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Ragnar Arnason*

Resource Rent Taxation: Is it Really Nondistortive?
A paper presented at the

2nd World Congress of Environmental and Resource Economists

Monterey June 24 - Jun 27, 2002

A Preliminary


* Department of Economics

University of Iceland
It is often taken for granted that taxation of rents is economically nondistortive. In certain areas of natural resource use, e.g. oil extraction and fisheries, this nondistortion principle has been used to justify taxation of what is regarded as resource rents. This paper challenges the view that such taxation is generally nondistortive. Within the framwork of a general model of natural resource extraction, the paper argues that taxation of resource rents will in general affect the time profile of natural resource extraction. The paper, moreover, argues that through its impact on exit and entry, resource rent taxation will generally affect the number and composition of firms in the industry and may in this way have a secondary efficiency impact.

0. Introduction
It is a common belief that taxation of natural resource rents is economically non-distortive and, as a result, superior to most other methods of raising government revenues. This presumption, combined with non-economic social sentiments, seems to have prompted several economists to recommend special taxes on various resource extraction activities including mining (Garnault and Clunies-Ross 1975, Fraser 1993, 1998, Miller et al. 2000) and fisheries (Grafton 1995, 1996). Similar considerations have apparently encouraged many governments (including for instance the UK, USA, Norway and New Zealand) to impose special heavier taxation on natural resource use (Miller et al. 2000).
It is interesting to note that the historical roots of this belief can be traced to the land tax initially proposed by James Mill (John Stuart’s father) on the theoretical basis laid by Ricardo (1821) and subsequently popularized by Henry George (1879) the initiator of the so-called Georgeism (Blaug, 1996). The basic justification for the land tax in the 19th Century was essentially the same as for the resource rent tax in modern times. Land was seen as fixed and indestructible. Its use generated land rents. Taxing these rents would not reduce land use. Therefore, land provided an ideal tax base from an economic perspective. This argument was further strengthened by the moral issue. Land was seen to belong to all  not just the formal owners of land. Hence, taxing land to finance public expenditures also seemed ethically attractive to many people.
These views have met with considerable practical success. Natural resource use (esp. land use, mining and lumbering) is now often more heavily taxed than other economic activities. In many countries natural resource extraction is, as a matter of course, subject to royalties, special income taxes, rent taxes and cost recovery charges over and above what is the rule for other industries. And when it comes to natural resource industries which are not already heavily taxed, considerable pressure is being exerted to impose such taxation or raise those already in place.1
Given all this, it seems in order to examine whether and to what extent taxation of natural resource rents is in fact non-distortive. This paper contributes to that task. To do so successfully, however, we must first define the concept of resource rents.
The concept of resource rents, or, for that matter, economic rents in general, has been somewhat loosely used in economic writings. For instance, in many influential papers on resource rent taxation (see e.g. Garnault and Clunies-Ross 1975 and 1979), resource rents seem to be used almost synonymously with profits. For our purposes, however, it is necessary to be completely clear about the concept. Armen Alchian in the New Palgrave Dictionary of Economics (1987) essentially defines economic rents as the payment (imputed or otherwise) to a factor in fixed supply. Alchian illustrates his definition with the familiar diagram in Figure 1 often used to illustrate Ricardo’s theory of land rents.

Figure 1

Economic Rents

In this diagram, the market-clearing price is p. However, since the quantity of the factor is assumed fixed, the corresponding supply, q, would be forthcoming even if the price were zero. Hence, the entire price, p, may be regarded as a surplus. The total surplus or economic rent attributable to the limited factor is the rectangle pq.

