Clarke's Analysis Research Articles

Tele-psychotherapy for individuals with obsessive-compulsive disorder during the COVID-19 outbreak: A qualitative study.

One way of delivering psychological services is tele-psychotherapy, which has attracted significant attention as a viable approach. This study aimed to identify important variables in the application of tele-counseling and psychotherapy for the treatment of patients with obsessive-compulsive disorder (OCD) in Isfahan, Iran. This research employed an exploratory qualitative methodology. The participants of this study consisted of all the clients with OCD and all the psychotherapists in the city of Isfahan. Purposive sampling was employed, and following a series of semi-structured interviews with 35 individuals with OCD and 11 counselors in this area, the sample size reached a saturation point. The data was analyzed by Braun and Clark's thematic analysis method. Based on the findings of Braun and Clark's analysis, three primary themes emerged concerning tele-counseling: opportunities, requirements, and challenges. According to the feedback received from therapists and clients, remote services could offer promising prospects to both groups by providing accessible locations and flexible time management. However, to get the full benefits of teletherapy, therapists should consider certain factors to enhance the therapeutic alliance. Moreover, there are challenges that need to be addressed.

Sevoflurane analysis in forensic cases using headspace-gas chromatography-mass spectrometry: A case study

The objective is to present a case study related to forensic analysis of Sevoflurane Using Head Space (HS)-GCMS. For qualitative detection of volatile substances, this methodology might be helpful in conducting forensic analysis of such substances. Sevoflurane is an ether inhalation general anaesthetic agent. Sevoflurane is a volatile nonflammable fluorinated methyl isopropyl ether inhaled anaesthetic, chemically related to desflurane and isoflurane (C. M. Rosales, J. Forensic Sci., 2007, 52, 1408–1410). The low solubility and the absence of pungency facilitate rapid mask induction. It has been used as an inhaled anaesthetic since 1985. Its major distribution is initially to areas of high blood flow (brain, heart, liver and kidney) and later to less perfused organs. Sevoflurane can cause cardio-respiratory depression, hypotension, and malignant hyperthermia (M. Adachi, J. Anaesth., 1992, 68, 214–215). Seizures (convulsions) can occur during anaesthesia with Sevoflurane but Sevoflurane related deaths are rare. Various studies have been conducted for detection and quantification of Sevoflurane in postmortem and toxicological studies. The case was submitted at PFSA (Punjab Forensic Science Agency) for analysis consisting of bottle of suspected narcotics. The bottle was recovered from accused committing offence of criminal intimidation, life threat and physically assaulting his ex-wife and children. He trespassed into house and sprayed her with some bottle in order to molest her. He also threatened her children and his father in-law with pistol. The suspected bottle of spray was analyzed qualitatively using HS-GC-MS with slight modification in already validated method. About 1–2 mL of liquid was taken in headspace vial and heated up to 50–60oC (for vaporization) and about 1–2 μL of headspace sample was injected manually in GC. A gas chromatographic system 7890B series (Agilent Technologies, Palo Alto, CA, USA) coupled to MS detector. Agilent HP-5MS Ultra Inert column (30 m length, 250 μm ID, with film thickness of 0.25 μm) (D. Bourdeaux, J. Chromatogr. B. Analyt. Technol. Biomed. Life Sci., 2010, 878, 45–50). was used for the separation of constituents. Injection volume of 1 μL was used in split mode in 20:1 ratio at 250 °C. Helium gas was used as carrier gas with 1 mL/min flow rate with inlet pressure 12.051 psi. Oven temperature for GC column at 50 °C upheld for 2 min and then gradually increased to 150 °C at 50 °C/min for 1 minute. The total run time was set up for 5 min. The temperature for MS source and MS Quad were 230 °C and 150 °C respectively. Scan mode for m/z from 43–220 was done. Agilent GC Chemstation was used for data analysis. Results were compared with reference book (C. Maffat, Clark's Analysis of Drug and Poisons. 3rd. London-Chicago: Pharmaceutical Press, 2004, 2, 1558–1559). This exceptional crime case of using sevoflurane bottle for threatening and attacking received in our lab was evaluated for the presence of suspected drug. The sample analyzed using HS-GCMS showed a single peak on chromatogram at 1.282 + 0.01 minutes and the MS ions were matched with reference MS spectrum showing Sevoflurane which is being used as inhalation anaesthetic. Various studies suggested that Sevoflurane could possible cause irreversible circulatory depression and hypoxia and may cause death. It is the new case of decapitation with sevoflurane. The reported method is quite short and efficient in detection of Sevoflurane using HS-GCMS.

