Renewal Fees

Patent Renewal Fees and Self-Funding Patent Offices

by

Joshua S. Gans, Stephen P. King and Ryan Lampe* University of Melbourne 17th May, 2004

A socially optimal structure of application and renewal fees for patents would encourage the maximal number of applications while reducing effective patent length. We find, however, that when patent offices are required to be selffunding, resource constraints can distort this fee structure. Specifically, a financially constrained, but welfare-oriented, patent office will tend to raise initial application fees while lowering renewal fees. This creates two detriments to social welfare as it discourages the filing of some patents while extending the effective life of others. Journal of Economic Literature Classification Number: O340. Keywords: patents, renewal fees, incentives, self-funding.

*

Intellectual Property Research Institute of Australia, Melbourne Business School and Department of Economics. We thank IPRIA for funding for this project and Richard Hayes for helpful discussions. All correspondence to Joshua Gans ([email protected]). The latest version of this paper is available at www.mbs.edu/jgans.

1 Patent offices in a variety of countries have become self-funding in recent years. In other words, the patent office must raise revenue from the fees that it charges for intellectual property (IP) services to at least cover its variable operating costs and, in some cases, to provide government with a return on capital. For example, in the UK, the Patent Office was made a ‘trading fund’ in 1991, meaning that it must be self-financing. In particular, it must achieve a rate of return on capital that is set by Treasury. From 1 April 2000 to 31 March 2005, this rate of return has been set at 6%.1 Similarly, the Canadian Intellectual Property Office is a “revenue-generating agency … financed … entirely from fees for intellectual property (IP) services provided”.2 In the United States, the Patent and Trademark Office Corporation Act (1995) ‘corporatised’ the US Patent Office including the requirement that it uses its various fees to cover ongoing costs. At first glance, it might be expected that although self-funding requirements might alter the level of fees charged by patent offices it would not alter its structure. The mix of initial and renewal fees and how these relate to patent length would be set to maximise the social returns from innovative activity. Imposing a budget constraint might be expected to have the same effect that a similar constraint might have on the pricing structure of a regulated multi-product firm; changing levels but not relative prices. The chief finding of this paper, however, is that this is not the case. Self-funding requirements create strong pressures to change fee structure. This is because the fee structure to maximise revenue is distinct from that designed to maximise the social value of innovative activity. Indeed, in fee setting those goals may conflict.

1 2

The Patent Office (UK), Annual report 2003, p.22. CIPO, Intellectual property – innovation on a global scale” Annual report 2001-02, p.2.

2 In this paper, we consider the effect of imposing a revenue raising requirement on a patent office; especially when offices may have difficulty covering their own costs.3 In particular, we consider how such a requirement will alter the fee structure established by the Patent Office and how this will affect the social benefits from IP protection. We show that imposing a revenue raising requirement on a patent office will tend to ‘flatten’ the fee structure set by the office. Initial patent application fees will tend to be set too high from a social perspective while renewal fees will be set too low. This will have the effect of leading to excessively long patents from a social perspective. Renewal fees for patents are fees that patent holders must pay to a relevant patent office if they wish to continue receiving the benefits of patent protection. Figure 1 lists these fees (in Australian dollar equivalents) for various patent offices around the world. The most visible feature of these fees is that they rise over the length of the patent. Moreover, for inventors who require a global patent, these fees can become quite considerable. This means that inventors who discover that their patent is not commercially valuable will likely not renew their patent.4

3

The Economist (“Inventive Ideas: Reforming America’s Patent System,” 6th November 2003) reported that the USPTO was facing resource constraints and a large backlog of patents. In this case, larger patent holders were actually lobbying Congress to raise fees as a means of improving the operation of the office. 4 This pattern is borne out empirically by Pakes (1986). He finds that most US patents are not renewed after 7 years and those that are, are renewed for the maximum patent length.