For later purposes it is useful to note that economic rents can also be written as D(q)q, where D(q) represents the value of the demand function at q. It is well known (see e.g. Varian 1984) that in competitive markets when the factor is used for production purposes D(q) represents the marginal profits of using the factor. When, on the other hand, the factor is used directly for consumption D(q) would be proportional to the marginal utility of consuming the factor.
Note that the economic rents depicted in Figure 1 also represent total profits2 to the owner of the factor in fixed supply. It doesn’t, however, represent the total economic benefits of the supply q. This is measured by the sum of economic rents and the demanders’ surplus represented by the upper triangle in the diagram. Thus, if the demanders are producers extracting (but not buying) a natural resource, their profits would be the sum of economic rents and the demanders’ surplus.
The concept of economic rents relies heavily on the assumption of a factor in fixed supply. If there is no such factor, economic rents are really not defined.3 While theoretically non-problematic, the empirical relevance of factors in fixed supply may be questioned. After all it is in the nature of the economic activity to find ways to adjust supply to demand, particularly when profits can be made doing it. Even, Ricardo’s (1821) argument in terms of the “original and indestructible powers of the soil” does not ring true. Surely, modern technology has enabled us to both damage and enhance these powers. Thus, it turns out to be difficult to find examples of factors that are truly in fixed supply especially in the long run.
In the very short run, on the other hand, many factors are in fixed supply and, consequently capable of earning economic rents. To represent this phenomenon of transient or temporary economic rents, Marshall (according to Achian 1987) apparently initiated the concept of quasi-rents.
This general theory of economic rents can easily be extended to natural resource extraction, at least in a formal sense. Let q represent the volume of natural resource extraction and (q) the associated profits. Then clearly the derived demand for q will be q(q) and the natural resource rents q(q)q.
The question of truly fixed supply, however, is no less pertinent to natural resource extraction than to other factors. In fact, for most natural resources it is technically possible and often economically advisable to vary the level of extraction over time. Moreover, at a point of time and for a given level of the resource, variations in the volume of extraction often involve costs, marginal user costs, giving rise to an upward sloping supply curve. Thus, in the case of natural resource extraction, it is often difficult to maintain the assumption of fixed supply. Nevertheless, this assumption seems to be at the root of the widespread belief that resource rent taxation is non-distortive.
Natural resource extraction is often associated with economic inefficiencies due to imperfect property rights resulting in externalities. In this paper we ignore complications of this nature. More to the point, we will assume that without taxation resource extraction is fully efficient. Taxation for management purposes, i.e. in order to further efficiency, is not a part of this study. Here we only consider taxation as a means to generate government revenues. Also, in this paper, we do not directly deal with the question of whether there exist neutral taxes. Our concern is only with the distortive or non-distortive properties resource rent taxes.
The rest of this paper is organized as follows: In the next section, section 1, a model of a natural extraction general enough to cover both renewable and non-renewable resources is presented. The following section examines the impact of resource rent taxation in a general setting concluding that such taxation would in general be economically distortive. Then, in section 3, numerical examples for non-renewable and renewable resource extraction industries are worked out. Finally, in section 4, the results of the paper and possible extensions are discussed.

  1. The natural resource extraction industry

Consider a natural resource extraction industry characterized by the instantaneous profit function:

  1. (q,x), defined for q,x0,

where q denotes resource extraction and x the stock of the resource both at time t. The profit function is taken to have the usual properties, i.e., a positive level of both arguments is needed for positive profits, to be monotonically increasing in the stock variable, x, to be increasing in the flow variable, q, up to a point, and to be concave. More formally: (0,x)=(q,0)0, x(q,x)>0 and q(q,x)>0 if q<. For analytical convenience it is, moreover, assumed that the profit function is differentiable as needed.

In what follows, we will variously refer to (q,x) as applying to individual firms and to the industry as a whole. To be able to do this consistently obviously requires considerable restrictions on the structure of the industry.4 However, explicit modelling of individual firms would substantially complicate the analysis with little additional insight for this inquiry.
The resource is assumed to evolve according to the differential equation:

  1. =G(x)-q, defined for x0,

where G(x) is the renewal function of the natural resource having the usual continuity and concavity properties and a point x1>0 such that such that G(x1)=0. Obviously, if the resource is non-renewable, G(x)0,  x. If the resources is renewable,  x such that G(x)>0. As the (q,x) function, the function G(x) is assumed to be as differentiable as needed.