Factors and Levels of Student Engagement in a State College: A Mixed-Methods Study

This sequential explanatory mixed-methods study determined the factors and levels of student engagement among the 493 students in Northwestern Mindanao State College of Science and Technology, Tangub City, Philippines. The quantitative data gathered using survey questionnaires revealed the following: the students’ levels of perception on the importance of competence, autonomy, relatedness, student-teacher transaction, and student-institution transaction to students’ engagement are very important; the levels of affective engagement, cognitive engagement, and behavioral engagement are very high, and social engagement is high; the factors and levels of student engagement have positive correlation; and the student-teacher transaction is the best predictor of student engagement. Using in-depth interviews of 12 participants picked using criterion purposive sampling, the qualitative data, analyzed using Braun and Clarke analysis, arrived at nine themes for the importance of the factors to students’ engagement and 15 themes for the students’ engagement in the four dimensions. The factors of student engagement are important since students are given the freedom to accomplish their dreams and develop themselves through good relationships with classmates, desirable personal and professional qualities of the teachers, and the support of the college. The students’ engagement in the four dimensions can be attributed to the goals that they have to achieve, the support from teachers and the school, their active participation, the guidance from the more knowledgeable others and the harmonious relationship with peers. It is recommended that the College invest in various support services to create a pleasant learning environment, devote itself to faculty training to prepare them for teaching, and implement activities that will enhance student engagement.

Simultaneous analysis of oxytetracycline hydrochloride, lidocaine, and bromhexine hydrochloride in the presence of many interfering excipients.

A gradient elution high-performance liquid chromatographic method with a diode array detector is introduced for the first time for the simultaneous estimation of three drugs, namely, oxytetracycline hydrochloride (OXT), lidocaine (LDC), and bromhexine hydrochloride (BRH), in a veterinary formulation (OxyClear® solution) that contains many interfering additives. The method used a C-8 column. The chromatographic eluting solution included acidified water (0.1% trifluoroacetic acid in water) and acetonitrile at a 1-ml/min flow rate and 254 nm as a nominated detection wavelength. The chromatographic process was assessed in terms of linearity, precision, accuracy, LOD, and LOQ. OXT, LDC, and BRH were linear in the range of 1-60, 5-100, and 1-60 μg/ml, respectively. The three drugs were determined successfully without the interference of three excipients having UV absorbances. Furthermore, the purities of the peaks of the three drugs were confirmed by comparing the UV spectra of investigated peaks to the UV reference spectra in Clarke's Analysis of Drugs and Poisons. The greenness value of the method was 0.69 with a faint green-colored pictogram using the AGREE tool. These merits recommend the application of the planned method in QC laboratories for purity testing and concentration assays for the pure drugs and commercial formulations.

Martin Delrio: Demonology and Scholarship in the Counter-Reformation

Martin Delrio: Demonology and Scholarship in the Counter-Reformation

A cross-sectional study of exposure to mercury in schoolchildren living near the eastern seaboard industrial estate of Thailand.

Industrial activity in Thailand's coastal areas has significantly increased mercury concentrations in seawater, causing accumulation through the food chain. Continuous exposure to mercury has been linked to bioaccumulation in living organisms and potential adverse health effects in children. Blood samples were collected from 873 schoolchildren aged 6-13 years living in four sites near the eastern seaboard industrial estates of the Gulf of Thailand in 2011. Total mercury level in whole blood (Hg-B) was compared with standard reference values. Mean (± standard deviation) concentrations of Hg-B from schoolgirls (2.19 ± 0.5 μg/L; n = 405) and schoolboys (2.29 ± 0.3 μg/L; n = 468) did not exceed the regulatory limits of the United States Environmental Protection Agency (US EPA), the German Commission on Human Biological Monitoring (HBM I, II) or Clarke's analysis of drugs and poisons reference values. Nevertheless, 67 children (34 girls and 33 boys) had individual values that exceeded the lowest of these standards (4 μg/L). The relatively low concentrations of Hg-B detected in this study suggested a relatively low risk for schoolchildren. However, 67 children had elevated mean total Hg-B concentrations, especially in the two sites located nearest the industrial area. This information may serve as an early warning of the potential for pollution to affect children living around industrial areas. Further regular monitoring, including studies assessing the health impact of mercury pollution in this region of Thailand, is to be encouraged.

