’ processes that can produce ‘m’ types of goods by generating ‘p’ types of pollution.
  3. There is only one homogenous pollutant, namely, carbon emissions; hence ‘p’=1. Therefore, ‘n’=‘m’+1.
  4. There exists a pure ‘clean-up technology’ in the firm that produces nothing but absorbs the pollutant.
  5. There is a choice of technique of production.
  6. The environmental agency which controls total emissions of the pollutant issues limited amount of permits and allows firms to operate under these capacities. Each such certificate entitles firms to dispose of one unit of pollutant. Permits not used can be used as ‘rent-seeking asset’ at the end of the period of production.
  7. The total amount of permits per period remains constant over time.

The first assumption is necessary as according to the classical concept of micro-economics, in the long-run, all costs are variable and in today’s world, constant technological upgradation is feasible, admittedly, with a certain cost.

The second assumption provides for the realization that outputs are distinguished as either goods or pollutants; whereas the third assumption is for the sake of simplicity of analysis.

The sixth assumption is a result of emergence of exogenous policy determining agencies operating as per conventions such as the Kyoto Protocol. The fourth and fifth are a result of the sixth assumption. Choice of technique provides the firm with an alternative to use a more or less polluting method or ones even ones that do not directly create pollution but require more/less pollution-intensive inputs.

The seventh assumption is a precondition for the application of the classical concept of a long-run equilibrium position.

The economic problem to be dealt with is to find activity levels of production processes without violating the environmental constraints that are cost-minimizing. Lager proposed a model using the indirect approach, by identifying a set of feasible production input-output equations and applying the environmental constraints to it. However, the direct approach is used in this report which addresses the choice of technique as the key component criteria

Mathematical model:

Let ‘y’ be the square matrix of inputs of commodities to per unit of output by ‘n’ processes. Let ‘x’ be the gross output of goods produced in ‘m’ types of commodities and ‘ε’ be the total amount of emissions created of ‘p’ types pf pollution. As per the assumption, m = n + p. (and p=1)

Therefore, the production function is: n(y) = m(x) + p(ε)

Since p = 1;

n(y) = m(x) + ε

Let the permissible level of emissions determined by the environmental authority be ἐ. In order to adhere to the requirements, firms must adopt a technique of production that includes a clean-up technology ‘s’ with ‘α’ level of efficiency in absorbing sufficient amounts of ε such that it is below or atleast equal to the permissible level, ἐ

Therefore, choose s→α ∀(ε-ἐ)→0.

Depending on the value of ‘α’, there are 3 possibilities that emerge;

(ε-ἐ) > 0; implying technology capable of reducing emissions to below the permitted level.

(ε-ἐ) = 0; where the technology is just sufficient to meet the mandated requirements.

(ε-ἐ) < 0; where technology is of an extremely low grade or insignificant in absorption of emissions.

Interpreting the model:

The incentives for firms to operate on a more efficient mode of production can be understood by the principles of the theory of differential rent as propounded by Ricardo.

As established by the 5th assumptions, permits to pollute are issued by the environmental agency external to the industry and can be used as rent-seeking assets at the end of the period of production. There is a cost involved to purchase such licenses at the start of the production period. This cost per unit ‘cº’ varies directly with the efficiency level of production, thus firms that opt for better technologies face lower costs and enjoy a per unit benefit of ‘1 - cº’. Again, as the firms succeed in reducing their carbon emission levels, they earn Certified Emission Reductions (CERs), the surplus of which can be sold at a price ‘c¹’ per unit to firms that face a deficit of the requirement. c¹ is given to be constant for that period as the number of such permits is itself constant.

‘Rent’ here can be understood as two kinds; direct rent earned by charging ‘c¹’ price per unit for transfer of ownership of carbon credits during that period. And additional per unit benefit of reduction of ‘1 - cº’ which must be also considered as rent because it is a factor reward for choosing production techniques that are relatively less harmful to nature.

Therefore, firms choosing s→α ∀(ε-ἐ) > 0 earn rate of rent = 1 - cº + c¹

Firms choosing s→α ∀(ε-ἐ) = 0 earn rate of rent = 1 - cº. (as c¹ = 0 for such firms)

However, firms that opt for s→α ∀(ε-ἐ) < 0 will earn no rent as cº + c¹ will be the unit cost incurred by the firm.

cost per unit cost per unit cost

-------------------------------------- ----------------------------- cº + c¹


Rent c¹

Highly efficient tech Medium efficient tech Low grade tech

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