The firms in the industry, and, consequently, the industry as a whole, are assumed to seek to maximize the present value of profits. For this purpose they can decide to be active and, if active, select a time path of extraction, {q}. Formally this problem can be expressed as:

  1. ,

Subject to: = G(x)-q

x(0) = x0

x, q,T  0.
The terminal time of the extraction activity is T. So choosing a finite T is equivalent to becoming inactive, i.e. leaving the industry. It is important to note that becoming inactive is qualitatively different from setting the extraction rate to zero. x(T) is the resource stock left at the terminal time. In the case T is finite and the resource is not completely exhausted, this will have to be determined. Finally, x0 is simply the stock of the resource available at the outset of the maximization programme.
According to the maximum principle (Pontryagin et al. 1962, Leonard and Long 1992). The necessary (and in this case sufficient) conditions for solving problem (I) include:

    1. q -  0, q  0, (q - )q = 0,

    2. - r = -x - Gx,

    3. = G(x)-q,

    4. H(T) = (q(T),x(T)) + (T)(G(x(T))-q(T))=0,

    5. (T)  0, x(T)  0, (T)x(T)=0.

Expressions (3.1)-(3.5) describe the behaviour of a profit maximizing resource extraction industry when there is no taxation. Comparing these conditions with the corresponding ones under taxation provides an indication of whether the taxation is distortive or not. It should be noted that since the industry takes prices as exogenous, conditions (3.1)-(3.5) also represent a social optimum if, as is usually assumed, the prevailing prices are true. It follows that any shift from these conditions represents a movement to a socially inferior position.

The above model is quite simplistic. In addition to its glossing over the aggregation issue it omits any consideration of physical capital and, consequently, investment therein. Moreover, it ignores the existence of uncertainty that constitutes an important aspect of most resource extraction industries. These simplifications, however, seem of little consequence for the subject of this study. If resource rent taxes turn out to be distortive in this simple models, it seems obvious that they will also be so in more realistic models where the scope for distortion is greater. If, on the other hand, resource rent taxes are found to be non-distortive in this simple model, they may, of course, still be distortive in a more realistic setting.
Now, as discussed in the previous section, resource rents may be are defined as

  1. R(q,x) = D(q,x)q = q(q,x)q,

where q(q,x) is the derived demand for the extracted resource. Note that these resource rents are instantaneous rents. They refer to a point in time. Resource rents for the extraction programme as a whole would be given by the present value of the complete time path of rents.

In the resource extraction industry defined above, the supply price of the resource at quantity q is given by the co-state variable or shadow price, . This, as shown by the conditions, (3.1)-(3.5), above is a function depending on the state of the resource, x, and the level of extraction, q, as well as the other variables of the problem. If positive extraction is optimal there is, at each point of time, a supply/demand equilibrium defined by the equation q= in expression (3.1). It follows that for a resource extraction industry, we may draw a resource rent diagram corresponding to the conventional one in Figure 1.

Figure 2

A Resource Extraction Industry: Resource Rents

As the supply curve of q (really the shadow price ) is drawn in Figure 2, the area referred to as “Resource rents” does not appear to be economic rents at all, although parts of it may represent a producer’s surplus (in this case resource owner’s surplus). Note, however, that  is merely an imputed or notional price. It represents the opportunity cost of reducing the size of the resource, sometimes referred to as a user cost (Scott 1955). It does not represent outlays of money. Thus, in a certain sense it is not marginal cost at all. It is certainly not a marginal cost in the sense of Ricardo and the definition of economic rents discussed in the previous section. Thus, the multiple q appears to represent economic rents in the traditional sense and this is the way we will regard it in this paper. In any case this multiple seems the closest parallel to economic rents that can be found in a resource extraction industry.