3 Figure 1: Patent Renewal Fees, 20035 Patent Renewal Fees 6000

5000

4000

Australia

AU$

USA 3000

UK Japan Canada

2000

1000

0 0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19

Year

Economists have found the rising fee structure to be a desirable feature of the patent renewal process. Scotchmer (1999) demonstrates that the renewal fee structure means that patent holders are, in effect, choosing from a menu of intellectual property protection options with a clear trade-off between the overall cost of a patent and its life. Figure 2 demonstrates this trade off for the USPTO and for a global patent. In an environment where policy-makers cannot observe the social value of an innovation, Scotchmer (1999) demonstrates that this renewal system is potentially equivalent to a direct revelation mechanism. She demonstrates that, under certain circumstances, the socially optimal patent system involves increasing renewal fees. Cornelli and 5

Published fees in 2003; for each country the total AU$ equivalent fee payable at a particular date is given. US and Canada based on large entity levels (small entity fees are half these)

4 Schankerman (1999) obtain a similar result. The idea is that with higher renewal fees, lower productivity researchers are revealed and accept lower length patents. This benefits social welfare at the same time as improving incentives to undertake R&D by higher productivity researchers. Figure 2: Total International Patent Fees by Length6 60000

50000

AU$

40000

Global US

30000

20000

10000

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Years

The previous literature has considered socially optimal renewal fees. However, as we show below, if a patent office faces a revenue constraint, it will alter the structure of application and renewal fees for patents. While the fee structure may continue to increase over time, it will tend to be ‘flatter’ and may in fact have a negative slope, with application fees exceeding renewal fees. In this sense, the revenue constraints that have 6

The global fees include the US, Australia, UK, Japan and Canada.

5 been imposed on patent offices in a variety of countries can result in highly suboptimal patent fees from a social perspective. Thus, any benefits7 a country saw from having a self-funding patent office could be offset by the social loss identified here that is created by an inappropriate structure of patent fees.

1.

Model Set-Up We consider a simple model of innovation and its social returns, common to the

literature on patent design (e.g., Nordhaus, 1969; Gilbert and Shapiro, 1990; Klemperer, 1990) but with the addition of uncertainty over the ‘success’ of an invention (Scotchmer, 1999). Let πn be the per period profits earned by an inventor while their invention is under patent and let πn ( < π n ) be their profits when the patent expires. Without loss in generality, we set π n = 0 .8 The subscript, n, denotes the realised state of nature describing the ‘success’ of the invention. We assume that n is distributed over the unit interval, [0,1] , according to a probability density function, g ( n) , and a twice continuously differentiable cumulative distribution function, G ( n) . We assume that an invention generates social welfare, sn, while a patent is in force and sn ( > sn ) following its expiry; both also dependent upon the state of nature, n. This captures the notion that patents reduce social welfare even though they might improve inventor profits. As social welfare encompasses profits it is clear that sn > π n .

7

Such as a reduction in the deadweight losses from distortionary taxation in a full general equilibrium model. 8 Taken literally this could reflect an assumption that following patent expiry, imitators compete away innovative rents. We need not make this assumption, however, but do so here to save on notation.

6 We order the states of nature so that if n′′ > n′ then sn′′ > sn′ , sn′′ > sn′ and

π n′′ > π n′ .9 For simplicity, we assume that π 0 ≥ 0 .10 Thus, if the invention were a process innovation, a lower state may indicate a smaller reduction in marginal production costs than a higher state. If it were a product innovation, a smaller state may indicate a new product that is a closer substitute to existing products than one with a higher ordered state. Our set-up here is general enough to cover a broad set of environments. 1

Let Eπ = ∫ π n g (n)dn be the expected per period profit received by the inventor if 0

the invention is covered by a patent for a period. Following the existing literature, we will assume that the initial cost of invention is F regardless of the state of nature that is 1

actually realised. We also denote the expected social surplus by Es = ∫ sn g (n)dn . 0

The Patent System It is assumed that the maximum length of a patent is two periods following invention and denote these periods by 1 and 2.11 In period 1, the inventor decides whether to take out a patent or not. If they do so, then they pay an initial patent fee, f1 , and is granted a patent for that period. In period 2, the patent-holder can choose to renew the patent or not. If the inventor renews the patent, it is extended for an additional period and the patent-holder pays an additional fee, f 2 . The discount factor between periods is δ.

9

This is an essentially an assumption that profits and social welfare are positively correlated. It simplifies the analysis but if this were not the case this could provide a justification for lower renewal fees. However, we believe that the positive correlation is a relatively safe assumption for inventions overall. 10 This can be easily generalised below, but allows us to avoid trivial cases where an inventor prefers not to renew a patent even at a zero fee because such renewal would create negative profit. 11 The model could easily be extended to the many period case but with the cost of additional notation and no change to the key findings below. For example, as inventors learn information about the profitability of their inventions, renewing them for an additional period has an option value. This will not alter the socially optimal fee structure but may mitigate some of the adverse consequences that arise from self-funded POs.