A comparison of the treatment effects of the Forsus Fatigue Resistance Device and the Twin Block appliance in patients with class II malocclusions.

ObjectivesWe evaluated the skeletal and dentoalveolar effects of the Forsus Fatigue Resistance Device (FRD) and the Twin Block appliance (TB) in comparison with nontreated controls in the treatment of patients with class II division 1 malocclusion.Materials and methodsThis retrospective study included three groups: TB (n=37; mean age, 11.2 years), FRD (n=30; mean age, 12.9 years), and controls (n=25; mean age, 12.6 years). Lateral cephalograms were evaluated at T1 (pretreatment) and at T2 (postappliance removal/equivalent time frame in controls). Cephalometric changes were evaluated using the Clark analysis, including 27 measurements.ResultsSagittal correction of class II malocclusion appeared to be mainly achieved by dentoalveolar changes in the FRD group. The TB was able to induce both skeletal and dentoalveolar changes. A favorable influence on facial convexity was achieved by both groups. Significant upper incisor retroclination occurred with the TB (−12.42°), whereas only −4° was observed in the FRD group. The lower incisors proclined more in the FRD group than the TB group. Incisor overjet reduction was 62% in the TB group versus 56% in the FRD group. Molar relation was corrected in both functional groups, resulting in a class I relation, although no change appeared in the control sample.ConclusionBoth appliances were effective in correcting the class II malocclusion. Both the FRD and the TB induced significant maxillary and mandibular dentoalveolar changes; skeletal changes were induced by TB but not FRD therapy.

Case reports in forensic toxicology

Case reports in forensic toxicology

The entrepreneurial university in the twenty-first century

Burton Clark's 1998 monograph, Creating Entrepreneurial Universities: Organizational Pathways of Transformation, has become seminal in the literature on entrepreneurialism in universities. In this paper I re-examine the validity of Clark's analysis through an interview study of one of his original entrepreneurial universities, namely Warwick University; at the same time, I seek to remedy some of the defects in Clark's original study. The study affirms that the entrepreneurial culture that Clark identified some 15 years ago still persists at Warwick University. I speculate on the reasons why this culture has persisted, discuss the suitability of the entrepreneurial university in the post-2012 era and stress the importance of distinguishing between commercialism and Clark's concept of entrepreneurialism.

Review of Clarke's Analysis of Drugs and Poisons, Fourth Edition

Review of Clarke's Analysis of Drugs and Poisons, Fourth Edition

Surgery, a prognostic marker for progression-free survival?