From the perspective of resource rent taxation, however, the crucial message of equation (4) is that resource rents are a function of both the extraction rate and the level of the resource as well as of other variables entering but not explicit in the profit function. We refer to this as result 1.
Result 1

Resource rents depend in general on extraction rates and the level of the resource.

So, the supply q giving rise to the resource rents q is not at all fixed in the traditional sense of Ricardo (1821) and Alchien (1987). It is the outcome of profit maximization by the resource extractor taking into account the state of the resource and other exogenous variables entering the profit function such as prices. Clearly, if these exogenous variables change, so will the optimal extraction quantity and hence resource rents.
Given this, it is useful to deduce as much as possible about the shape of resource rent function, R(q,x). Clearly, Rq(q,x)=D(q)(Dq(q)q/D(q) +1). So, the effect of increased extraction on rents is positive if the elasticity of demand5 is less than unity and vice versa. By the same token rents are maximized at the level where the elasticity of demand equals unity. Moreover, if qqq0, R(q,x) will be concave in q. Finally, Rx(q,x)>0 iff qx(q,x)>0.
Given that some level of resource extraction is profitable resource rents are nonnegative. We refer to this result as result 2.
Result 2

Assuming that extraction is profitable resources rents in the resource extraction industry defined by (1) and (2) are nonnegative.


If extraction is profitable, the optimal extraction q*>0. Therefore, q(q*,x)= according to (3.1). It is well known (see e.g. Leonard and Long 1992) that along the optimal path, the shadow value of the resource, *=V*/x, where V* refers to the maximal value of the programme. If extraction is profitable V*/x cannot be negative. It follows that R(q*,x)=q(q*,x)q*=*q*0. 

  1. Resource rent taxation: General analysis

Consider now the imposition of a tax on resource rents. Let the amount of the tax be:6

  1. T = R(q,x),

where R(q,x) represents resource rents as defined in the previous section and is the rate of taxation. From the perspective of the industry the profit maximization problem now is:

  1. ,

Subject to: = G(x)-q

x(0) = x0

x,q,T  0.
The necessary conditions for solving (II) include:

    1. q - Rq -  0, q  0, (q - Rq - )q = 0,

    2. - r = -x + Rx - Gx,

    3. = G(x)-q,

    4. H(T) = (q(T),x(T)) - R(q(T),x(T))+ (T)(G(x(T))-q(T))=0,

    5. (T)  0, x(T)  0, (T)x(T)=0.

Comparing these necessary conditions with the ones without taxation, i.e. (3.1)-(3.5) shows that the imposition of a resource tax modifies conditions (3.1), (3.2) and (3.4). Modification of the first two necessary conditions will in general alter the optimal paths of the control and state variables as well as the equilibrium position of these variables in the case of renewable resources. Modification of the fourth necessary condition suggests that the imposition of a resource rent tax may influence when a programme is terminated.

It is important to realize that condition (6.4) is really a component of a set of more general entry/exit conditions. Condition (6.4) represents the condition for the optimal exit of firms already in the industry. The corresponding condition for optimal entry of firms into the industry would be

    1. H(0) = (q(0),x(0)) - R(q(0),x(0))+ °(0)(G(x(0))-q(0))0,

where °(0) represents the firms’ shadow value of the resource.