7 We only consider situations where f1 and f2 are non-negative. In other words, the Patent Office (PO) cannot subsidise inventions.12 We suppose that the PO has a fixed cost per invention that is patented regardless of whether or not that invention has its patent renewed. This is consistent with the relevant costs for a patent office being concentrated on the initial evaluation of inventions. We denote this fixed ‘per invention’ cost by C > 0. We assume that C + F ≤ (1 + δ ) Es , so that it is socially worthwhile to encourage innovations even if they

are patented.13 The timing of our game is as follows: STAGE 1: The PO chooses fees, f1 and f2; STAGE 2: The inventor chooses whether to pay f1 and obtain a patent; STAGE 3: The patent holder observes the state of nature, n, and decides whether to renew the patent and pay f2. There are three key features of this extensive form game: 1.

There is only a single renewal decision over the life of the patent. This is a simplification and easily capable of generalisation.

2.

It is assumed that the inventor does not know the patent’s commercial value in the first period but learns that value before the commencement of the second period. This captures the notion that commercialisation

12

The usual justification for this is based on reality but also could be based on moral hazard problems from spurious patent applications. Relaxing this assumption will not alter the general qualitative findings on the distortions to fee structures that would arise if POs are forced to be self-funding. 13 One could imagine that for some individual inventions, it is not worthwhile incurring patenting costs. However, here, as our focus is on renewals we are considering situations where both the inventor and the PO do not know the patent’s true value until after a patent has been granted. In this situation, this assumption on the ex ante social welfare of patenting is innocuous.

8 prospects are often uncertain at the time a patent is initially granted and may become more apparent by the time the patent is up for renewal.14 3.

The PO chooses the fee structure f1 and f2 knowing both the fixed cost of invention F and the distribution of states of nature G, but without knowing the exact state of nature. This can reflect two alternative situations. The first (and the one followed below) is that the PO must set the patent fees prior to invention taking place and cannot alter these fees ex post. Alternatively, we could think of the PO setting the patent fees without any ability to learn the state of nature through the first patent period. Thus, the PO cannot learn about the state of nature before it sets f2.

The inventor will only invent if it is profitable to patent the invention for at least one period. Further, the inventor does not know the state of nature prior to seeking a patent so that the expected first period profits from invention are just given by Eπ − f1 − F . Given the patent renewal fee f2, the inventor will only seek to renew the patent in period 2 if

π n − f 2 ≥ 0 . For any value of f2, let n% denote the state of nature such that π n% − f 2 = 0 . If π n − f 2 > 0 for all n then we define n% equal to 0. If π n − f 2 < 0 for all n then we define n% equal to 1. Thus, for any level of patent fees set by the PO, the ex ante expected profits 1

for the inventor are given by: Eπ + δ ∫ π n g (n)dn − f1 − δ f 2 − F . Clearly, these ex ante n%

expected profits must be positive if any invention is to take place.

14

This is verified by a number of past researchers (Pakes, 1986; Lanjouw, 1998).

9

2.

Socially Optimal Patent Fees We begin by considering the fees f1 and f2 that would be set by a PO to maximise

social welfare. Noting that the inventor must receive at least one period of patent cover for

invention

to

be

profitable,

n%

1

0

n%

social

welfare

is

given

by

W = Es − C − F + δ ∫ sn g (n)dn + δ ∫ sn g (n)dn . Notice that social welfare does not include the patent fees as these are merely transfers. The optimal fees must allow the inventor to make non-negative ex ante expected profits for any invention to occur. Thus, the PO will set f1 and f2 to maximise W subject to 1