Clarke and colleagues1 are to be congratulated for their recently reported retrospective analysis of whether surgery is a prognostic factor for progression-free survival (PFS) based upon 2 datasets of patients (1 each in the pre- and post-temozolomide eras) treated according to the North American Brain Tumor Consortium phase II trials in recurrent glioblastoma (GB). We would like to make several comments regarding the report and the role of resective (nonbiopsy) surgery in the management of patients with recurrent GB. Counterintuitive results were reported, as surgery preceding enrollment in a clinical trial for recurrent GB did not affect the primary outcome of the analysis, which was 6-month PFS or overall survival. It is generally believed as a tenet of neuro-oncology treatment that reoperation for patients with recurrent GB is of value and positively influences outcome both by decreasing mass and attendant side effects and by improving results of subsequent therapy (either radiotherapy or chemotherapy) by diminishing tumor burden. The analysis of Clarke et al, however, suggests no difference in outcome in patients undergoing surgery, and consequently patients with smaller tumor masses at time of enrollment (the postsurgery cohort) in a clinical trial fared no better than patients not otherwise undergoing reoperation and with presumably larger tumors at the time of salvage treatment. Not clear from the analysis is whether patients undergoing surgery did indeed have smaller tumors than patients not undergoing reoperation. There was no re-analysis of tumor volume as defined by magnetic resonance imaging prior to study entry, so the statement that patients undergoing re-resection had smaller tumors is conjectural. Also not clear from the analysis was how a decision to undertake repeat surgery was determined. At present there are no clear guidelines for reoperation in patients with GB aside from the belief that reoperation is of value (diminishing tumor burden as well as decreasing side effects related to intracranial mass) and favorably influences outcome as defined by PFS and overall survival, a view that appears to be at odds with the Clarke analysis. Park and colleagues, in a recent provocative study,2 suggested 3 criteria for determining best candidates for reoperation in patients with recurrent GB: location in the brain (eloquent or non-eloquent), performance status (independent or otherwise), and expected survival ( 3 months). In most neuro-oncology centers, reoperation is driven primarily by tumor location, resectability, and performance and secondarily by symptoms related to tumor mass and the age of the patient. These less codified criteria are similar to those reported by Park et al but lack outcome data such as those provided by the Park researchers suggesting that there are clear candidates for which reoperation may have limited value. Importantly, it is unclear what criteria were used to suggest re-resection in the study by Clarke et al. How then to interpret this retrospective analysis? And does it affect present management of recurrent GB? Clarke et al1 conclude that surgery continues to offer benefit by reducing tumor mass–related symptoms, although no data were provided suggesting how many of the repeat surgery cohort in fact underwent surgery due to symptomatic tumor. In addition, repeat surgery may pathologically distinguish recurrent GB from treatment-related side effects such as pseudoprogression and radiation necrosis. Again, there are no data provided in the analysis by Clarke et al to indicate how often repeat surgery was used to make this clinically relevant distinction. Currently, there are no formal neuropathological criteria for grading previously treated gliomas. Because glioma grading was based on the most recent surgery, tumors that were lower grade at the initial surgery may have been upgraded and included in the GB group for further analysis. Tumors in the group that did not undergo reoperation were GB at the initial surgery. This may be an additional source of bias. Lastly, Clarke et al1 opine that repeat surgery allowed patients to enter a clinical trial that may have not been possible due to size of tumor and performance status. However, there are no data to support that the surgical cohort underwent surgery and converted from ineligible to eligible for a clinical trial. Furthermore, there are no data about preoperative and postoperative tumor volumes, or any comparison of volumes in the surgical and nonsurgical cohorts. A more provocative, and perhaps counterintuitive, conclusion based on the available data would be that repeat surgery does not impact survival, and consequently the value of repeat surgery in patients with recurrent GB otherwise eligible for a salvage clinical trial is poorly defined and perhaps minimal. As this conclusion is supported by the data presented, perhaps a re-analysis of the database, with inclusion of omitted information, such as surgical criteria, tumor volumes, alterations of performance status by surgery, extent of resection, and change in initial tumor grade, would help to determine whether or not this conclusion is valid.

Book Review: Clarke's Analysis of Drugs and Poisons, 4th Edition

Book Review: Clarke's Analysis of Drugs and Poisons, 4th Edition

Review of: Clarke's Analysis of Drugs and Poisons, Third Edition

Abstract Clarke's Analysis of Drugs and Poisons is a fully revised and expanded third edition of the book formerly known as Clarke's Isolation and Identification of Drugs. The latter has been a standard reference text in most laboratories for several decades. There are few practicing toxicologists that have not relied on this foundational text during the course of their work. It has become a staple for toxicologists in clinical, forensic, analytical, workplace and sports drugs testing, medical examiner, behavioral and research settings.