Condition (6.6) must be carefully interpreted. First, although it could apply to a whole industry, it is more natural to interpret it in terms of a single firm. As such, this is a condition for a given firm to enter the industry. Second, °(0) is the shadow value of the resource as seen from a firm outside the industry. This does not have to be in accordance with the shadow value assessed by firms in the industry. For a firm outside the industry °(0) could easily be zero. But it could just as well take on another value if the resource has alternative (possibly non-extractive) uses for the firm7. If this shadow value is zero, however, (6.6) reduces to the more familiar entry condition (q(0),x(0))-R(q(0),x(0))0, i.e., hat expected profits are positive. Third, the variables q(0) and x(0) represent the optimal levels of these variable, if the firm enters. Finally, the resource rent tax, R(q(0),x(0)), should be interpreted as what the firm expects to be charged.8
Taking, (6.4) and (6.6) together, it is clear that resource rent taxes may alter the conditions for entry to and exit from the industry. Hence, if firms are not identical, such taxes, even if they will not close the industry prematurely, may alter the composition of firms participating in the industry.9
To summarize, we have found that resource rent taxes will generally affect extraction paths, sustainable equilibria, the opening and closing of the industry and the composition of companies in the industry. We thus have the basic result:
Proposition 1.

Resource rent taxes are in general distortive.

The economic rationale for Proposition 1 is straight-forward. Resource rents depend on the extraction path selected by the industry. They also depend on the participation of individual firms or the industry as a whole in the extraction activity. Thus, the industry and its constituent firms can to some extent counteract the burden of the taxation by modifying these variables.
It is important to realize, however, that Proposition 1 does not assert that that resource rent taxes are distortive in all cases. There are situations, probably unrealistically simple, under which resource rent taxes may not have any distortive impact. One such case, for instance, is a renewable resource industry with linear extraction technology and identical firms.

  1. Examples

We will now illustrate the distortive nature of resource rent taxation by numerical examples from non-renewable and renewable resource extraction industries. For ease of computation and exposition these examples will be based on very simple models.

A non-renewable resource industry: Mining
Consider a simple mining industry with the cost of production independent of the quantity of reserves. More to the point, let the profit function of this industry be:

  1. (q)= pqC(q) = pq – (a+bq2),

where, as before, q refers to extracted quantity at a point of time, p denotes its unit price and a and b are positive parameters.

Substituting this specification and the condition that G(x)0, all x, into the necessary conditions (3.1) to (3.5) we can easily derive the following optimality results:

  1. The available resources will be exhausted in finite time

  2. The terminal time, T, is determined by the equation:

(7.1) ,

where x0 represents the initial reserves and r is the rate of discount.

  1. The extraction path is given by:

(7.2) .

As discussed in the previous section, a resource tax on this industry would be:
(8) R(q,x) = q(q,x)q = ( pq – 2bq2)
Subtracting (8) from the RHS of (7) yields the profit function after taxes as:

  1. (q,)= p(1-)q – (a+(1-2)bq2).

So, in this case, the impact of the resource rent tax is to reduce the net price of production and the marginal costs of extraction. The first effect is quite intuitive. The second stems from the fact that increased production is now less costly than before because it reduces resource rent taxes.

Substituting p(1-) and (1-2)b in for a and b in (7.1) and (7.2) it is now straight-forward to calculate the terminal time and extraction path for the resource rent case. Briefly, the imposition of the resource rent tax leads more intense extraction and earlier exhaustion time than would otherwise be the case. So, interestingly, the resource rent tax discourages conservation.
Assuming certain numerical values of the parameters this result can be illustrated. The parameter values chosen are:













Let us moreover set the tax rate at =0.2. This means that 20% of resource rents are taxed away.

The impact of this tax on the profit maximizing extraction paths is illustrated in Figure 3

Figure 3

Impact of resource rent taxes on extraction: An example

As shown in Figure 3, this resource rent tax (=0.2) has a very significant impact on the extraction profile. The impact on the present value of total social benefits (profits before taxes) from the extraction activity, however, is not very great. This is only reduced by some 7%. Company profits, however, are reduced by some 25%. If the resource rent tax were raised to 0.35, however, the distortive effect of the tax would be much greater. Social benefits would be reduced by about 40% and retained profits by the firms by over 90%.

A renewable resource industry: A fishery
Consider a simple fishery with a profit function

  1. (q,x)= pqC(q,x) = pq – (a+bq2x-1),

where q represents the harvest rate and x the fish stock biomass both at a point of time. p is the unit price of harvest and a and b are positive parameters.