Eπ − f1 + δ ∫ (π n − f 2 ) g (n)dn − F ≥ 0 . If we denote the multiplier on the profit constraint n%

by λ , the first order conditions for this maximisation with respect to f1 and f2 are given by λ ≥ 0 (= 0 if f1 > 0) and −δ [ sn% − sn% ] g (n% ) dfdn%2 + λδ [π n% − f 2 ] g (n% ) dfdn%2 + λδ [1 − G (n% ) ] ≥ 0 (= 0 if f2 > 0) respectively. There are two relevant cases. First, the profit constraint for the inventor may be slack in the sense that Eπ − F ≥ 0 . In this situation, the inventor only requires a one period patent to create an incentive to invent. Note, however, that social welfare only depends on f2 in the sense that lowering f2 increases the likelihood that the patent will be extended in the second period. Thus, in this case, the social planner will set

f1* ∈ [ 0, Eπ − F ] and f 2* ≥ π 1 . The inventor will always invent and patent for only one period so that the invention is freely available in the second period. The PO is indifferent to the exact value of the fees so long as the first period fee is not ‘too high’ and the

10 second period fee is not ‘too low’. For example, f1* = 0 and f 2* = π 1 will maximise social welfare in this case. Second, and of more interest here, is when the inventor must receive at least some profits in the second period in order to have the incentive to invent. In this case, the profit constraint binds so that λ > 0 and f1* = 0 . The optimal value of f2, f 2* , is set to just 1

satisfy the inventor’s profit constraint so that Eπ + δ ∫ (π n − f 2* ) g (n)dn − F = 0 . In other n%

words, the PO maintains f1 at zero but lowers f2 until the inventor is just willing to undertake the inventive activity ex ante. The social cost is that in some high profit (and high social welfare) states of nature in the second period, the inventor extends the patent, despite this being socially inefficient ex post.15 The following proposition summarises these results: Proposition 1. The social planner will set: f1* ∈ [ 0, Eπ − F ] , f 2* ≥ π 1 1

f1* = 0, f 2* = δ G1( n ) ( Eπ + δ ∫ π n g (n)dn − F )

F ≤ Eπ if

n%

1

F ∈ [ Eπ + δ ∫ π n g (n)dn, Eπ )

.

n%

It follows from this analysis that a social welfare maximising PO will set renewal fees as high as possible and initial patent application fees as low as possible subject to encouraging invention. As noted in the introduction, this socially optimal structure of renewal fees is in line with the overall structure of renewal fees for patent offices around the world: that is, renewal fees increase over the life of the patent. In this sense, our basic model extends Cornelli and Schankerman (1999).16

The shadow price of the profit constraint, λ, is given by substituting the value of f2 from the profit constraint into the first order condition for f2. 16 The main model in Cornelli and Schankerman (1999) is general but does not involve post-patent learning. Cornelli and Schankerman also consider a simpler model of ex post learning than that given here. 15

11 Nonetheless, the observation that theoretically optimal patent fees and actual renewal fees have a consistent ‘rising’ pattern does not mean that patent offices are in fact setting socially optimal fees. Indeed, it could be argued that observed patent fees are not ‘steep enough’ to be consistent with socially optimal fees. The actual rate of increase of these fees over the patent period does not appear to be particularly high. In contrast, our model suggests that optimal fees should rapidly increase over time. According to our model, initial fees should be negligible while latter stage (say, > 10 year) renewal fees should be very high. There are a number of potential explanations for this discrepancy. For example, it might be the case that ‘average’ inventions are unprofitable. In other words, the PO might face a situation where many inventions are marginal even if they have long patent lives. As ‘marginal’ and ‘highly desirable’ inventions are not able to be separately identified ex ante, it might be socially optimal to have low patent renewal fees. Even though this leads to a social loss by having patent cover extended high value inventions, it may be more than justified by its effect on encouraging invention in the first place. Our interest here, however, is on the role of the PO in raising revenue. As already noted patent offices in a variety of countries are required to raise funds, for example to cover their own costs. If a PO seeks to raise revenue then it will not in general set the socially optimal schedule of patent renewal fees. In the next section, we consider the optimal renewal fees set by a PO facing a revenue constraint and note that the schedule of these fees is ‘flatter’ than the socially optimal fees.

12

3.