Clarke's Analysis of Drugs and Poisons

Clarke's Analysis of Drugs and Poisons, 3rd Edition A. C. Moffatt, M. D. Osselton & B. Widdop Published by The Pharmaceutical Press, 2004 Price £350 ISBN 0-85369-473-7 In our laboratory, I have been the guardian of Clarke's Analysis of Drugs and Poisons whose 2nd edition was published in 1986. I have lost count of the number of colleagues, graduate and undergraduate students who have come into my office and asked ‘Can I borrow Clarke?’ Of course the next question is ‘When are we getting a new edition of Clarke?’ Well here it is – the 3rd edition, all two volumes and 2136 pages. It is also available as a fully searchable CD-ROM, as well as online. Was it worth the long wait? Emphatically yes, despite the prohibitive cost. Updating ‘Clarke’ must have been a Herculean task. The first volume contains 31 chapters covering very comprehensively, the various techniques used in the analysis of drugs and those used in analytical and forensic toxicology. For anyone wanting a balanced, readable introduction to, for example, high performance liquid chromatography, this volume of ‘Clarke’ fulfils the need commendably. However, the experienced analyst will perhaps find less interest in this material, and I do question whether the collation and tabulation of the vast amount of data on chromatographic conditions for individual drugs is worthwhile. This brings us to volume 2, the ‘meat’ of ‘Clarke’. The very clearly laid out monographs of virtually all the drugs (and industrial chemicals) listed in the previous edition have been expanded and contain a wealth of analytical, pharmacokinetic (including information for some drugs on the role of individual cytochrome P450 enzymes in their metabolism) and toxicological data. The addition of mass spectra for many of the compounds is particularly welcome. Probably the most useful information contained in these monographs, at least for our own laboratory, relates to the physicochemical properties of drugs (e.g. solubility, partition coefficient, pKa), and the description of the analytical methods for their measurement in biological fluids. When setting up a new method, ‘Clarke’ is our first port of call. As the authors acknowledge, since publication of the 2nd edition, several hundred new chemical entities have been brought to the market. Some 400 new monographs have been added, an increase of about 30 %, which is praiseworthy. Indeed, few new drugs are missing. Furthermore, the published literature is cited up to and including 2002 for drugs both old and new. Now that the word has got around about the new edition of ‘Clarke’, I can see the queue forming at my door. I am sure we will get our money's worth. However, the problem with reference books like this, is that they do need updating regularly. Eighteen years is far too long a gap between editions. Whether the authors have the energy and stamina to take on this task in say 5 years time, remains to be seen. Rather them than me!

COEXISTENCE OR EXCLUSION IN A COMPETITIVE COMMON‐POOL FISHERY: A REVISIONIST VIEW

ABSTRACT. One of the earliest applications of game theory to renewable resource modeling was Colin Clark's analysis, in 1980, of the competitive exploitation of a common‐pool resource. His model described the dynamics of a single Gordon‐Schaeffer fish stock, being harvested non‐cooperatively by two or more independently managed fleets. He showed that aggressive harvesting by all fleets (a Nash equilibrium) would lead to stock drawdown to a level which would successively eliminate all of the less efficient harvesters. Furthermore, when the fleets were closely matched, the survivor(s) of this aggressive competition would be forced, by the threat of competitors' reentry, to hold the stock in its severely degraded state, and hence to harvest at only marginal profitability. This outcome has often been compared to the open access “tragedy of the commons.” and to the outcome of the well‐known “prisoners' dilemma” game.In this article I will argue that, for closely matched fleets, a more likely outcome is that the fleets will tacitly agree, without overt communication, to focus simultaneously on a specific set of coordinated policies which will permit their continuing coexistence and profitable operation. This policy profile also forms a Nash equilibrium, one which is secured by the mutual ability of the fleets to quickly recognize and credibly punish any unilateral deviations from the anticipated actions. Thus the dynamic harvesting game more nearly resembles the repeated prisoners' dilemma than it does the classical single stage version.

Food and feeding of sperm whales Physeter macrocephalus off the west coast of South Africa

The stomach contents of 1 268 sperm whales Physeter macrocephalus processed at the Donkergat whaling station, South Africa, were examined during the 1962 and 1963 whaling seasons. Results were compared with Clarke's analysis of cephalopod beaks collected in 1963 (Clarke 1980). There was no significant difference in the incidence of food in the stomachs between whales taken in the morning (07:15–11:15), at midday (11:15–15:15) or in the afternoon (after 15:15). The incidence of food remains was less in medium-sized (12.2–13.7 m) and large (≥ 14 m) males than in small (≤ 11.9 m) males and females, and their stomachs more frequently contained the beaks of cephalopod species from the Antarctic or subAntarctic. These phenomena were related to a winter migration of medium-sized and large males into the whaling ground from south of the Subtropical Convergence. Medium-sized and large males fed more frequently on larger species of endemic cephalopods than females or small males, whereas males in general ate larger...