The biomass growth function is taken to be the the logistic function:

  1. G(x) = x - x2,

where  and  are parameters with  representing the intrinsic growth rate and / the maximum equilibrium biomass often referred to as the virgin stock equilibrium.

Now, inspection of the necessary conditions (3.1) to (3.5) reveals that if the fishery is productive enough, dynamic optimization will involve a non-zero equilibrium for q and x defined by10:

    1. G(x) + x/q = r,

    2. G(x) – q = 0.

It may be mentioned that the second term on the LHS of (12.1) is often referred to as the marginal stock effect (Clark and Munro 1975). In an optimal equilibrium, this term is positive encouraging conservation of the resource.

Substituting (10) and (11) into these equilibrium conditions we can easily derive the following optimality equilibrium conditions for our special model:

    1. x - x2 = 0.

As discussed in the section 2 above, a resource tax on this industry is defined as:

(14) R(q,x) = q(q,x)q = ( pq – 2bq2x-1)
Subtracting (14) from the profit function defined by (10) produces after some rearrangements:

  1. (q,x,)= p(1-)q – (a+(1-2)bq2x-1).

So, just as in the mining example above, the impact of the resource rent tax is to reduce the net price of production and the marginal costs of extraction.

Substituting p(1-) and (1-2)b in for p and b in (13.1) it is now straight-forward to derive the profit maximizing equilibrium conditions under the resource rent tax. The result is:
(16.1) ,

    1. x - x2 = 0.

So, clearly, the equilibrium conditions are modified by the imposition of the resource rent tax.11 It obviously follows that the resource rent tax will also alter the optimal adjustment paths of the fishery.

Inspection of (16.1) reveals that a positive resource rent tax will reduce the marginal stock effect (the third term in (16.1)) and, consequently, lead to a lower equilibrium biomass level. Obviously, if there is no resource rent tax, =0, (16.1) reduces to (13.1).
By assuming certain values of the parameters, it is possible to numerically illustrate this result. The parameter values are:













Given these parameters, we can now calculate the equilibrium biomass level and the corresponding social profits and tax revenues as a function of the tax rate, . The relationship between the biomass level and the tax rate is illustrated in Figure 4.

Figure 4

Resource rent taxation and the optimal equilibrium biomass: An example

As illustrated in Figure 4, the optimal equilibrium biomass level is monotonically declining and quite sensitive to the resource rent tax rate. Thus, a resource rent tax rate of 0.5 reduces the equilibrium biomass by almost 20% and a tax rate of 0.9 reduces the it by by about 50%. The harvest rate, also depicted in Figure 4, is, on the other hand, much less sensitive to the resource rent tax. This, of course, is because the resource rent tax initially moves the equilibrium biomass toward the maximum sustainable level. Thus with a resource tax rate of 0.5 the harvest increases by 1.4% compared to no resource rent tax.

Figure 5

Resource rent taxation and the optimal equilibrium biomass: An example

Social benefits (profits before taxes), as predicted, decline monotonically with the tax rate. The tax revenue, on the other hand increases up to a certain point and declines after that. These relationships are illustrated in Figure 5.