Self-Funding Patent Offices Suppose that a patent office is required to be self funding, such as in the UK,

Canada and the US. How does this funding requirement alter the fee schedule set by the PO? The patent office must establish patent application and renewal fees to cover the per invention cost of C. However, the actual revenue received from a particular invention will depend on the success of that invention and whether or not the patent on that invention is renewed. The average (or expected) present-value revenue received by the PO from fees for any particular invention is given by f1 + δ f 2 (1 − G (n% ) ) . Thus, so long as the PO faces a large pool of inventions, it will recover its costs through patent fees if it sets f1 and f2 so that f1 + δ f 2 (1 − G (n% ) ) − C ≥ 0 . The PO will only be able to be self-funding if the maximum fees that it can set covers the per invention cost. Thus, we assume that (1 + δ ) Eπ − F > C . If this did not hold then the PO could never be self-funding as even maximal expected inventors’ profits would not cover the per invention PO costs. We assume that the PO still seeks to maximise social welfare (W) subject to the inventive activity being undertaken and the additional self-funding constraint. Again there are two relevant cases to consider. First, if the socially optimal fee structure (as presented above) satisfies the revenue constraint then this is clearly the optimal outcome for the PO. In this situation, f1 equals zero with f2 greater than zero but less than π1, so that some patents are renewed in the second period.

13 Alternatively, suppose that the socially optimal fee structure does not meet the revenue constraint. The only way that the PO can raise revenue received by either itself or inventors in such circumstances is to lower f2. This raises the inventors’ expected profits from invention as more inventions will now be profitably renewed in the second period. Clearly the PO will not find it optimal in this situation to leave ‘excessive’ profits with inventors but rather transfer these increased profits to its own revenue requirements. As such, the PO will raise f1 as it lowers f2 so that inventors continue to find invention just profitable in expectation. The extra profit associated with increased patent renewals is seized by the PO through higher patent application fees. The PO will continue to raise f1 and simultaneously lower f2 until it just satisfies its self-funding constraint. To see this second case more formally, note that if the PO just satisfies the selffunding constraint then

f1 + δ f 2 (1 − G (n% ) ) − C = 0 . Denote the PO’s revenue by

R = f1 + δ f 2 (1 − G (n% ) ) and suppose that R < C at the socially optimal fee structure so that such a fee structure is infeasible for a self-funding patent office. For any value of f2, the maximum value of f1 that can be set by the PO is given by the inventors’ profit constraint. Thus,

if

the

PO

sets

f1

to

seize

any

inventor

expected

profits

then

f1 = Eπ − F + δ ∫ π n g (n)dn − δ f 2 (1 − G (n% ) ) . In this case, the POs revenue is given by 1

n%

1

R = Eπ − F + δ ∫ π n g (n)dn . The derivative of R with respect to f2 is given by n%

−δπ n% g (n% ) dfdn%2 and this is negative. The PO needs to increase its revenue relative to the socially optimal patent fees in order to satisfy its funding constraint and the only way to do this is to lower f2. But this is associated with a rise in f1. In particular,

14 df1 df 2

= −δ [π n% − f 2 ] g ( n% ) dfdn%2 − δ [1 − G ( n% ) ] . Remembering that, by definition, π n% − f 2 = 0 , a

fall in f2 will be associated with a rise in f1, allowing the PO to gain more revenue from fees and satisfy its self-funding constraint. The following proposition summarises this result: 2. Suppose that at the socially optimal fees, * * f1 + δ f 2 (1 − G (n% ) ) < C , then a self-funding PO will set, f1 > f1* and f 2 < f 2* .

Proposition

( f1* , f 2* ) ,

If the socially optimal patent fees do not raise sufficient revenue for the PO to cover per invention costs (C), then the PO will have to lower the patent renewal fee below its socially optimal level and simultaneously raise the patent application fee until the selffunding constraint is met. The shadow price of the self-funding constraint can be gained from the first order condition for f2 at the constrained-optimal level of fees. An immediate implication of this analysis is that self-funding patent offices will tend to have fee structures that are ‘flatter’ than the socially optimal fee structures. More inventions will have their patents renewed relative to the socially optimal fee structure with a loss in social welfare given by sn − sn for the relevant inventions. Our analysis allows for simple comparative statics. The greater is the revenue constraint faced by the PO, the lower will be f2 and the higher will be f1. These changes in the optimal schedule will occur until f 2 = π 0 . For this, and any lower, renewal fees, all inventions will be renewed. The PO can, without loss of generality, be considered to set f2 = 0 and R = f1 = (1 + δ ) Eπ − F . In other words, as the self-funding constraint faced by the PO tightens, the PO will alter fees to encourage more patent renewals. This, in turn, raises expected inventors’ profit. But the inventors do not retain this increased expected profit, which is seized by the PO through higher patent application fees. In the extreme,