Spatial Autocorrelation and the Classic Maya Collapse revisited: Refined techniques and new conclusions

A recent paper in this journal [Whitley & Clark (1985) Spatial Autocorrelation Tests and the Classic Maya Collapse: Methods and Inferences. Journal of Archaeological Science 12, 377–395.] presented an introduction to the topic of spatial autocorrelation. That paper focused particularly on a spatial autocorrelation test for a variable distributed in areal units (e.g. counties or countries). The test was employed to analyse the terminal distribution of dated monuments at lowland Classic Maya sites which yielded the conclusion of a lack of geographic pattern in the dates and, by inference, the Maya collapse itself. This result is particularly surprising because pattern clearly is indicated in a simple plot of the data and a host of archaeologists have perceived, or have shown with other techniques, pattern in the distribution of these dates. Whitley & Clark's analysis is shown to be seriously flawed, however, because their use of an area-based statistic forced them to severely compromise the quality of the point-pattern data set they analysed. A revised spatial autocorrelation test for point-distributed data is presented that may generally be more appropriate for archaeological data. This test is used to re-analyse the Maya data and it is demonstrated that significant geographic pattern does indeed exist, thus agreeing with the perceptions and findings of Mayanists. Owing to the contradictory findings obtained by two very similar analyses, the need for a careful and thoughtful approach to the analysis of data is emphasized as is the importance of matching appropriate inference methods to the problem at hand.

An Analysis of Changes in the Distribution of Employment Between the Manufacturing and Service Industries 1960-1970

SINCE the formulation of the Fisher-Clark hypothesis of structural change, which associates changes in the distribution of employment between industries with changes in levels of real income per head, economists have been interested in the reasons behind changes in industry structure.' interest has received a fillip in recent years with an apparent acceleration in the rate of growth of employment in the service sector compared with that in the manufacturing sector.2 Recent empirical studies by, for example, Fuchs (1965) and Dowie (1970) have sought to explain the relatively faster rate of growth of employment in service industries than in manufacturing (or goods) industries in terms of the supply and demand characteristics of the products of the two sectors. In both studies it was found that the ratio of product of the two sectors remained fairly constant but that there was an appreciably faster rate of growth in productivity in manufacturing than in the service industries. It is concluded that difference in the supply characteristics of the two sectors is the main cause of the structural change. Both writers also suggest that constancy of product shares implies similar income elasticities of demand for the product of the two sectors. These conclusions, however, must be subject to two qualifications. First, the approach adopted does not allow for possible interaction between demand and supply.3 Demand and supply effects are assumed to be independent. But, as shown below, supply effects, as a result of differences in rates of productivity change, are likely to affect the relative rates of growth of product of the two sectors. Hence, constancy of product shares does not necessarily imply that demand factors are neutral. Interactive effects occur because different rates of productivity change, affect relative prices, which in turn lead to price substitution between the products of the two sectors.4 importance of these effects depends therefore on the differences in the rates of productivity change and the price elasticities of demand for the products of the sectors. following illustration shows how the effect operates.5 Let m equal the continuously compounded percentage rate of change in service sector employment over time minus the percentage rate of change in goods sector employment. Then as an approximation where r is the percentage rate m -r(nn,) + (rr,)(-1), of increase in real income, ns is the income elasticity of demand for services, nt0 is the income elasticity of demand for goods, rs is the percentage rate of increase in total factor proReceived for publication January 23, 1973. Revision accepted for publication January 30, 1974. * All the computer simulations required for this study were carried out by Margaret Wood. Helpful comments on an earlier draft were made by Dr. C. I. Higgins, Dr. R. G. Gregory, Mr. J. S. Marsden. Some of the data needed for this study are not available in official Australian statistics and were specially estimated. Notes on estimates are available from the author. complete set of equations used in the model, together with the usual tests of significance, are also available from the author. 1 In the first (1940) edition of The Conditions of Economic Progress Clark observed that studying economic progress in relation to the economic structure of different countries, we find a very firmly established generalization that a higher average level of real income per head is always associated with a high proportion of the working population engaged in tertiary industries . (pp. 6-7). Clark was not, of course, the first economist to discuss changes in industry structure; see, for example, Marshall (1938), pp. 276-277, and Clark himself drew attention to Petty's writings on this topic, in the 17th century (Clark (1957), pp. 176-177). But Clark's analysis is, however, more comprehensive than that of earlier writers. 2 For example, in Australia (Dowie (1970), p. 222) and in the United States (Fuchs (1957), pp. 6-8). Comparison of rates of increase in employment by sector for other countries is given in O.E.C.D. (1970). 3 This does not imply that Fuchs and Dowie are unaware of the importance of the interaction, but the results assume that they are insignificant. 4 cf. Baumol (1967) for a discussion of the relationship between changes in productivity, prices and demand. 5 This formulation was suggested by a referee.