4. Discussion
The basic result of this paper is that resource rent taxation is generally distortive. As demonstrated, it normally induces firms to alter the time path of extraction and may influence their entry and exit decisions as well as the particular resource stocks that come under exploitation.
Although this result contradicts certain widely held beliefs concerning resource rent taxation, it can hardly be said to be surprising. After all, resources rents clearly depend on the level of extraction. Consequently, the same applies to the resource rent tax. This means that firms can reduce their resource rent tax-burden by adjusting the level of extraction. This they will do if it increases their retained profits. The paper suggests that only in very special situations, namely linear profit functions and identical firms, will this not necessarily be the case.
The model on which these results are based is quite simple. This, however, apparently does not subtract from the generality of the results. The indications are that the more general the model the less likely it is that resource rent taxation will be nondistortive. Among other things not allowed for in the model are explorations and investment in new resource developments. It seems pretty obvious, however, that resource rent taxation will reduce such activities if only for the reason that the expected returns will now be less than before. If the companies are risk averse the impact will be greater.
The situation, of course, is changed if the tax collector, presumably the government, is in a position to fix the quantity extracted. Then the resource rent is fixed and we are back in the Ricardian-Alchian framework of fixed supply. Thus, under those circumstances, the firms cannot avoid the resource rent tax by adjusting the extraction rate. It would be premature, however, to conclude that the resource rent tax was non-distortive. The tax could still affect entry and exit and therefore the composition of firms in the industry. By a similar argument, it could also affect the resource stocks being exploited. Another serious disadvantage is that the tax collector would not be in strong position to set the optimal quantity of extraction which moreover varies over time and fluctuates with the parameters of the situation. It is well known that due to information, calculation and implementation problems governments generally fail miserably in economic micro management of this kind. Therefore, even if the resource rent tax could, in theory, be rendered non-distortive by the government fixing the quantity of extraction, the inefficiency would reappear in suboptimal choices of the extraction quantity.
In the examples presented it was found that the distortionary impact of resource rent taxation is toward less conservation of natural resources than would otherwise be the case. While, this has not been established as a general principle, this finding may be a matter of some additional concern.
By its distortionary impact, resource rent taxation reduces the funds available for consumption and investment. For this reason, resource rent taxation is likely to have a negative impact on aggregate investment and hence the growth path of the economy. This negative impact will be counteracted if the resource tax revenues are more effectively used by the tax collector (government) than the private sector and exacerbated if the opposite holds true. For economies heavily dependent on natural resource extraction industries, these macro-economic impacts of resource rent taxation may be quite significant.
It is important to realize that the distortionary impact of resource rent taxation does not by any means rule it out as a sensible tax alternative. When it comes to the financing of government expenditures the relevant question is not whether a given tax option is distortive or not, but whether it is more or less distortive than the other alternatives available. The above analysis does not answer this question. In fact, a priori, it seems unlikely that this question can be answered on a theoretical basis.
The result that resource rent taxation is generally distortive raises the question of whether there exists a form of taxation to collect resource rents that is non-distortive. The above analysis says nothing about that. Note, however, that such non-distortive taxation, if it exists, would not be resource rent taxation. It would be something else. Indeed, if it is to be truly non-distortive it could not be related to any decision variables of the firms.

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1 Fisheries provide is a case in point. Special fisheries taxation has for instance been advocated in New Zealand (Johnson 1995, New Zealand Fishing Industry Board 1993) and Iceland (Arnason and Jonsson 1993, Auðlindanefnd 2000) on precisely these grounds.

2 Note that since the factor is by assumption in fixed supply, there can be no opportunity costs associated with its supply.

3It may be noted that for factors in elastic supply, the concept of producers’ surplus applies. In fact, economic rents may be regarded as the special case of producers’ surplus applying when the elasticity of supply equals zero.

4 A sufficient condition is that the firms are identical.

5 Defined as (Dq(q)q/D(q))-1.

6 More generally a resource rent tax would be T = (R(q,x)), where is an increasing function. This generalization, however, would not qualitatively alter the results of the analysis.

7 Consider for instance the case of a firm in tourism which can use a particular spot of nature for purposes of tourism and/or mining.

8 If entry or exit are not costless, there would be a need to form expectations about future taxation as well.

9 Or, from a slightly different perspective, alter the natural resources that are exploited.

10 Equilibrium is characterized by ==0. Thus, if the equilibrium q is positive, (3.1) and (3.2) are reduced to: q =  and r = -x - Gx,, respectively. From these two equations (12.1) is easily derived. (12.2) follows immediately from (3.3).

11 This confirms a result previously derived by Johnson (1995).

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