15 the maximum revenue that can be raised by the PO is given by the expected inventors’ profit absent any renewal fees – when all patents are renewed. If the revenue constraint exceeds this level then it will be unobtainable by the PO. Requiring that a patent office be self-funding can lead to decreasing rather than increasing patent fees over time as reflected by our comparative static results. Indeed, a revenue maximising PO may not charge any renewal fee at all and would certainly set f2 at no greater than π 0 . In such circumstances, inventors’ expected profits are maximised by maximising patent life on all inventions, and all of these profits above the minimal level are earned by the PO.

4.

Conclusion In this paper we have considered how the fee structure set by a patent office

changes if that office is required to be self-funding. Such self-funding requirements have been introduced in a number of countries in recent years. Our analysis shows that requiring the patent office to be self-funding can distort patent fees in a way that lowers social welfare. In particular, a self-funding patent office has an incentive to encourage too many patent renewals from a social perspective. Increasing the number of renewals by lowering renewal fees increases inventors’ expected profit and this profit can be appropriated by the patent office through initial patent application fees. It might seem incongruous that a self-funding requirement for the patent office can lead to lower patent renewal fees. However, what the patent office does when faced by a binding self-funding constraint is to rebalance the patent fees. It is this rebalancing

16 by lowering renewal fees but raising application fees that distorts social welfare. In our framework the same number of inventions are patented but from the social perspective too many of these inventions effectively gain a ‘long’ patent. Of course, the simple structure of the model we have presented may disguise some complications. Importantly, at issue is whether self-funding constraints will bind. For instance, moving beyond two periods would add given renewals an option value as inventors learn more information about the profitability of their intellectual property. While a fiscally constrained patent office will still flatten its fee structure in this case, the option value will reduce the chance such constraints bind. On the other hand, patent offices involve overhead costs in additional to marginal application costs considered here. Our result on the flattening of the fee structure will be strengthened in this case as the revenue target across all inventions will be more likely to bind and it is this rather than the precise structure of patent office costs that motivates a reliance on application as opposed to renewal fees as a revenue raising instrument. Our model provides a clear empirical prediction about the implications of introducing a self-funding requirement on a patent office. To the extent that this constraint binds, we would expect to see the patent office rebalance its fees by raising application fees relative to renewal fees. Indeed, Lerner’s (2000) study of the evolution of patent office practices finds evidence consistent with this prediction. He demonstrates that the ‘steepness’ of the slope of renewal fees (as measured by the proportion of total fees charged in the second half of the life of a patent) across countries and time is explained by changes in the complexity of national economies as measured by population, international trade intensity and also GDP per capita. While, as Lerner

17 suggests (based on Cornelli and Schankerman, 1999; and Scotchmer, 1999), increasing information asymmetries could be at the heart of this, it could also be the case that as economies grow, self-funding constraints become weaker. Perhaps by including measures of the subsidy to patent offices over time, this explanation could be explored.

18

References Cornelli, F. and M. Schankerman (1999), “Patent Renewals and R&D Incentives,” RAND Journal of Economics, 30 (2), pp.197-213. Gilbert, R. and C. Shapiro (1990), “Optimal Patent Length and Breadth,” RAND Journal of Economics, 21 (1), pp.106-112. Klemperer, P. (1990), “How Broad should the Scope of Patent Protection Be?” RAND Journal of Economics, 21 (1), pp.113-130. Lanjouw, J.O. (1998), “Patent Value in the Shadow of Infringement: Simulation Estimations of Patent Value,” Review of Economic Studies, 65 (3), pp.671-710. Lerner, J. (2000), “150 Years of Patent Office Practice,” Working Paper, No. 7478, NBER. Nordhaus, W. (1969), Invention, Growth and Welfare: A Theoretical Treatment of Technological Change, MIT Press: Cambridge (MA). Pakes, A.S. (1986), “Patents as Options: Some Estimates of the Value of Holding European Patent Stocks,” Econometrica, 54 (3), pp.755-784. Scotchmer, S. (1999), “On the Optimality of the Patent Renewal System,” RAND Journal of Economics, 30 (2), pp.181-196.